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Sublinear Optimization for Machine Learning | cs.LG | We give sublinear-time approximation algorithms for some optimization
problems arising in machine learning, such as training linear classifiers and
finding minimum enclosing balls. Our algorithms can be extended to some
kernelized versions of these problems, such as SVDD, hard margin SVM, and
L2-SVM, for which sublinear-time algorithms were not known before. These new
algorithms use a combination of a novel sampling techniques and a new
multiplicative update algorithm. We give lower bounds which show the running
times of many of our algorithms to be nearly best possible in the unit-cost RAM
model. We also give implementations of our algorithms in the semi-streaming
setting, obtaining the first low pass polylogarithmic space and sublinear time
algorithms achieving arbitrary approximation factor.
| Kenneth L. Clarkson and Elad Hazan and David P. Woodruff | null | 1010.4408 | null | null |
On the Foundations of Adversarial Single-Class Classification | cs.LG cs.AI | Motivated by authentication, intrusion and spam detection applications we
consider single-class classification (SCC) as a two-person game between the
learner and an adversary. In this game the learner has a sample from a target
distribution and the goal is to construct a classifier capable of
distinguishing observations from the target distribution from observations
emitted from an unknown other distribution. The ideal SCC classifier must
guarantee a given tolerance for the false-positive error (false alarm rate)
while minimizing the false negative error (intruder pass rate). Viewing SCC as
a two-person zero-sum game we identify both deterministic and randomized
optimal classification strategies for different game variants. We demonstrate
that randomized classification can provide a significant advantage. In the
deterministic setting we show how to reduce SCC to two-class classification
where in the two-class problem the other class is a synthetically generated
distribution. We provide an efficient and practical algorithm for constructing
and solving the two class problem. The algorithm distinguishes low density
regions of the target distribution and is shown to be consistent.
| Ran El-Yaniv and Mordechai Nisenson | null | 1010.4466 | null | null |
Local Component Analysis for Nonparametric Bayes Classifier | cs.CV cs.LG | The decision boundaries of Bayes classifier are optimal because they lead to
maximum probability of correct decision. It means if we knew the prior
probabilities and the class-conditional densities, we could design a classifier
which gives the lowest probability of error. However, in classification based
on nonparametric density estimation methods such as Parzen windows, the
decision regions depend on the choice of parameters such as window width.
Moreover, these methods suffer from curse of dimensionality of the feature
space and small sample size problem which severely restricts their practical
applications. In this paper, we address these problems by introducing a novel
dimension reduction and classification method based on local component
analysis. In this method, by adopting an iterative cross-validation algorithm,
we simultaneously estimate the optimal transformation matrices (for dimension
reduction) and classifier parameters based on local information. The proposed
method can classify the data with complicated boundary and also alleviate the
course of dimensionality dilemma. Experiments on real data show the superiority
of the proposed algorithm in term of classification accuracies for pattern
classification applications like age, facial expression and character
recognition. Keywords: Bayes classifier, curse of dimensionality dilemma,
Parzen window, pattern classification, subspace learning.
| Mahmoud Khademi, Mohammad T. Manzuri-Shalmani, and Meharn safayani | null | 1010.4951 | null | null |
Converged Algorithms for Orthogonal Nonnegative Matrix Factorizations | cs.LG cs.NA | This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix
factorization algorithms with robust convergence proofs. We design the
algorithms based on the work of Lee and Seung [1], and derive the converged
versions by utilizing ideas from the work of Lin [2]. The experimental results
confirm the theoretical guarantees of the convergences.
| Andri Mirzal | null | 1010.5290 | null | null |
Resource-bounded Dimension in Computational Learning Theory | cs.CC cs.LG | This paper focuses on the relation between computational learning theory and
resource-bounded dimension. We intend to establish close connections between
the learnability/nonlearnability of a concept class and its corresponding size
in terms of effective dimension, which will allow the use of powerful dimension
techniques in computational learning and viceversa, the import of learning
results into complexity via dimension. Firstly, we obtain a tight result on the
dimension of online mistake-bound learnable classes. Secondly, in relation with
PAC learning, we show that the polynomial-space dimension of PAC learnable
classes of concepts is zero. This provides a hypothesis on effective dimension
that implies the inherent unpredictability of concept classes (the classes that
verify this property are classes not efficiently PAC learnable using any
hypothesis). Thirdly, in relation to space dimension of classes that are
learnable by membership query algorithms, the main result proves that
polynomial-space dimension of concept classes learnable by a membership-query
algorithm is zero.
| Ricard Gavalda, Maria Lopez-Valdes, Elvira Mayordomo, N. V.
Vinodchandran | null | 1010.5470 | null | null |
Efficient Minimization of Decomposable Submodular Functions | cs.LG math.OC | Many combinatorial problems arising in machine learning can be reduced to the
problem of minimizing a submodular function. Submodular functions are a natural
discrete analog of convex functions, and can be minimized in strongly
polynomial time. Unfortunately, state-of-the-art algorithms for general
submodular minimization are intractable for larger problems. In this paper, we
introduce a novel subclass of submodular minimization problems that we call
decomposable. Decomposable submodular functions are those that can be
represented as sums of concave functions applied to modular functions. We
develop an algorithm, SLG, that can efficiently minimize decomposable
submodular functions with tens of thousands of variables. Our algorithm
exploits recent results in smoothed convex minimization. We apply SLG to
synthetic benchmarks and a joint classification-and-segmentation task, and show
that it outperforms the state-of-the-art general purpose submodular
minimization algorithms by several orders of magnitude.
| Peter Stobbe, Andreas Krause | null | 1010.5511 | null | null |
Analysing the behaviour of robot teams through relational sequential
pattern mining | cs.AI cs.LG cs.MA | This report outlines the use of a relational representation in a Multi-Agent
domain to model the behaviour of the whole system. A desired property in this
systems is the ability of the team members to work together to achieve a common
goal in a cooperative manner. The aim is to define a systematic method to
verify the effective collaboration among the members of a team and comparing
the different multi-agent behaviours. Using external observations of a
Multi-Agent System to analyse, model, recognize agent behaviour could be very
useful to direct team actions. In particular, this report focuses on the
challenge of autonomous unsupervised sequential learning of the team's
behaviour from observations. Our approach allows to learn a symbolic sequence
(a relational representation) to translate raw multi-agent, multi-variate
observations of a dynamic, complex environment, into a set of sequential
behaviours that are characteristic of the team in question, represented by a
set of sequences expressed in first-order logic atoms. We propose to use a
relational learning algorithm to mine meaningful frequent patterns among the
relational sequences to characterise team behaviours. We compared the
performance of two teams in the RoboCup four-legged league environment, that
have a very different approach to the game. One uses a Case Based Reasoning
approach, the other uses a pure reactive behaviour.
| Grazia Bombini, Raquel Ros, Stefano Ferilli, Ramon Lopez de Mantaras | null | 1010.6234 | null | null |
Predictive State Temporal Difference Learning | cs.LG cs.AI | We propose a new approach to value function approximation which combines
linear temporal difference reinforcement learning with subspace identification.
In practical applications, reinforcement learning (RL) is complicated by the
fact that state is either high-dimensional or partially observable. Therefore,
RL methods are designed to work with features of state rather than state
itself, and the success or failure of learning is often determined by the
suitability of the selected features. By comparison, subspace identification
(SSID) methods are designed to select a feature set which preserves as much
information as possible about state. In this paper we connect the two
approaches, looking at the problem of reinforcement learning with a large set
of features, each of which may only be marginally useful for value function
approximation. We introduce a new algorithm for this situation, called
Predictive State Temporal Difference (PSTD) learning. As in SSID for predictive
state representations, PSTD finds a linear compression operator that projects a
large set of features down to a small set that preserves the maximum amount of
predictive information. As in RL, PSTD then uses a Bellman recursion to
estimate a value function. We discuss the connection between PSTD and prior
approaches in RL and SSID. We prove that PSTD is statistically consistent,
perform several experiments that illustrate its properties, and demonstrate its
potential on a difficult optimal stopping problem.
| Byron Boots and Geoffrey J. Gordon | null | 1011.0041 | null | null |
Sparse Inverse Covariance Selection via Alternating Linearization
Methods | cs.LG math.OC stat.ML | Gaussian graphical models are of great interest in statistical learning.
Because the conditional independencies between different nodes correspond to
zero entries in the inverse covariance matrix of the Gaussian distribution, one
can learn the structure of the graph by estimating a sparse inverse covariance
matrix from sample data, by solving a convex maximum likelihood problem with an
$\ell_1$-regularization term. In this paper, we propose a first-order method
based on an alternating linearization technique that exploits the problem's
special structure; in particular, the subproblems solved in each iteration have
closed-form solutions. Moreover, our algorithm obtains an $\epsilon$-optimal
solution in $O(1/\epsilon)$ iterations. Numerical experiments on both synthetic
and real data from gene association networks show that a practical version of
this algorithm outperforms other competitive algorithms.
| Katya Scheinberg, Shiqian Ma, Donald Goldfarb | null | 1011.0097 | null | null |
Developing courses with HoloRena, a framework for scenario- and game
based e-learning environments | cs.LG cs.HC cs.SE | However utilizing rich, interactive solutions can make learning more
effective and attractive, scenario- and game-based educational resources on the
web are not widely used. Creating these applications is a complex, expensive
and challenging process. Development frameworks and authoring tools hardly
support reusable components, teamwork and learning management
system-independent courseware architecture. In this article we initiate the
concept of a low-level, thick-client solution addressing these problems. With
some example applications we try to demonstrate, how a framework, based on this
concept can be useful for developing scenario- and game-based e-learning
environments.
| Laszlo Juracz | null | 1011.0350 | null | null |
Learning Networks of Stochastic Differential Equations | math.ST cond-mat.stat-mech cs.IT cs.LG math.IT stat.TH | We consider linear models for stochastic dynamics. To any such model can be
associated a network (namely a directed graph) describing which degrees of
freedom interact under the dynamics. We tackle the problem of learning such a
network from observation of the system trajectory over a time interval $T$.
We analyze the $\ell_1$-regularized least squares algorithm and, in the
setting in which the underlying network is sparse, we prove performance
guarantees that are \emph{uniform in the sampling rate} as long as this is
sufficiently high. This result substantiates the notion of a well defined `time
complexity' for the network inference problem.
| Jos\'e Bento, Morteza Ibrahimi, and Andrea Montanari | null | 1011.0415 | null | null |
From Sparse Signals to Sparse Residuals for Robust Sensing | stat.ML cs.IT cs.LG math.IT | One of the key challenges in sensor networks is the extraction of information
by fusing data from a multitude of distinct, but possibly unreliable sensors.
Recovering information from the maximum number of dependable sensors while
specifying the unreliable ones is critical for robust sensing. This sensing
task is formulated here as that of finding the maximum number of feasible
subsystems of linear equations, and proved to be NP-hard. Useful links are
established with compressive sampling, which aims at recovering vectors that
are sparse. In contrast, the signals here are not sparse, but give rise to
sparse residuals. Capitalizing on this form of sparsity, four sensing schemes
with complementary strengths are developed. The first scheme is a convex
relaxation of the original problem expressed as a second-order cone program
(SOCP). It is shown that when the involved sensing matrices are Gaussian and
the reliable measurements are sufficiently many, the SOCP can recover the
optimal solution with overwhelming probability. The second scheme is obtained
by replacing the initial objective function with a concave one. The third and
fourth schemes are tailored for noisy sensor data. The noisy case is cast as a
combinatorial problem that is subsequently surrogated by a (weighted) SOCP.
Interestingly, the derived cost functions fall into the framework of robust
multivariate linear regression, while an efficient block-coordinate descent
algorithm is developed for their minimization. The robust sensing capabilities
of all schemes are verified by simulated tests.
| Vassilis Kekatos and Georgios B. Giannakis | 10.1109/TSP.2011.2141661 | 1011.0450 | null | null |
Regularized Risk Minimization by Nesterov's Accelerated Gradient
Methods: Algorithmic Extensions and Empirical Studies | cs.LG | Nesterov's accelerated gradient methods (AGM) have been successfully applied
in many machine learning areas. However, their empirical performance on
training max-margin models has been inferior to existing specialized solvers.
In this paper, we first extend AGM to strongly convex and composite objective
functions with Bregman style prox-functions. Our unifying framework covers both
the $\infty$-memory and 1-memory styles of AGM, tunes the Lipschiz constant
adaptively, and bounds the duality gap. Then we demonstrate various ways to
apply this framework of methods to a wide range of machine learning problems.
Emphasis will be given on their rate of convergence and how to efficiently
compute the gradient and optimize the models. The experimental results show
that with our extensions AGM outperforms state-of-the-art solvers on max-margin
models.
| Xinhua Zhang and Ankan Saha and S.V.N. Vishwanathan | null | 1011.0472 | null | null |
A Reduction of Imitation Learning and Structured Prediction to No-Regret
Online Learning | cs.LG cs.AI stat.ML | Sequential prediction problems such as imitation learning, where future
observations depend on previous predictions (actions), violate the common
i.i.d. assumptions made in statistical learning. This leads to poor performance
in theory and often in practice. Some recent approaches provide stronger
guarantees in this setting, but remain somewhat unsatisfactory as they train
either non-stationary or stochastic policies and require a large number of
iterations. In this paper, we propose a new iterative algorithm, which trains a
stationary deterministic policy, that can be seen as a no regret algorithm in
an online learning setting. We show that any such no regret algorithm, combined
with additional reduction assumptions, must find a policy with good performance
under the distribution of observations it induces in such sequential settings.
We demonstrate that this new approach outperforms previous approaches on two
challenging imitation learning problems and a benchmark sequence labeling
problem.
| Stephane Ross, Geoffrey J. Gordon, J. Andrew Bagnell | null | 1011.0686 | null | null |
Multiarmed Bandit Problems with Delayed Feedback | cs.DS cs.LG | In this paper we initiate the study of optimization of bandit type problems
in scenarios where the feedback of a play is not immediately known. This arises
naturally in allocation problems which have been studied extensively in the
literature, albeit in the absence of delays in the feedback. We study this
problem in the Bayesian setting. In presence of delays, no solution with
provable guarantees is known to exist with sub-exponential running time.
We show that bandit problems with delayed feedback that arise in allocation
settings can be forced to have significant structure, with a slight loss in
optimality. This structure gives us the ability to reason about the
relationship of single arm policies to the entangled optimum policy, and
eventually leads to a O(1) approximation for a significantly general class of
priors. The structural insights we develop are of key interest and carry over
to the setting where the feedback of an action is available instantaneously,
and we improve all previous results in this setting as well.
| Sudipto Guha and Kamesh Munagala and Martin Pal | null | 1011.1161 | null | null |
Privately Releasing Conjunctions and the Statistical Query Barrier | cs.DS cs.CR cs.LG | Suppose we would like to know all answers to a set of statistical queries C
on a data set up to small error, but we can only access the data itself using
statistical queries. A trivial solution is to exhaustively ask all queries in
C. Can we do any better?
+ We show that the number of statistical queries necessary and sufficient for
this task is---up to polynomial factors---equal to the agnostic learning
complexity of C in Kearns' statistical query (SQ) model. This gives a complete
answer to the question when running time is not a concern.
+ We then show that the problem can be solved efficiently (allowing arbitrary
error on a small fraction of queries) whenever the answers to C can be
described by a submodular function. This includes many natural concept classes,
such as graph cuts and Boolean disjunctions and conjunctions.
While interesting from a learning theoretic point of view, our main
applications are in privacy-preserving data analysis:
Here, our second result leads to the first algorithm that efficiently
releases differentially private answers to of all Boolean conjunctions with 1%
average error. This presents significant progress on a key open problem in
privacy-preserving data analysis.
Our first result on the other hand gives unconditional lower bounds on any
differentially private algorithm that admits a (potentially
non-privacy-preserving) implementation using only statistical queries. Not only
our algorithms, but also most known private algorithms can be implemented using
only statistical queries, and hence are constrained by these lower bounds. Our
result therefore isolates the complexity of agnostic learning in the SQ-model
as a new barrier in the design of differentially private algorithms.
| Anupam Gupta, Moritz Hardt, Aaron Roth, Jonathan Ullman | null | 1011.1296 | null | null |
Robust Matrix Decomposition with Outliers | stat.ML cs.LG math.NA | Suppose a given observation matrix can be decomposed as the sum of a low-rank
matrix and a sparse matrix (outliers), and the goal is to recover these
individual components from the observed sum. Such additive decompositions have
applications in a variety of numerical problems including system
identification, latent variable graphical modeling, and principal components
analysis. We study conditions under which recovering such a decomposition is
possible via a combination of $\ell_1$ norm and trace norm minimization. We are
specifically interested in the question of how many outliers are allowed so
that convex programming can still achieve accurate recovery, and we obtain
stronger recovery guarantees than previous studies. Moreover, we do not assume
that the spatial pattern of outliers is random, which stands in contrast to
related analyses under such assumptions via matrix completion.
| Daniel Hsu, Sham M. Kakade, Tong Zhang | null | 1011.1518 | null | null |
Online Importance Weight Aware Updates | cs.LG | An importance weight quantifies the relative importance of one example over
another, coming up in applications of boosting, asymmetric classification
costs, reductions, and active learning. The standard approach for dealing with
importance weights in gradient descent is via multiplication of the gradient.
We first demonstrate the problems of this approach when importance weights are
large, and argue in favor of more sophisticated ways for dealing with them. We
then develop an approach which enjoys an invariance property: that updating
twice with importance weight $h$ is equivalent to updating once with importance
weight $2h$. For many important losses this has a closed form update which
satisfies standard regret guarantees when all examples have $h=1$. We also
briefly discuss two other reasonable approaches for handling large importance
weights. Empirically, these approaches yield substantially superior prediction
with similar computational performance while reducing the sensitivity of the
algorithm to the exact setting of the learning rate. We apply these to online
active learning yielding an extraordinarily fast active learning algorithm that
works even in the presence of adversarial noise.
| Nikos Karampatziakis and John Langford | null | 1011.1576 | null | null |
Least Squares Ranking on Graphs | cs.NA cs.LG math.NA | Given a set of alternatives to be ranked, and some pairwise comparison data,
ranking is a least squares computation on a graph. The vertices are the
alternatives, and the edge values comprise the comparison data. The basic idea
is very simple and old: come up with values on vertices such that their
differences match the given edge data. Since an exact match will usually be
impossible, one settles for matching in a least squares sense. This formulation
was first described by Leake in 1976 for rankingfootball teams and appears as
an example in Professor Gilbert Strang's classic linear algebra textbook. If
one is willing to look into the residual a little further, then the problem
really comes alive, as shown effectively by the remarkable recent paper of
Jiang et al. With or without this twist, the humble least squares problem on
graphs has far-reaching connections with many current areas ofresearch. These
connections are to theoretical computer science (spectral graph theory, and
multilevel methods for graph Laplacian systems); numerical analysis (algebraic
multigrid, and finite element exterior calculus); other mathematics (Hodge
decomposition, and random clique complexes); and applications (arbitrage, and
ranking of sports teams). Not all of these connections are explored in this
paper, but many are. The underlying ideas are easy to explain, requiring only
the four fundamental subspaces from elementary linear algebra. One of our aims
is to explain these basic ideas and connections, to get researchers in many
fields interested in this topic. Another aim is to use our numerical
experiments for guidance on selecting methods and exposing the need for further
development.
| Anil N. Hirani, Kaushik Kalyanaraman, Seth Watts | null | 1011.1716 | null | null |
Blackwell Approachability and Low-Regret Learning are Equivalent | cs.LG cs.GT | We consider the celebrated Blackwell Approachability Theorem for two-player
games with vector payoffs. We show that Blackwell's result is equivalent, via
efficient reductions, to the existence of "no-regret" algorithms for Online
Linear Optimization. Indeed, we show that any algorithm for one such problem
can be efficiently converted into an algorithm for the other. We provide a
useful application of this reduction: the first efficient algorithm for
calibrated forecasting.
| Jacob Abernethy, Peter L. Bartlett, Elad Hazan | null | 1011.1936 | null | null |
Extended Active Learning Method | cs.AI cs.LG | Active Learning Method (ALM) is a soft computing method which is used for
modeling and control, based on fuzzy logic. Although ALM has shown that it acts
well in dynamic environments, its operators cannot support it very well in
complex situations due to losing data. Thus ALM can find better membership
functions if more appropriate operators be chosen for it. This paper
substituted two new operators instead of ALM original ones; which consequently
renewed finding membership functions in a way superior to conventional ALM.
This new method is called Extended Active Learning Method (EALM).
| Ali Akbar Kiaei, Saeed Bagheri Shouraki, Seyed Hossein Khasteh,
Mahmoud Khademi, and Alireza Ghatreh Samani | null | 1011.2512 | null | null |
Clustering using Unsupervised Binary Trees: CUBT | stat.ME cs.LG stat.CO | We herein introduce a new method of interpretable clustering that uses
unsupervised binary trees. It is a three-stage procedure, the first stage of
which entails a series of recursive binary splits to reduce the heterogeneity
of the data within the new subsamples. During the second stage (pruning),
consideration is given to whether adjacent nodes can be aggregated. Finally,
during the third stage (joining), similar clusters are joined together, even if
they do not share the same parent originally. Consistency results are obtained,
and the procedure is used on simulated and real data sets.
| Ricardo Fraiman, Badih Ghattas and Marcela Svarc | null | 1011.2624 | null | null |
Regularization Strategies and Empirical Bayesian Learning for MKL | stat.ML cs.LG | Multiple kernel learning (MKL), structured sparsity, and multi-task learning
have recently received considerable attention. In this paper, we show how
different MKL algorithms can be understood as applications of either
regularization on the kernel weights or block-norm-based regularization, which
is more common in structured sparsity and multi-task learning. We show that
these two regularization strategies can be systematically mapped to each other
through a concave conjugate operation. When the kernel-weight-based regularizer
is separable into components, we can naturally consider a generative
probabilistic model behind MKL. Based on this model, we propose learning
algorithms for the kernel weights through the maximization of marginal
likelihood. We show through numerical experiments that $\ell_2$-norm MKL and
Elastic-net MKL achieve comparable accuracy to uniform kernel combination.
Although uniform kernel combination might be preferable from its simplicity,
$\ell_2$-norm MKL and Elastic-net MKL can learn the usefulness of the
information sources represented as kernels. In particular, Elastic-net MKL
achieves sparsity in the kernel weights.
| Ryota Tomioka, Taiji Suzuki | null | 1011.3090 | null | null |
Online Learning: Beyond Regret | stat.ML cs.GT cs.LG | We study online learnability of a wide class of problems, extending the
results of (Rakhlin, Sridharan, Tewari, 2010) to general notions of performance
measure well beyond external regret. Our framework simultaneously captures such
well-known notions as internal and general Phi-regret, learning with
non-additive global cost functions, Blackwell's approachability, calibration of
forecasters, adaptive regret, and more. We show that learnability in all these
situations is due to control of the same three quantities: a martingale
convergence term, a term describing the ability to perform well if future is
known, and a generalization of sequential Rademacher complexity, studied in
(Rakhlin, Sridharan, Tewari, 2010). Since we directly study complexity of the
problem instead of focusing on efficient algorithms, we are able to improve and
extend many known results which have been previously derived via an algorithmic
construction.
| Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari | null | 1011.3168 | null | null |
A Probabilistic Approach for Learning Folksonomies from Structured Data | cs.AI cs.CY cs.LG | Learning structured representations has emerged as an important problem in
many domains, including document and Web data mining, bioinformatics, and image
analysis. One approach to learning complex structures is to integrate many
smaller, incomplete and noisy structure fragments. In this work, we present an
unsupervised probabilistic approach that extends affinity propagation to
combine the small ontological fragments into a collection of integrated,
consistent, and larger folksonomies. This is a challenging task because the
method must aggregate similar structures while avoiding structural
inconsistencies and handling noise. We validate the approach on a real-world
social media dataset, comprised of shallow personal hierarchies specified by
many individual users, collected from the photosharing website Flickr. Our
empirical results show that our proposed approach is able to construct deeper
and denser structures, compared to an approach using only the standard affinity
propagation algorithm. Additionally, the approach yields better overall
integration quality than a state-of-the-art approach based on incremental
relational clustering.
| Anon Plangprasopchok, Kristina Lerman, Lise Getoor | null | 1011.3557 | null | null |
PADDLE: Proximal Algorithm for Dual Dictionaries LEarning | cs.LG cs.IT math.IT stat.ML | Recently, considerable research efforts have been devoted to the design of
methods to learn from data overcomplete dictionaries for sparse coding.
However, learned dictionaries require the solution of an optimization problem
for coding new data. In order to overcome this drawback, we propose an
algorithm aimed at learning both a dictionary and its dual: a linear mapping
directly performing the coding. By leveraging on proximal methods, our
algorithm jointly minimizes the reconstruction error of the dictionary and the
coding error of its dual; the sparsity of the representation is induced by an
$\ell_1$-based penalty on its coefficients. The results obtained on synthetic
data and real images show that the algorithm is capable of recovering the
expected dictionaries. Furthermore, on a benchmark dataset, we show that the
image features obtained from the dual matrix yield state-of-the-art
classification performance while being much less computational intensive.
| Curzio Basso and Matteo Santoro and Alessandro Verri and Silvia Villa | null | 1011.3728 | null | null |
Clustering and Latent Semantic Indexing Aspects of the Singular Value
Decomposition | cs.LG cs.NA math.SP | This paper discusses clustering and latent semantic indexing (LSI) aspects of
the singular value decomposition (SVD). The purpose of this paper is twofold.
The first is to give an explanation on how and why the singular vectors can be
used in clustering. And the second is to show that the two seemingly unrelated
SVD aspects actually originate from the same source: related vertices tend to
be more clustered in the graph representation of lower rank approximate matrix
using the SVD than in the original semantic graph. Accordingly, the SVD can
improve retrieval performance of an information retrieval system since queries
made to the approximate matrix can retrieve more relevant documents and filter
out more irrelevant documents than the same queries made to the original
matrix. By utilizing this fact, we will devise an LSI algorithm that mimicks
SVD capability in clustering related vertices. Convergence analysis shows that
the algorithm is convergent and produces a unique solution for each input.
Experimental results using some standard datasets in LSI research show that
retrieval performances of the algorithm are comparable to the SVD's. In
addition, the algorithm is more practical and easier to use because there is no
need to determine decomposition rank which is crucial in driving retrieval
performance of the SVD.
| Andri Mirzal | null | 1011.4104 | null | null |
Combinatorial Network Optimization with Unknown Variables: Multi-Armed
Bandits with Linear Rewards | math.OC cs.LG cs.NI math.PR | In the classic multi-armed bandits problem, the goal is to have a policy for
dynamically operating arms that each yield stochastic rewards with unknown
means. The key metric of interest is regret, defined as the gap between the
expected total reward accumulated by an omniscient player that knows the reward
means for each arm, and the expected total reward accumulated by the given
policy. The policies presented in prior work have storage, computation and
regret all growing linearly with the number of arms, which is not scalable when
the number of arms is large. We consider in this work a broad class of
multi-armed bandits with dependent arms that yield rewards as a linear
combination of a set of unknown parameters. For this general framework, we
present efficient policies that are shown to achieve regret that grows
logarithmically with time, and polynomially in the number of unknown parameters
(even though the number of dependent arms may grow exponentially). Furthermore,
these policies only require storage that grows linearly in the number of
unknown parameters. We show that this generalization is broadly applicable and
useful for many interesting tasks in networks that can be formulated as
tractable combinatorial optimization problems with linear objective functions,
such as maximum weight matching, shortest path, and minimum spanning tree
computations.
| Yi Gai, Bhaskar Krishnamachari and Rahul Jain | null | 1011.4748 | null | null |
The Non-Bayesian Restless Multi-Armed Bandit: a Case of Near-Logarithmic
Regret | math.OC cs.LG cs.NI math.PR | In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are
$N$ arms, with rewards on all arms evolving at each time as Markov chains with
known parameters. A player seeks to activate $K \geq 1$ arms at each time in
order to maximize the expected total reward obtained over multiple plays. RMAB
is a challenging problem that is known to be PSPACE-hard in general. We
consider in this work the even harder non-Bayesian RMAB, in which the
parameters of the Markov chain are assumed to be unknown \emph{a priori}. We
develop an original approach to this problem that is applicable when the
corresponding Bayesian problem has the structure that, depending on the known
parameter values, the optimal solution is one of a prescribed finite set of
policies. In such settings, we propose to learn the optimal policy for the
non-Bayesian RMAB by employing a suitable meta-policy which treats each policy
from this finite set as an arm in a different non-Bayesian multi-armed bandit
problem for which a single-arm selection policy is optimal. We demonstrate this
approach by developing a novel sensing policy for opportunistic spectrum access
over unknown dynamic channels. We prove that our policy achieves
near-logarithmic regret (the difference in expected reward compared to a
model-aware genie), which leads to the same average reward that can be achieved
by the optimal policy under a known model. This is the first such result in the
literature for a non-Bayesian RMAB.
| Wenhan Dai, Yi Gai, Bhaskar Krishnamachari, Qing Zhao | null | 1011.4752 | null | null |
Learning in A Changing World: Restless Multi-Armed Bandit with Unknown
Dynamics | math.OC cs.LG math.PR | We consider the restless multi-armed bandit (RMAB) problem with unknown
dynamics in which a player chooses M out of N arms to play at each time. The
reward state of each arm transits according to an unknown Markovian rule when
it is played and evolves according to an arbitrary unknown random process when
it is passive. The performance of an arm selection policy is measured by
regret, defined as the reward loss with respect to the case where the player
knows which M arms are the most rewarding and always plays the M best arms. We
construct a policy with an interleaving exploration and exploitation epoch
structure that achieves a regret with logarithmic order when arbitrary (but
nontrivial) bounds on certain system parameters are known. When no knowledge
about the system is available, we show that the proposed policy achieves a
regret arbitrarily close to the logarithmic order. We further extend the
problem to a decentralized setting where multiple distributed players share the
arms without information exchange. Under both an exogenous restless model and
an endogenous restless model, we show that a decentralized extension of the
proposed policy preserves the logarithmic regret order as in the centralized
setting. The results apply to adaptive learning in various dynamic systems and
communication networks, as well as financial investment.
| Haoyang Liu, Keqin Liu, Qing Zhao | null | 1011.4969 | null | null |
Tight Sample Complexity of Large-Margin Learning | cs.LG math.PR math.ST stat.ML stat.TH | We obtain a tight distribution-specific characterization of the sample
complexity of large-margin classification with L_2 regularization: We introduce
the \gamma-adapted-dimension, which is a simple function of the spectrum of a
distribution's covariance matrix, and show distribution-specific upper and
lower bounds on the sample complexity, both governed by the
\gamma-adapted-dimension of the source distribution. We conclude that this new
quantity tightly characterizes the true sample complexity of large-margin
classification. The bounds hold for a rich family of sub-Gaussian
distributions.
| Sivan Sabato, Nathan Srebro, Naftali Tishby | null | 1011.5053 | null | null |
Classifying Clustering Schemes | stat.ML cs.LG | Many clustering schemes are defined by optimizing an objective function
defined on the partitions of the underlying set of a finite metric space. In
this paper, we construct a framework for studying what happens when we instead
impose various structural conditions on the clustering schemes, under the
general heading of functoriality. Functoriality refers to the idea that one
should be able to compare the results of clustering algorithms as one varies
the data set, for example by adding points or by applying functions to it. We
show that within this framework, one can prove a theorems analogous to one of
J. Kleinberg, in which for example one obtains an existence and uniqueness
theorem instead of a non-existence result.
We obtain a full classification of all clustering schemes satisfying a
condition we refer to as excisiveness. The classification can be changed by
varying the notion of maps of finite metric spaces. The conditions occur
naturally when one considers clustering as the statistical version of the
geometric notion of connected components. By varying the degree of
functoriality that one requires from the schemes it is possible to construct
richer families of clustering schemes that exhibit sensitivity to density.
| Gunnar Carlsson and Facundo Memoli | null | 1011.5270 | null | null |
The Sample Complexity of Dictionary Learning | stat.ML cs.LG | A large set of signals can sometimes be described sparsely using a
dictionary, that is, every element can be represented as a linear combination
of few elements from the dictionary. Algorithms for various signal processing
applications, including classification, denoising and signal separation, learn
a dictionary from a set of signals to be represented. Can we expect that the
representation found by such a dictionary for a previously unseen example from
the same source will have L_2 error of the same magnitude as those for the
given examples? We assume signals are generated from a fixed distribution, and
study this questions from a statistical learning theory perspective.
We develop generalization bounds on the quality of the learned dictionary for
two types of constraints on the coefficient selection, as measured by the
expected L_2 error in representation when the dictionary is used. For the case
of l_1 regularized coefficient selection we provide a generalization bound of
the order of O(sqrt(np log(m lambda)/m)), where n is the dimension, p is the
number of elements in the dictionary, lambda is a bound on the l_1 norm of the
coefficient vector and m is the number of samples, which complements existing
results. For the case of representing a new signal as a combination of at most
k dictionary elements, we provide a bound of the order O(sqrt(np log(m k)/m))
under an assumption on the level of orthogonality of the dictionary (low Babel
function). We further show that this assumption holds for most dictionaries in
high dimensions in a strong probabilistic sense. Our results further yield fast
rates of order 1/m as opposed to 1/sqrt(m) using localized Rademacher
complexity. We provide similar results in a general setting using kernels with
weak smoothness requirements.
| Daniel Vainsencher, Shie Mannor, Alfred M. Bruckstein | 10.1016/j.specom.2013.01.005 | 1011.5395 | null | null |
On Theorem 2.3 in "Prediction, Learning, and Games" by Cesa-Bianchi and
Lugosi | cs.LG | The note presents a modified proof of a loss bound for the exponentially
weighted average forecaster with time-varying potential. The regret term of the
algorithm is upper-bounded by sqrt{n ln(N)} (uniformly in n), where N is the
number of experts and n is the number of steps.
| Alexey Chernov | null | 1011.5668 | null | null |
In All Likelihood, Deep Belief Is Not Enough | stat.ML cs.LG | Statistical models of natural stimuli provide an important tool for
researchers in the fields of machine learning and computational neuroscience. A
canonical way to quantitatively assess and compare the performance of
statistical models is given by the likelihood. One class of statistical models
which has recently gained increasing popularity and has been applied to a
variety of complex data are deep belief networks. Analyses of these models,
however, have been typically limited to qualitative analyses based on samples
due to the computationally intractable nature of the model likelihood.
Motivated by these circumstances, the present article provides a consistent
estimator for the likelihood that is both computationally tractable and simple
to apply in practice. Using this estimator, a deep belief network which has
been suggested for the modeling of natural image patches is quantitatively
investigated and compared to other models of natural image patches. Contrary to
earlier claims based on qualitative results, the results presented in this
article provide evidence that the model under investigation is not a
particularly good model for natural images
| Lucas Theis, Sebastian Gerwinn, Fabian Sinz and Matthias Bethge | null | 1011.6086 | null | null |
Classifying extremely imbalanced data sets | physics.data-an cs.LG hep-ex stat.ML | Imbalanced data sets containing much more background than signal instances
are very common in particle physics, and will also be characteristic for the
upcoming analyses of LHC data. Following up the work presented at ACAT 2008, we
use the multivariate technique presented there (a rule growing algorithm with
the meta-methods bagging and instance weighting) on much more imbalanced data
sets, especially a selection of D0 decays without the use of particle
identification. It turns out that the quality of the result strongly depends on
the number of background instances used for training. We discuss methods to
exploit this in order to improve the results significantly, and how to handle
and reduce the size of large training sets without loss of result quality in
general. We will also comment on how to take into account statistical
fluctuation in receiver operation characteristic curves (ROC) for comparing
classifier methods.
| Markward Britsch (1), Nikolai Gagunashvili (2), Michael Schmelling (1)
((1) Max-Planck-Institut f\"ur Kernphysik, (2) University of Akureyri) | null | 1011.6224 | null | null |
Estimating Probabilities in Recommendation Systems | cs.LG | Recommendation systems are emerging as an important business application with
significant economic impact. Currently popular systems include Amazon's book
recommendations, Netflix's movie recommendations, and Pandora's music
recommendations. In this paper we address the problem of estimating
probabilities associated with recommendation system data using non-parametric
kernel smoothing. In our estimation we interpret missing items as randomly
censored observations and obtain efficient computation schemes using
combinatorial properties of generating functions. We demonstrate our approach
with several case studies involving real world movie recommendation data. The
results are comparable with state-of-the-art techniques while also providing
probabilistic preference estimates outside the scope of traditional recommender
systems.
| Mingxuan Sun, Guy Lebanon, Paul Kidwell | null | 1012.0498 | null | null |
Agnostic Learning of Monomials by Halfspaces is Hard | cs.CC cs.AI cs.LG | We prove the following strong hardness result for learning: Given a
distribution of labeled examples from the hypercube such that there exists a
monomial consistent with $(1-\eps)$ of the examples, it is NP-hard to find a
halfspace that is correct on $(1/2+\eps)$ of the examples, for arbitrary
constants $\eps > 0$. In learning theory terms, weak agnostic learning of
monomials is hard, even if one is allowed to output a hypothesis from the much
bigger concept class of halfspaces. This hardness result subsumes a long line
of previous results, including two recent hardness results for the proper
learning of monomials and halfspaces. As an immediate corollary of our result
we show that weak agnostic learning of decision lists is NP-hard.
Our techniques are quite different from previous hardness proofs for
learning. We define distributions on positive and negative examples for
monomials whose first few moments match. We use the invariance principle to
argue that regular halfspaces (all of whose coefficients have small absolute
value relative to the total $\ell_2$ norm) cannot distinguish between
distributions whose first few moments match. For highly non-regular subspaces,
we use a structural lemma from recent work on fooling halfspaces to argue that
they are ``junta-like'' and one can zero out all but the top few coefficients
without affecting the performance of the halfspace. The top few coefficients
form the natural list decoding of a halfspace in the context of dictatorship
tests/Label Cover reductions.
We note that unlike previous invariance principle based proofs which are only
known to give Unique-Games hardness, we are able to reduce from a version of
Label Cover problem that is known to be NP-hard. This has inspired follow-up
work on bypassing the Unique Games conjecture in some optimal geometric
inapproximability results.
| Vitaly Feldman, Venkatesan Guruswami, Prasad Raghavendra, Yi Wu | null | 1012.0729 | null | null |
Closed-set-based Discovery of Bases of Association Rules | cs.LG cs.AI cs.LO math.LO | The output of an association rule miner is often huge in practice. This is
why several concise lossless representations have been proposed, such as the
"essential" or "representative" rules. We revisit the algorithm given by
Kryszkiewicz (Int. Symp. Intelligent Data Analysis 2001, Springer-Verlag LNCS
2189, 350-359) for mining representative rules. We show that its output is
sometimes incomplete, due to an oversight in its mathematical validation. We
propose alternative complete generators and we extend the approach to an
existing closure-aware basis similar to, and often smaller than, the
representative rules, namely the basis B*.
| Jos\'e L. Balc\'azar, Diego Garc\'ia-Saiz, Domingo G\'omez-P\'erez,
Cristina T\^irn\u{a}uc\u{a} | null | 1012.0735 | null | null |
Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices | cs.AI cs.LG math.LO | The Border algorithm and the iPred algorithm find the Hasse diagrams of FCA
lattices. We show that they can be generalized to arbitrary lattices. In the
case of iPred, this requires the identification of a join-semilattice
homomorphism into a distributive lattice.
| Jos\'e L. Balc\'azar, Cristina T\^irn\u{a}uc\u{a} | null | 1012.0742 | null | null |
An Inverse Power Method for Nonlinear Eigenproblems with Applications in
1-Spectral Clustering and Sparse PCA | cs.LG math.OC stat.ML | Many problems in machine learning and statistics can be formulated as
(generalized) eigenproblems. In terms of the associated optimization problem,
computing linear eigenvectors amounts to finding critical points of a quadratic
function subject to quadratic constraints. In this paper we show that a certain
class of constrained optimization problems with nonquadratic objective and
constraints can be understood as nonlinear eigenproblems. We derive a
generalization of the inverse power method which is guaranteed to converge to a
nonlinear eigenvector. We apply the inverse power method to 1-spectral
clustering and sparse PCA which can naturally be formulated as nonlinear
eigenproblems. In both applications we achieve state-of-the-art results in
terms of solution quality and runtime. Moving beyond the standard eigenproblem
should be useful also in many other applications and our inverse power method
can be easily adapted to new problems.
| Matthias Hein and Thomas B\"uhler | null | 1012.0774 | null | null |
Automated Query Learning with Wikipedia and Genetic Programming | cs.AI cs.IR cs.LG cs.NE | Most of the existing information retrieval systems are based on bag of words
model and are not equipped with common world knowledge. Work has been done
towards improving the efficiency of such systems by using intelligent
algorithms to generate search queries, however, not much research has been done
in the direction of incorporating human-and-society level knowledge in the
queries. This paper is one of the first attempts where such information is
incorporated into the search queries using Wikipedia semantics. The paper
presents an essential shift from conventional token based queries to concept
based queries, leading to an enhanced efficiency of information retrieval
systems. To efficiently handle the automated query learning problem, we propose
Wikipedia-based Evolutionary Semantics (Wiki-ES) framework where concept based
queries are learnt using a co-evolving evolutionary procedure. Learning concept
based queries using an intelligent evolutionary procedure yields significant
improvement in performance which is shown through an extensive study using
Reuters newswire documents. Comparison of the proposed framework is performed
with other information retrieval systems. Concept based approach has also been
implemented on other information retrieval systems to justify the effectiveness
of a transition from token based queries to concept based queries.
| Pekka Malo and Pyry Siitari and Ankur Sinha | null | 1012.0841 | null | null |
Generalized Species Sampling Priors with Latent Beta reinforcements | math.ST cs.LG stat.ME stat.TH | Many popular Bayesian nonparametric priors can be characterized in terms of
exchangeable species sampling sequences. However, in some applications,
exchangeability may not be appropriate. We introduce a {novel and
probabilistically coherent family of non-exchangeable species sampling
sequences characterized by a tractable predictive probability function with
weights driven by a sequence of independent Beta random variables. We compare
their theoretical clustering properties with those of the Dirichlet Process and
the two parameters Poisson-Dirichlet process. The proposed construction
provides a complete characterization of the joint process, differently from
existing work. We then propose the use of such process as prior distribution in
a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte
Carlo sampler for posterior inference. We evaluate the performance of the prior
and the robustness of the resulting inference in a simulation study, providing
a comparison with popular Dirichlet Processes mixtures and Hidden Markov
Models. Finally, we develop an application to the detection of chromosomal
aberrations in breast cancer by leveraging array CGH data.
| Edoardo M. Airoldi, Thiago Costa, Federico Bassetti, Fabrizio Leisen
and Michele Guindani | null | 1012.0866 | null | null |
Efficient Optimization of Performance Measures by Classifier Adaptation | cs.LG cs.AI | In practical applications, machine learning algorithms are often needed to
learn classifiers that optimize domain specific performance measures.
Previously, the research has focused on learning the needed classifier in
isolation, yet learning nonlinear classifier for nonlinear and nonsmooth
performance measures is still hard. In this paper, rather than learning the
needed classifier by optimizing specific performance measure directly, we
circumvent this problem by proposing a novel two-step approach called as CAPO,
namely to first train nonlinear auxiliary classifiers with existing learning
methods, and then to adapt auxiliary classifiers for specific performance
measures. In the first step, auxiliary classifiers can be obtained efficiently
by taking off-the-shelf learning algorithms. For the second step, we show that
the classifier adaptation problem can be reduced to a quadratic program
problem, which is similar to linear SVMperf and can be efficiently solved. By
exploiting nonlinear auxiliary classifiers, CAPO can generate nonlinear
classifier which optimizes a large variety of performance measures including
all the performance measure based on the contingency table and AUC, whilst
keeping high computational efficiency. Empirical studies show that CAPO is
effective and of high computational efficiency, and even it is more efficient
than linear SVMperf.
| Nan Li and Ivor W. Tsang and Zhi-Hua Zhou | 10.1109/TPAMI.2012.172 | 1012.0930 | null | null |
Split Bregman Method for Sparse Inverse Covariance Estimation with
Matrix Iteration Acceleration | stat.ML cs.LG | We consider the problem of estimating the inverse covariance matrix by
maximizing the likelihood function with a penalty added to encourage the
sparsity of the resulting matrix. We propose a new approach based on the split
Bregman method to solve the regularized maximum likelihood estimation problem.
We show that our method is significantly faster than the widely used graphical
lasso method, which is based on blockwise coordinate descent, on both
artificial and real-world data. More importantly, different from the graphical
lasso, the split Bregman based method is much more general, and can be applied
to a class of regularization terms other than the $\ell_1$ norm
| Gui-Bo Ye, Jian-Feng Cai, Xiaohui Xie | null | 1012.0975 | null | null |
Optimal Distributed Online Prediction using Mini-Batches | cs.LG cs.DC math.OC | Online prediction methods are typically presented as serial algorithms
running on a single processor. However, in the age of web-scale prediction
problems, it is increasingly common to encounter situations where a single
processor cannot keep up with the high rate at which inputs arrive. In this
work, we present the \emph{distributed mini-batch} algorithm, a method of
converting many serial gradient-based online prediction algorithms into
distributed algorithms. We prove a regret bound for this method that is
asymptotically optimal for smooth convex loss functions and stochastic inputs.
Moreover, our analysis explicitly takes into account communication latencies
between nodes in the distributed environment. We show how our method can be
used to solve the closely-related distributed stochastic optimization problem,
achieving an asymptotically linear speed-up over multiple processors. Finally,
we demonstrate the merits of our approach on a web-scale online prediction
problem.
| Ofer Dekel, Ran Gilad-Bachrach, Ohad Shamir and Lin Xiao | null | 1012.1367 | null | null |
Robust Distributed Online Prediction | cs.LG math.OC | The standard model of online prediction deals with serial processing of
inputs by a single processor. However, in large-scale online prediction
problems, where inputs arrive at a high rate, an increasingly common necessity
is to distribute the computation across several processors. A non-trivial
challenge is to design distributed algorithms for online prediction, which
maintain good regret guarantees. In \cite{DMB}, we presented the DMB algorithm,
which is a generic framework to convert any serial gradient-based online
prediction algorithm into a distributed algorithm. Moreover, its regret
guarantee is asymptotically optimal for smooth convex loss functions and
stochastic inputs. On the flip side, it is fragile to many types of failures
that are common in distributed environments. In this companion paper, we
present variants of the DMB algorithm, which are resilient to many types of
network failures, and tolerant to varying performance of the computing nodes.
| Ofer Dekel, Ran Gilad-Bachrach, Ohad Shamir and Lin Xiao | null | 1012.1370 | null | null |
Shaping Level Sets with Submodular Functions | cs.LG stat.ML | We consider a class of sparsity-inducing regularization terms based on
submodular functions. While previous work has focused on non-decreasing
functions, we explore symmetric submodular functions and their \lova
extensions. We show that the Lovasz extension may be seen as the convex
envelope of a function that depends on level sets (i.e., the set of indices
whose corresponding components of the underlying predictor are greater than a
given constant): this leads to a class of convex structured regularization
terms that impose prior knowledge on the level sets, and not only on the
supports of the underlying predictors. We provide a unified set of optimization
algorithms, such as proximal operators, and theoretical guarantees (allowed
level sets and recovery conditions). By selecting specific submodular
functions, we give a new interpretation to known norms, such as the total
variation; we also define new norms, in particular ones that are based on order
statistics with application to clustering and outlier detection, and on noisy
cuts in graphs with application to change point detection in the presence of
outliers.
| Francis Bach (LIENS, INRIA Paris - Rocquencourt) | null | 1012.1501 | null | null |
Bridging the Gap between Reinforcement Learning and Knowledge
Representation: A Logical Off- and On-Policy Framework | cs.AI cs.LG cs.LO | Knowledge Representation is important issue in reinforcement learning. In
this paper, we bridge the gap between reinforcement learning and knowledge
representation, by providing a rich knowledge representation framework, based
on normal logic programs with answer set semantics, that is capable of solving
model-free reinforcement learning problems for more complex do-mains and
exploits the domain-specific knowledge. We prove the correctness of our
approach. We show that the complexity of finding an offline and online policy
for a model-free reinforcement learning problem in our approach is NP-complete.
Moreover, we show that any model-free reinforcement learning problem in MDP
environment can be encoded as a SAT problem. The importance of that is
model-free reinforcement
| Emad Saad | null | 1012.1552 | null | null |
Low-Rank Structure Learning via Log-Sum Heuristic Recovery | cs.NA cs.IT cs.LG math.IT | Recovering intrinsic data structure from corrupted observations plays an
important role in various tasks in the communities of machine learning and
signal processing. In this paper, we propose a novel model, named log-sum
heuristic recovery (LHR), to learn the essential low-rank structure from
corrupted data. Different from traditional approaches, which directly utilize
$\ell_1$ norm to measure the sparseness, LHR introduces a more reasonable
log-sum measurement to enhance the sparsity in both the intrinsic low-rank
structure and in the sparse corruptions. Although the proposed LHR optimization
is no longer convex, it still can be effectively solved by a
majorization-minimization (MM) type algorithm, with which the non-convex
objective function is iteratively replaced by its convex surrogate and LHR
finally falls into the general framework of reweighed approaches. We prove that
the MM-type algorithm can converge to a stationary point after successive
iteration. We test the performance of our proposed model by applying it to
solve two typical problems: robust principal component analysis (RPCA) and
low-rank representation (LRR).
For RPCA, we compare LHR with the benchmark Principal Component Pursuit (PCP)
method from both the perspectives of simulations and practical applications.
For LRR, we apply LHR to compute the low-rank representation matrix for motion
segmentation and stock clustering. Experimental results on low rank structure
learning demonstrate that the proposed Log-sum based model performs much better
than the $\ell_1$-based method on for data with higher rank and with denser
corruptions.
| Yue Deng, Qionghai Dai, Risheng Liu, Zengke Zhang and Sanqing Hu | 10.1109/TNNLS.2012.2235082 | 1012.1919 | null | null |
Context Aware End-to-End Connectivity Management | cs.LG cs.NI | In a dynamic heterogeneous environment, such as pervasive and ubiquitous
computing, context-aware adaptation is a key concept to meet the varying
requirements of different users. Connectivity is an important context source
that can be utilized for optimal management of diverse networking resources.
Application QoS (Quality of service) is another important issue that should be
taken into consideration for design of a context-aware system. This paper
presents connectivity from the view point of context awareness, identifies
various relevant raw connectivity contexts, and discusses how high-level
context information can be abstracted from the raw context information.
Further, rich context information is utilized in various policy representation
with respect to user profile and preference, application characteristics,
device capability, and network QoS conditions. Finally, a context-aware
end-to-end evaluation algorithm is presented for adaptive connectivity
management in a multi-access wireless network. Unlike the currently existing
algorithms, the proposed algorithm takes into account user QoS parameters, and
therefore, it is more practical.
| Jaydip Sen, P. Balamuralidhar, M. Girish Chandra, Harihara S.G., and
Harish Reddy | 10.13140/RG.2.1.3436.8247 | 1012.2514 | null | null |
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with
Application to Active User Modeling and Hierarchical Reinforcement Learning | cs.LG | We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences.
| Eric Brochu and Vlad M. Cora and Nando de Freitas | null | 1012.2599 | null | null |
Inverse-Category-Frequency based supervised term weighting scheme for
text categorization | cs.LG cs.AI | Term weighting schemes often dominate the performance of many classifiers,
such as kNN, centroid-based classifier and SVMs. The widely used term weighting
scheme in text categorization, i.e., tf.idf, is originated from information
retrieval (IR) field. The intuition behind idf for text categorization seems
less reasonable than IR. In this paper, we introduce inverse category frequency
(icf) into term weighting scheme and propose two novel approaches, i.e., tf.icf
and icf-based supervised term weighting schemes. The tf.icf adopts icf to
substitute idf factor and favors terms occurring in fewer categories, rather
than fewer documents. And the icf-based approach combines icf and relevance
frequency (rf) to weight terms in a supervised way. Our cross-classifier and
cross-corpus experiments have shown that our proposed approaches are superior
or comparable to six supervised term weighting schemes and three traditional
schemes in terms of macro-F1 and micro-F1.
| Deqing Wang, Hui Zhang | null | 1012.2609 | null | null |
On the Combinatorial Multi-Armed Bandit Problem with Markovian Rewards | math.OC cs.LG cs.NI cs.SY math.PR | We consider a combinatorial generalization of the classical multi-armed
bandit problem that is defined as follows. There is a given bipartite graph of
$M$ users and $N \geq M$ resources. For each user-resource pair $(i,j)$, there
is an associated state that evolves as an aperiodic irreducible finite-state
Markov chain with unknown parameters, with transitions occurring each time the
particular user $i$ is allocated resource $j$. The user $i$ receives a reward
that depends on the corresponding state each time it is allocated the resource
$j$. The system objective is to learn the best matching of users to resources
so that the long-term sum of the rewards received by all users is maximized.
This corresponds to minimizing regret, defined here as the gap between the
expected total reward that can be obtained by the best-possible static matching
and the expected total reward that can be achieved by a given algorithm. We
present a polynomial-storage and polynomial-complexity-per-step
matching-learning algorithm for this problem. We show that this algorithm can
achieve a regret that is uniformly arbitrarily close to logarithmic in time and
polynomial in the number of users and resources. This formulation is broadly
applicable to scheduling and switching problems in networks and significantly
extends prior results in the area.
| Yi Gai, Bhaskar Krishnamachari and Mingyan Liu | null | 1012.3005 | null | null |
Analysis of Agglomerative Clustering | cs.DS cs.CG cs.LG | The diameter $k$-clustering problem is the problem of partitioning a finite
subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum
diameter of the clusters is minimized. One early clustering algorithm that
computes a hierarchy of approximate solutions to this problem (for all values
of $k$) is the agglomerative clustering algorithm with the complete linkage
strategy. For decades, this algorithm has been widely used by practitioners.
However, it is not well studied theoretically. In this paper, we analyze the
agglomerative complete linkage clustering algorithm. Assuming that the
dimension $d$ is a constant, we show that for any $k$ the solution computed by
this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering
problem. Our analysis does not only hold for the Euclidean distance but for any
metric that is based on a norm. Furthermore, we analyze the closely related
$k$-center and discrete $k$-center problem. For the corresponding agglomerative
algorithms, we deduce an approximation factor of $O(\log k)$ as well.
| Marcel R. Ackermann, Johannes Bl\"omer, Daniel Kuntze and Christian
Sohler | 10.1007/s00453-012-9717-4 | 1012.3697 | null | null |
Queue-Aware Dynamic Clustering and Power Allocation for Network MIMO
Systems via Distributive Stochastic Learning | cs.LG | In this paper, we propose a two-timescale delay-optimal dynamic clustering
and power allocation design for downlink network MIMO systems. The dynamic
clustering control is adaptive to the global queue state information (GQSI)
only and computed at the base station controller (BSC) over a longer time
scale. On the other hand, the power allocations of all the BSs in one cluster
are adaptive to both intra-cluster channel state information (CCSI) and
intra-cluster queue state information (CQSI), and computed at the cluster
manager (CM) over a shorter time scale. We show that the two-timescale
delay-optimal control can be formulated as an infinite-horizon average cost
Constrained Partially Observed Markov Decision Process (CPOMDP). By exploiting
the special problem structure, we shall derive an equivalent Bellman equation
in terms of Pattern Selection Q-factor to solve the CPOMDP. To address the
distributive requirement and the issue of exponential memory requirement and
computational complexity, we approximate the Pattern Selection Q-factor by the
sum of Per-cluster Potential functions and propose a novel distributive online
learning algorithm to estimate the Per-cluster Potential functions (at each CM)
as well as the Lagrange multipliers (LM) (at each BS). We show that the
proposed distributive online learning algorithm converges almost surely (with
probability 1). By exploiting the birth-death structure of the queue dynamics,
we further decompose the Per-cluster Potential function into sum of Per-cluster
Per-user Potential functions and formulate the instantaneous power allocation
as a Per-stage QSI-aware Interference Game played among all the CMs. We also
propose a QSI-aware Simultaneous Iterative Water-filling Algorithm (QSIWFA) and
show that it can achieve the Nash Equilibrium (NE).
| Ying Cui, Qingqing Huang, Vincent K.N.Lau | 10.1109/TSP.2010.2097253 | 1012.3877 | null | null |
Survey & Experiment: Towards the Learning Accuracy | cs.LG | To attain the best learning accuracy, people move on with difficulties and
frustrations. Though one can optimize the empirical objective using a given set
of samples, its generalization ability to the entire sample distribution
remains questionable. Even if a fair generalization guarantee is offered, one
still wants to know what is to happen if the regularizer is removed, and/or how
well the artificial loss (like the hinge loss) relates to the accuracy.
For such reason, this report surveys four different trials towards the
learning accuracy, embracing the major advances in supervised learning theory
in the past four years. Starting from the generic setting of learning, the
first two trials introduce the best optimization and generalization bounds for
convex learning, and the third trial gets rid of the regularizer. As an
innovative attempt, the fourth trial studies the optimization when the
objective is exactly the accuracy, in the special case of binary
classification. This report also analyzes the last trial through experiments.
| Zeyuan Allen Zhu | null | 1012.4051 | null | null |
Travel Time Estimation Using Floating Car Data | cs.LG | This report explores the use of machine learning techniques to accurately
predict travel times in city streets and highways using floating car data
(location information of user vehicles on a road network). The aim of this
report is twofold, first we present a general architecture of solving this
problem, then present and evaluate few techniques on real floating car data
gathered over a month on a 5 Km highway in New Delhi.
| Raffi Sevlian, Ram Rajagopal | null | 1012.4249 | null | null |
How I won the "Chess Ratings - Elo vs the Rest of the World" Competition | cs.LG | This article discusses in detail the rating system that won the kaggle
competition "Chess Ratings: Elo vs the rest of the world". The competition
provided a historical dataset of outcomes for chess games, and aimed to
discover whether novel approaches can predict the outcomes of future games,
more accurately than the well-known Elo rating system. The winning rating
system, called Elo++ in the rest of the article, builds upon the Elo rating
system. Like Elo, Elo++ uses a single rating per player and predicts the
outcome of a game, by using a logistic curve over the difference in ratings of
the players. The major component of Elo++ is a regularization technique that
avoids overfitting these ratings. The dataset of chess games and outcomes is
relatively small and one has to be careful not to draw "too many conclusions"
out of the limited data. Many approaches tested in the competition showed signs
of such an overfitting. The leader-board was dominated by attempts that did a
very good job on a small test dataset, but couldn't generalize well on the
private hold-out dataset. The Elo++ regularization takes into account the
number of games per player, the recency of these games and the ratings of the
opponents. Finally, Elo++ employs a stochastic gradient descent scheme for
training the ratings, and uses only two global parameters (white's advantage
and regularization constant) that are optimized using cross-validation.
| Yannis Sismanis | null | 1012.4571 | null | null |
Calibration Using Matrix Completion with Application to Ultrasound
Tomography | cs.LG cs.IT math.IT | We study the calibration process in circular ultrasound tomography devices
where the sensor positions deviate from the circumference of a perfect circle.
This problem arises in a variety of applications in signal processing ranging
from breast imaging to sensor network localization. We introduce a novel method
of calibration/localization based on the time-of-flight (ToF) measurements
between sensors when the enclosed medium is homogeneous. In the presence of all
the pairwise ToFs, one can easily estimate the sensor positions using
multi-dimensional scaling (MDS) method. In practice however, due to the
transitional behaviour of the sensors and the beam form of the transducers, the
ToF measurements for close-by sensors are unavailable. Further, random
malfunctioning of the sensors leads to random missing ToF measurements. On top
of the missing entries, in practice an unknown time delay is also added to the
measurements. In this work, we incorporate the fact that a matrix defined from
all the ToF measurements is of rank at most four. In order to estimate the
missing ToFs, we apply a state-of-the-art low-rank matrix completion algorithm,
OPTSPACE . To find the correct positions of the sensors (our ultimate goal) we
then apply MDS. We show analytic bounds on the overall error of the whole
process in the presence of noise and hence deduce its robustness. Finally, we
confirm the functionality of our method in practice by simulations mimicking
the measurements of a circular ultrasound tomography device.
| Reza Parhizkar, Amin Karbasi, Sewoong Oh, Martin Vetterli | 10.1109/TSP.2013.2272925 | 1012.4928 | null | null |
Conditional information and definition of neighbor in categorical random
fields | math.ST cs.LG stat.TH | We show that the definition of neighbor in Markov random fields as defined by
Besag (1974) when the joint distribution of the sites is not positive is not
well-defined. In a random field with finite number of sites we study the
conditions under which giving the value at extra sites will change the belief
of an agent about one site. Also the conditions under which the information
from some sites is equivalent to giving the value at all other sites is
studied. These concepts provide an alternative to the concept of neighbor for
general case where the positivity condition of the joint does not hold.
| Reza Hosseini | null | 1101.0255 | null | null |
The Local Optimality of Reinforcement Learning by Value Gradients, and
its Relationship to Policy Gradient Learning | cs.LG cs.AI | In this theoretical paper we are concerned with the problem of learning a
value function by a smooth general function approximator, to solve a
deterministic episodic control problem in a large continuous state space. It is
shown that learning the gradient of the value-function at every point along a
trajectory generated by a greedy policy is a sufficient condition for the
trajectory to be locally extremal, and often locally optimal, and we argue that
this brings greater efficiency to value-function learning. This contrasts to
traditional value-function learning in which the value-function must be learnt
over the whole of state space.
It is also proven that policy-gradient learning applied to a greedy policy on
a value-function produces a weight update equivalent to a value-gradient weight
update, which provides a surprising connection between these two alternative
paradigms of reinforcement learning, and a convergence proof for control
problems with a value function represented by a general smooth function
approximator.
| Michael Fairbank and Eduardo Alonso | null | 1101.0428 | null | null |
Sparsity regret bounds for individual sequences in online linear
regression | stat.ML cs.LG math.ST stat.TH | We consider the problem of online linear regression on arbitrary
deterministic sequences when the ambient dimension d can be much larger than
the number of time rounds T. We introduce the notion of sparsity regret bound,
which is a deterministic online counterpart of recent risk bounds derived in
the stochastic setting under a sparsity scenario. We prove such regret bounds
for an online-learning algorithm called SeqSEW and based on exponential
weighting and data-driven truncation. In a second part we apply a
parameter-free version of this algorithm to the stochastic setting (regression
model with random design). This yields risk bounds of the same flavor as in
Dalalyan and Tsybakov (2011) but which solve two questions left open therein.
In particular our risk bounds are adaptive (up to a logarithmic factor) to the
unknown variance of the noise if the latter is Gaussian. We also address the
regression model with fixed design.
| S\'ebastien Gerchinovitz (DMA, INRIA Paris - Rocquencourt) | null | 1101.1057 | null | null |
Review and Evaluation of Feature Selection Algorithms in Synthetic
Problems | cs.AI cs.LG | The main purpose of Feature Subset Selection is to find a reduced subset of
attributes from a data set described by a feature set. The task of a feature
selection algorithm (FSA) is to provide with a computational solution motivated
by a certain definition of relevance or by a reliable evaluation measure. In
this paper several fundamental algorithms are studied to assess their
performance in a controlled experimental scenario. A measure to evaluate FSAs
is devised that computes the degree of matching between the output given by a
FSA and the known optimal solutions. An extensive experimental study on
synthetic problems is carried out to assess the behaviour of the algorithms in
terms of solution accuracy and size as a function of the relevance,
irrelevance, redundancy and size of the data samples. The controlled
experimental conditions facilitate the derivation of better-supported and
meaningful conclusions.
| L.A. Belanche and F.F. Gonz\'alez | null | 1101.2320 | null | null |
Support vector machines/relevance vector machine for remote sensing
classification: A review | cs.CV cs.LG | Kernel-based machine learning algorithms are based on mapping data from the
original input feature space to a kernel feature space of higher dimensionality
to solve a linear problem in that space. Over the last decade, kernel based
classification and regression approaches such as support vector machines have
widely been used in remote sensing as well as in various civil engineering
applications. In spite of their better performance with different datasets,
support vector machines still suffer from shortcomings such as
visualization/interpretation of model, choice of kernel and kernel specific
parameter as well as the regularization parameter. Relevance vector machines
are another kernel based approach being explored for classification and
regression with in last few years. The advantages of the relevance vector
machines over the support vector machines is the availability of probabilistic
predictions, using arbitrary kernel functions and not requiring setting of the
regularization parameter. This paper presents a state-of-the-art review of SVM
and RVM in remote sensing and provides some details of their use in other civil
engineering application also.
| Mahesh Pal | null | 1101.2987 | null | null |
Classification under Data Contamination with Application to Remote
Sensing Image Mis-registration | stat.ME cs.LG stat.ML | This work is motivated by the problem of image mis-registration in remote
sensing and we are interested in determining the resulting loss in the accuracy
of pattern classification. A statistical formulation is given where we propose
to use data contamination to model and understand the phenomenon of image
mis-registration. This model is widely applicable to many other types of errors
as well, for example, measurement errors and gross errors etc. The impact of
data contamination on classification is studied under a statistical learning
theoretical framework. A closed-form asymptotic bound is established for the
resulting loss in classification accuracy, which is less than
$\epsilon/(1-\epsilon)$ for data contamination of an amount of $\epsilon$. Our
bound is sharper than similar bounds in the domain adaptation literature and,
unlike such bounds, it applies to classifiers with an infinite
Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on
both synthetic and real datasets under various types of data contamination,
including label flipping, feature swapping and the replacement of feature
values with data generated from a random source such as a Gaussian or Cauchy
distribution. Our simulation results show that the bound we derive is fairly
tight.
| Donghui Yan, Peng Gong, Aiyou Chen and Liheng Zhong | null | 1101.3594 | null | null |
Dyna-H: a heuristic planning reinforcement learning algorithm applied to
role-playing-game strategy decision systems | cs.AI cs.LG cs.SY math.OC | In a Role-Playing Game, finding optimal trajectories is one of the most
important tasks. In fact, the strategy decision system becomes a key component
of a game engine. Determining the way in which decisions are taken (online,
batch or simulated) and the consumed resources in decision making (e.g.
execution time, memory) will influence, in mayor degree, the game performance.
When classical search algorithms such as A* can be used, they are the very
first option. Nevertheless, such methods rely on precise and complete models of
the search space, and there are many interesting scenarios where their
application is not possible. Then, model free methods for sequential decision
making under uncertainty are the best choice. In this paper, we propose a
heuristic planning strategy to incorporate the ability of heuristic-search in
path-finding into a Dyna agent. The proposed Dyna-H algorithm, as A* does,
selects branches more likely to produce outcomes than other branches. Besides,
it has the advantages of being a model-free online reinforcement learning
algorithm. The proposal was evaluated against the one-step Q-Learning and
Dyna-Q algorithms obtaining excellent experimental results: Dyna-H
significantly overcomes both methods in all experiments. We suggest also, a
functional analogy between the proposed sampling from worst trajectories
heuristic and the role of dreams (e.g. nightmares) in human behavior.
| Matilde Santos, Jose Antonio Martin H., Victoria Lopez and Guillermo
Botella | null | 1101.4003 | null | null |
The Role of Normalization in the Belief Propagation Algorithm | cs.LG | An important part of problems in statistical physics and computer science can
be expressed as the computation of marginal probabilities over a Markov Random
Field. The belief propagation algorithm, which is an exact procedure to compute
these marginals when the underlying graph is a tree, has gained its popularity
as an efficient way to approximate them in the more general case. In this
paper, we focus on an aspect of the algorithm that did not get that much
attention in the literature, which is the effect of the normalization of the
messages. We show in particular that, for a large class of normalization
strategies, it is possible to focus only on belief convergence. Following this,
we express the necessary and sufficient conditions for local stability of a
fixed point in terms of the graph structure and the beliefs values at the fixed
point. We also explicit some connexion between the normalization constants and
the underlying Bethe Free Energy.
| Victorin Martin and Jean-Marc Lasgouttes and Cyril Furtlehner | null | 1101.4170 | null | null |
Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs | physics.data-an cond-mat.dis-nn cond-mat.stat-mech cs.LG | We theoretically study semi-supervised clustering in sparse graphs in the
presence of pairwise constraints on the cluster assignments of nodes. We focus
on bi-cluster graphs, and study the impact of semi-supervision for varying
constraint density and overlap between the clusters. Recent results for
unsupervised clustering in sparse graphs indicate that there is a critical
ratio of within-cluster and between-cluster connectivities below which clusters
cannot be recovered with better than random accuracy. The goal of this paper is
to examine the impact of pairwise constraints on the clustering accuracy. Our
results suggests that the addition of constraints does not provide automatic
improvement over the unsupervised case. When the density of the constraints is
sufficiently small, their only impact is to shift the detection threshold while
preserving the criticality. Conversely, if the density of (hard) constraints is
above the percolation threshold, the criticality is suppressed and the
detection threshold disappears.
| Greg Ver Steeg, Aram Galstyan, Armen E. Allahverdyan | 10.1088/1742-5468/2011/08/P08009 | 1101.4227 | null | null |
Reproducing Kernel Banach Spaces with the l1 Norm | stat.ML cs.LG math.FA | Targeting at sparse learning, we construct Banach spaces B of functions on an
input space X with the properties that (1) B possesses an l1 norm in the sense
that it is isometrically isomorphic to the Banach space of integrable functions
on X with respect to the counting measure; (2) point evaluations are continuous
linear functionals on B and are representable through a bilinear form with a
kernel function; (3) regularized learning schemes on B satisfy the linear
representer theorem. Examples of kernel functions admissible for the
construction of such spaces are given.
| Guohui Song, Haizhang Zhang, Fred J. Hickernell | 10.1016/j.acha.2012.03.009 | 1101.4388 | null | null |
Reproducing Kernel Banach Spaces with the l1 Norm II: Error Analysis for
Regularized Least Square Regression | stat.ML cs.LG math.FA | A typical approach in estimating the learning rate of a regularized learning
scheme is to bound the approximation error by the sum of the sampling error,
the hypothesis error and the regularization error. Using a reproducing kernel
space that satisfies the linear representer theorem brings the advantage of
discarding the hypothesis error from the sum automatically. Following this
direction, we illustrate how reproducing kernel Banach spaces with the l1 norm
can be applied to improve the learning rate estimate of l1-regularization in
machine learning.
| Guohui Song, Haizhang Zhang | null | 1101.4439 | null | null |
Close the Gaps: A Learning-while-Doing Algorithm for a Class of
Single-Product Revenue Management Problems | cs.LG | We consider a retailer selling a single product with limited on-hand
inventory over a finite selling season. Customer demand arrives according to a
Poisson process, the rate of which is influenced by a single action taken by
the retailer (such as price adjustment, sales commission, advertisement
intensity, etc.). The relationship between the action and the demand rate is
not known in advance. However, the retailer is able to learn the optimal action
"on the fly" as she maximizes her total expected revenue based on the observed
demand reactions.
Using the pricing problem as an example, we propose a dynamic
"learning-while-doing" algorithm that only involves function value estimation
to achieve a near-optimal performance. Our algorithm employs a series of
shrinking price intervals and iteratively tests prices within that interval
using a set of carefully chosen parameters. We prove that the convergence rate
of our algorithm is among the fastest of all possible algorithms in terms of
asymptotic "regret" (the relative loss comparing to the full information
optimal solution). Our result closes the performance gaps between parametric
and non-parametric learning and between a post-price mechanism and a
customer-bidding mechanism. Important managerial insight from this research is
that the values of information on both the parametric form of the demand
function as well as each customer's exact reservation price are less important
than prior literature suggests. Our results also suggest that firms would be
better off to perform dynamic learning and action concurrently rather than
sequentially.
| Zizhuo Wang, Shiming Deng and Yinyu Ye | null | 1101.4681 | null | null |
Online Adaptive Decision Fusion Framework Based on Entropic Projections
onto Convex Sets with Application to Wildfire Detection in Video | cs.CV cs.LG | In this paper, an Entropy functional based online Adaptive Decision Fusion
(EADF) framework is developed for image analysis and computer vision
applications. In this framework, it is assumed that the compound algorithm
consists of several sub-algorithms each of which yielding its own decision as a
real number centered around zero, representing the confidence level of that
particular sub-algorithm. Decision values are linearly combined with weights
which are updated online according to an active fusion method based on
performing entropic projections onto convex sets describing sub-algorithms. It
is assumed that there is an oracle, who is usually a human operator, providing
feedback to the decision fusion method. A video based wildfire detection system
is developed to evaluate the performance of the algorithm in handling the
problems where data arrives sequentially. In this case, the oracle is the
security guard of the forest lookout tower verifying the decision of the
combined algorithm. Simulation results are presented. The EADF framework is
also tested with a standard dataset.
| Osman Gunay and Behcet Ugur Toreyin and Kivanc Kose and A. Enis Cetin | 10.1117/1.3595426 | 1101.4749 | null | null |
A Primal-Dual Convergence Analysis of Boosting | cs.LG math.OC | Boosting combines weak learners into a predictor with low empirical risk. Its
dual constructs a high entropy distribution upon which weak learners and
training labels are uncorrelated. This manuscript studies this primal-dual
relationship under a broad family of losses, including the exponential loss of
AdaBoost and the logistic loss, revealing:
- Weak learnability aids the whole loss family: for any {\epsilon}>0,
O(ln(1/{\epsilon})) iterations suffice to produce a predictor with empirical
risk {\epsilon}-close to the infimum;
- The circumstances granting the existence of an empirical risk minimizer may
be characterized in terms of the primal and dual problems, yielding a new proof
of the known rate O(ln(1/{\epsilon}));
- Arbitrary instances may be decomposed into the above two, granting rate
O(1/{\epsilon}), with a matching lower bound provided for the logistic loss.
| Matus Telgarsky | null | 1101.4752 | null | null |
Using Feature Weights to Improve Performance of Neural Networks | cs.LG cs.AI cs.CV | Different features have different relevance to a particular learning problem.
Some features are less relevant; while some very important. Instead of
selecting the most relevant features using feature selection, an algorithm can
be given this knowledge of feature importance based on expert opinion or prior
learning. Learning can be faster and more accurate if learners take feature
importance into account. Correlation aided Neural Networks (CANN) is presented
which is such an algorithm. CANN treats feature importance as the correlation
coefficient between the target attribute and the features. CANN modifies normal
feed-forward Neural Network to fit both correlation values and training data.
Empirical evaluation shows that CANN is faster and more accurate than applying
the two step approach of feature selection and then using normal learning
algorithms.
| Ridwan Al Iqbal | null | 1101.4918 | null | null |
A Generalized Method for Integrating Rule-based Knowledge into Inductive
Methods Through Virtual Sample Creation | cs.LG cs.AI cs.CV | Hybrid learning methods use theoretical knowledge of a domain and a set of
classified examples to develop a method for classification. Methods that use
domain knowledge have been shown to perform better than inductive learners.
However, there is no general method to include domain knowledge into all
inductive learning algorithms as all hybrid methods are highly specialized for
a particular algorithm. We present an algorithm that will take domain knowledge
in the form of propositional rules, generate artificial examples from the rules
and also remove instances likely to be flawed. This enriched dataset then can
be used by any learning algorithm. Experimental results of different scenarios
are shown that demonstrate this method to be more effective than simple
inductive learning.
| Ridwan Al Iqbal | null | 1101.4924 | null | null |
A Novel Template-Based Learning Model | cs.LG | This article presents a model which is capable of learning and abstracting
new concepts based on comparing observations and finding the resemblance
between the observations. In the model, the new observations are compared with
the templates which have been derived from the previous experiences. In the
first stage, the objects are first represented through a geometric description
which is used for finding the object boundaries and a descriptor which is
inspired by the human visual system and then they are fed into the model. Next,
the new observations are identified through comparing them with the
previously-learned templates and are used for producing new templates. The
comparisons are made based on measures like Euclidean or correlation distance.
The new template is created by applying onion-pealing algorithm. The algorithm
consecutively uses convex hulls which are made by the points representing the
objects. If the new observation is remarkably similar to one of the observed
categories, it is no longer utilized in creating a new template. The existing
templates are used to provide a description of the new observation. This
description is provided in the templates space. Each template represents a
dimension of the feature space. The degree of the resemblance each template
bears to each object indicates the value associated with the object in that
dimension of the templates space. In this way, the description of the new
observation becomes more accurate and detailed as the time passes and the
experiences increase. We have used this model for learning and recognizing the
new polygons in the polygon space. Representing the polygons was made possible
through employing a geometric method and a method inspired by human visual
system. Various implementations of the model have been compared. The evaluation
results of the model prove its efficiency in learning and deriving new
templates.
| Mohammadreza Abolghasemi-Dahaghani, Farzad Didehvar (1), Alireza
Nowroozi | null | 1101.5039 | null | null |
Infinite Multiple Membership Relational Modeling for Complex Networks | cs.SI cs.LG physics.soc-ph | Learning latent structure in complex networks has become an important problem
fueled by many types of networked data originating from practically all fields
of science. In this paper, we propose a new non-parametric Bayesian
multiple-membership latent feature model for networks. Contrary to existing
multiple-membership models that scale quadratically in the number of vertices
the proposed model scales linearly in the number of links admitting
multiple-membership analysis in large scale networks. We demonstrate a
connection between the single membership relational model and multiple
membership models and show on "real" size benchmark network data that
accounting for multiple memberships improves the learning of latent structure
as measured by link prediction while explicitly accounting for multiple
membership result in a more compact representation of the latent structure of
networks.
| Morten M{\o}rup, Mikkel N. Schmidt, Lars Kai Hansen | null | 1101.5097 | null | null |
A Complex Networks Approach for Data Clustering | physics.data-an cs.LG cs.SI physics.soc-ph | Many methods have been developed for data clustering, such as k-means,
expectation maximization and algorithms based on graph theory. In this latter
case, graphs are generally constructed by taking into account the Euclidian
distance as a similarity measure, and partitioned using spectral methods.
However, these methods are not accurate when the clusters are not well
separated. In addition, it is not possible to automatically determine the
number of clusters. These limitations can be overcome by taking into account
network community identification algorithms. In this work, we propose a
methodology for data clustering based on complex networks theory. We compare
different metrics for quantifying the similarity between objects and take into
account three community finding techniques. This approach is applied to two
real-world databases and to two sets of artificially generated data. By
comparing our method with traditional clustering approaches, we verify that the
proximity measures given by the Chebyshev and Manhattan distances are the most
suitable metrics to quantify the similarity between objects. In addition, the
community identification method based on the greedy optimization provides the
smallest misclassification rates.
| Francisco A. Rodrigues, Guilherme Ferraz de Arruda, Luciano da
Fontoura Costa | null | 1101.5141 | null | null |
Active Markov Information-Theoretic Path Planning for Robotic
Environmental Sensing | cs.LG cs.AI cs.MA cs.RO | Recent research in multi-robot exploration and mapping has focused on
sampling environmental fields, which are typically modeled using the Gaussian
process (GP). Existing information-theoretic exploration strategies for
learning GP-based environmental field maps adopt the non-Markovian problem
structure and consequently scale poorly with the length of history of
observations. Hence, it becomes computationally impractical to use these
strategies for in situ, real-time active sampling. To ease this computational
burden, this paper presents a Markov-based approach to efficient
information-theoretic path planning for active sampling of GP-based fields. We
analyze the time complexity of solving the Markov-based path planning problem,
and demonstrate analytically that it scales better than that of deriving the
non-Markovian strategies with increasing length of planning horizon. For a
class of exploration tasks called the transect sampling task, we provide
theoretical guarantees on the active sampling performance of our Markov-based
policy, from which ideal environmental field conditions and sampling task
settings can be established to limit its performance degradation due to
violation of the Markov assumption. Empirical evaluation on real-world
temperature and plankton density field data shows that our Markov-based policy
can generally achieve active sampling performance comparable to that of the
widely-used non-Markovian greedy policies under less favorable realistic field
conditions and task settings while enjoying significant computational gain over
them.
| Kian Hsiang Low, John M. Dolan, and Pradeep Khosla | null | 1101.5632 | null | null |
On the Local Correctness of L^1 Minimization for Dictionary Learning | cs.IT cs.LG math.IT | The idea that many important classes of signals can be well-represented by
linear combinations of a small set of atoms selected from a given dictionary
has had dramatic impact on the theory and practice of signal processing. For
practical problems in which an appropriate sparsifying dictionary is not known
ahead of time, a very popular and successful heuristic is to search for a
dictionary that minimizes an appropriate sparsity surrogate over a given set of
sample data. While this idea is appealing, the behavior of these algorithms is
largely a mystery; although there is a body of empirical evidence suggesting
they do learn very effective representations, there is little theory to
guarantee when they will behave correctly, or when the learned dictionary can
be expected to generalize. In this paper, we take a step towards such a theory.
We show that under mild hypotheses, the dictionary learning problem is locally
well-posed: the desired solution is indeed a local minimum of the $\ell^1$
norm. Namely, if $\mb A \in \Re^{m \times n}$ is an incoherent (and possibly
overcomplete) dictionary, and the coefficients $\mb X \in \Re^{n \times p}$
follow a random sparse model, then with high probability $(\mb A,\mb X)$ is a
local minimum of the $\ell^1$ norm over the manifold of factorizations $(\mb
A',\mb X')$ satisfying $\mb A' \mb X' = \mb Y$, provided the number of samples
$p = \Omega(n^3 k)$. For overcomplete $\mb A$, this is the first result showing
that the dictionary learning problem is locally solvable. Our analysis draws on
tools developed for the problem of completing a low-rank matrix from a small
subset of its entries, which allow us to overcome a number of technical
obstacles; in particular, the absence of the restricted isometry property.
| Quan Geng and Huan Wang and John Wright | null | 1101.5672 | null | null |
Statistical Compressed Sensing of Gaussian Mixture Models | cs.CV cs.LG | A novel framework of compressed sensing, namely statistical compressed
sensing (SCS), that aims at efficiently sampling a collection of signals that
follow a statistical distribution, and achieving accurate reconstruction on
average, is introduced. SCS based on Gaussian models is investigated in depth.
For signals that follow a single Gaussian model, with Gaussian or Bernoulli
sensing matrices of O(k) measurements, considerably smaller than the O(k
log(N/k)) required by conventional CS based on sparse models, where N is the
signal dimension, and with an optimal decoder implemented via linear filtering,
significantly faster than the pursuit decoders applied in conventional CS, the
error of SCS is shown tightly upper bounded by a constant times the best k-term
approximation error, with overwhelming probability. The failure probability is
also significantly smaller than that of conventional sparsity-oriented CS.
Stronger yet simpler results further show that for any sensing matrix, the
error of Gaussian SCS is upper bounded by a constant times the best k-term
approximation with probability one, and the bound constant can be efficiently
calculated. For Gaussian mixture models (GMMs), that assume multiple Gaussian
distributions and that each signal follows one of them with an unknown index, a
piecewise linear estimator is introduced to decode SCS. The accuracy of model
selection, at the heart of the piecewise linear decoder, is analyzed in terms
of the properties of the Gaussian distributions and the number of sensing
measurements. A maximum a posteriori expectation-maximization algorithm that
iteratively estimates the Gaussian models parameters, the signals model
selection, and decodes the signals, is presented for GMM-based SCS. In real
image sensing applications, GMM-based SCS is shown to lead to improved results
compared to conventional CS, at a considerably lower computational cost.
| Guoshen Yu and Guillermo Sapiro | 10.1109/TSP.2011.2168521 | 1101.5785 | null | null |
The VC-Dimension of Queries and Selectivity Estimation Through Sampling | cs.DB cs.DS cs.LG | We develop a novel method, based on the statistical concept of the
Vapnik-Chervonenkis dimension, to evaluate the selectivity (output cardinality)
of SQL queries - a crucial step in optimizing the execution of large scale
database and data-mining operations. The major theoretical contribution of this
work, which is of independent interest, is an explicit bound to the
VC-dimension of a range space defined by all possible outcomes of a collection
(class) of queries. We prove that the VC-dimension is a function of the maximum
number of Boolean operations in the selection predicate and of the maximum
number of select and join operations in any individual query in the collection,
but it is neither a function of the number of queries in the collection nor of
the size (number of tuples) of the database. We leverage on this result and
develop a method that, given a class of queries, builds a concise random sample
of a database, such that with high probability the execution of any query in
the class on the sample provides an accurate estimate for the selectivity of
the query on the original large database. The error probability holds
simultaneously for the selectivity estimates of all queries in the collection,
thus the same sample can be used to evaluate the selectivity of multiple
queries, and the sample needs to be refreshed only following major changes in
the database. The sample representation computed by our method is typically
sufficiently small to be stored in main memory. We present extensive
experimental results, validating our theoretical analysis and demonstrating the
advantage of our technique when compared to complex selectivity estimation
techniques used in PostgreSQL and the Microsoft SQL Server.
| Matteo Riondato, Mert Akdere, Ugur Cetintemel, Stanley B. Zdonik, Eli
Upfal | null | 1101.5805 | null | null |
Spatially-Aware Comparison and Consensus for Clusterings | cs.LG cs.CG cs.DB | This paper proposes a new distance metric between clusterings that
incorporates information about the spatial distribution of points and clusters.
Our approach builds on the idea of a Hilbert space-based representation of
clusters as a combination of the representations of their constituent points.
We use this representation and the underlying metric to design a
spatially-aware consensus clustering procedure. This consensus procedure is
implemented via a novel reduction to Euclidean clustering, and is both simple
and efficient. All of our results apply to both soft and hard clusterings. We
accompany these algorithms with a detailed experimental evaluation that
demonstrates the efficiency and quality of our techniques.
| Parasaran Raman, Jeff M. Phillips and Suresh Venkatasubramanian | null | 1102.0026 | null | null |
Statistical methods for tissue array images - algorithmic scoring and
co-training | stat.ME cs.CE cs.CV cs.LG q-bio.QM | Recent advances in tissue microarray technology have allowed
immunohistochemistry to become a powerful medium-to-high throughput analysis
tool, particularly for the validation of diagnostic and prognostic biomarkers.
However, as study size grows, the manual evaluation of these assays becomes a
prohibitive limitation; it vastly reduces throughput and greatly increases
variability and expense. We propose an algorithm - Tissue Array Co-Occurrence
Matrix Analysis (TACOMA) - for quantifying cellular phenotypes based on
textural regularity summarized by local inter-pixel relationships. The
algorithm can be easily trained for any staining pattern, is absent of
sensitive tuning parameters and has the ability to report salient pixels in an
image that contribute to its score. Pathologists' input via informative
training patches is an important aspect of the algorithm that allows the
training for any specific marker or cell type. With co-training, the error rate
of TACOMA can be reduced substantially for a very small training sample (e.g.,
with size 30). We give theoretical insights into the success of co-training via
thinning of the feature set in a high-dimensional setting when there is
"sufficient" redundancy among the features. TACOMA is flexible, transparent and
provides a scoring process that can be evaluated with clarity and confidence.
In a study based on an estrogen receptor (ER) marker, we show that TACOMA is
comparable to, or outperforms, pathologists' performance in terms of accuracy
and repeatability.
| Donghui Yan, Pei Wang, Michael Linden, Beatrice Knudsen, Timothy
Randolph | 10.1214/12-AOAS543 | 1102.0059 | null | null |
EigenNet: A Bayesian hybrid of generative and conditional models for
sparse learning | cs.LG | It is a challenging task to select correlated variables in a high dimensional
space. To address this challenge, the elastic net has been developed and
successfully applied to many applications. Despite its great success, the
elastic net does not explicitly use correlation information embedded in data to
select correlated variables. To overcome this limitation, we present a novel
Bayesian hybrid model, the EigenNet, that uses the eigenstructures of data to
guide variable selection. Specifically, it integrates a sparse conditional
classification model with a generative model capturing variable correlations in
a principled Bayesian framework. We reparameterize the hybrid model in the
eigenspace to avoid overfiting and to increase the computational efficiency of
its MCMC sampler. Furthermore, we provide an alternative view to the EigenNet
from a regularization perspective: the EigenNet has an adaptive
eigenspace-based composite regularizer, which naturally generalizes the
$l_{1/2}$ regularizer used by the elastic net. Experiments on synthetic and
real data show that the EigenNet significantly outperforms the lasso, the
elastic net, and the Bayesian lasso in terms of prediction accuracy, especially
when the number of training samples is smaller than the number of variables.
| Yuan Qi, Feng Yan | null | 1102.0836 | null | null |
Evidence Feed Forward Hidden Markov Model: A New Type of Hidden Markov
Model | cs.AI cs.CV cs.LG math.NA math.PR | The ability to predict the intentions of people based solely on their visual
actions is a skill only performed by humans and animals. The intelligence of
current computer algorithms has not reached this level of complexity, but there
are several research efforts that are working towards it. With the number of
classification algorithms available, it is hard to determine which algorithm
works best for a particular situation. In classification of visual human intent
data, Hidden Markov Models (HMM), and their variants, are leading candidates.
The inability of HMMs to provide a probability in the observation to
observation linkages is a big downfall in this classification technique. If a
person is visually identifying an action of another person, they monitor
patterns in the observations. By estimating the next observation, people have
the ability to summarize the actions, and thus determine, with pretty good
accuracy, the intention of the person performing the action. These visual cues
and linkages are important in creating intelligent algorithms for determining
human actions based on visual observations.
The Evidence Feed Forward Hidden Markov Model is a newly developed algorithm
which provides observation to observation linkages. The following research
addresses the theory behind Evidence Feed Forward HMMs, provides mathematical
proofs of their learning of these parameters to optimize the likelihood of
observations with a Evidence Feed Forwards HMM, which is important in all
computational intelligence algorithm, and gives comparative examples with
standard HMMs in classification of both visual action data and measurement
data; thus providing a strong base for Evidence Feed Forward HMMs in
classification of many types of problems.
| Michael DelRose, Christian Wagner, Philip Frederick | 10.5121/ijaia.2011.2101 | 1102.0899 | null | null |
Collective Classification of Textual Documents by Guided
Self-Organization in T-Cell Cross-Regulation Dynamics | cs.IR cs.AI cs.LG nlin.AO q-bio.OT | We present and study an agent-based model of T-Cell cross-regulation in the
adaptive immune system, which we apply to binary classification. Our method
expands an existing analytical model of T-cell cross-regulation (Carneiro et
al. in Immunol Rev 216(1):48-68, 2007) that was used to study the
self-organizing dynamics of a single population of T-Cells in interaction with
an idealized antigen presenting cell capable of presenting a single antigen.
With agent-based modeling we are able to study the self-organizing dynamics of
multiple populations of distinct T-cells which interact via antigen presenting
cells that present hundreds of distinct antigens. Moreover, we show that such
self-organizing dynamics can be guided to produce an effective binary
classification of antigens, which is competitive with existing machine learning
methods when applied to biomedical text classification. More specifically, here
we test our model on a dataset of publicly available full-text biomedical
articles provided by the BioCreative challenge (Krallinger in The biocreative
ii. 5 challenge overview, p 19, 2009). We study the robustness of our model's
parameter configurations, and show that it leads to encouraging results
comparable to state-of-the-art classifiers. Our results help us understand both
T-cell cross-regulation as a general principle of guided self-organization, as
well as its applicability to document classification. Therefore, we show that
our bio-inspired algorithm is a promising novel method for biomedical article
classification and for binary document classification in general.
| Alaa Abi-Haidar and Luis M. Rocha | 10.1007/s12065-011-0052-5 | 1102.1027 | null | null |
Phase transition in the detection of modules in sparse networks | cond-mat.stat-mech cs.LG cs.SI physics.soc-ph | We present an asymptotically exact analysis of the problem of detecting
communities in sparse random networks. Our results are also applicable to
detection of functional modules, partitions, and colorings in noisy planted
models. Using a cavity method analysis, we unveil a phase transition from a
region where the original group assignment is undetectable to one where
detection is possible. In some cases, the detectable region splits into an
algorithmically hard region and an easy one. Our approach naturally translates
into a practical algorithm for detecting modules in sparse networks, and
learning the parameters of the underlying model.
| Aurelien Decelle, Florent Krzakala, Cristopher Moore and Lenka
Zdeborov\'a | 10.1103/PhysRevLett.107.065701 | 1102.1182 | null | null |
Refinement of Operator-valued Reproducing Kernels | cs.LG math.FA | This paper studies the construction of a refinement kernel for a given
operator-valued reproducing kernel such that the vector-valued reproducing
kernel Hilbert space of the refinement kernel contains that of the given one as
a subspace. The study is motivated from the need of updating the current
operator-valued reproducing kernel in multi-task learning when underfitting or
overfitting occurs. Numerical simulations confirm that the established
refinement kernel method is able to meet this need. Various characterizations
are provided based on feature maps and vector-valued integral representations
of operator-valued reproducing kernels. Concrete examples of refining
translation invariant and finite Hilbert-Schmidt operator-valued reproducing
kernels are provided. Other examples include refinement of Hessian of
scalar-valued translation-invariant kernels and transformation kernels.
Existence and properties of operator-valued reproducing kernels preserved
during the refinement process are also investigated.
| Yuesheng Xu, Haizhang Zhang, Qinghui Zhang | null | 1102.1324 | null | null |
An Introduction to Artificial Prediction Markets for Classification | stat.ML cs.LG math.ST stat.TH | Prediction markets are used in real life to predict outcomes of interest such
as presidential elections. This paper presents a mathematical theory of
artificial prediction markets for supervised learning of conditional
probability estimators. The artificial prediction market is a novel method for
fusing the prediction information of features or trained classifiers, where the
fusion result is the contract price on the possible outcomes. The market can be
trained online by updating the participants' budgets using training examples.
Inspired by the real prediction markets, the equations that govern the market
are derived from simple and reasonable assumptions. Efficient numerical
algorithms are presented for solving these equations. The obtained artificial
prediction market is shown to be a maximum likelihood estimator. It generalizes
linear aggregation, existent in boosting and random forest, as well as logistic
regression and some kernel methods. Furthermore, the market mechanism allows
the aggregation of specialized classifiers that participate only on specific
instances. Experimental comparisons show that the artificial prediction markets
often outperform random forest and implicit online learning on synthetic data
and real UCI datasets. Moreover, an extensive evaluation for pelvic and
abdominal lymph node detection in CT data shows that the prediction market
improves adaboost's detection rate from 79.6% to 81.2% at 3 false
positives/volume.
| Adrian Barbu, Nathan Lay | null | 1102.1465 | null | null |
From Machine Learning to Machine Reasoning | cs.AI cs.LG | A plausible definition of "reasoning" could be "algebraically manipulating
previously acquired knowledge in order to answer a new question". This
definition covers first-order logical inference or probabilistic inference. It
also includes much simpler manipulations commonly used to build large learning
systems. For instance, we can build an optical character recognition system by
first training a character segmenter, an isolated character recognizer, and a
language model, using appropriate labeled training sets. Adequately
concatenating these modules and fine tuning the resulting system can be viewed
as an algebraic operation in a space of models. The resulting model answers a
new question, that is, converting the image of a text page into a computer
readable text.
This observation suggests a conceptual continuity between algebraically rich
inference systems, such as logical or probabilistic inference, and simple
manipulations, such as the mere concatenation of trainable learning systems.
Therefore, instead of trying to bridge the gap between machine learning systems
and sophisticated "all-purpose" inference mechanisms, we can instead
algebraically enrich the set of manipulations applicable to training systems,
and build reasoning capabilities from the ground up.
| Leon Bottou | null | 1102.1808 | null | null |
Universal Learning Theory | cs.LG cs.IT math.IT | This encyclopedic article gives a mini-introduction into the theory of
universal learning, founded by Ray Solomonoff in the 1960s and significantly
developed and extended in the last decade. It explains the spirit of universal
learning, but necessarily glosses over technical subtleties.
| Marcus Hutter | null | 1102.2467 | null | null |
The KL-UCB Algorithm for Bounded Stochastic Bandits and Beyond | math.ST cs.LG cs.SY math.OC stat.TH | This paper presents a finite-time analysis of the KL-UCB algorithm, an
online, horizon-free index policy for stochastic bandit problems. We prove two
distinct results: first, for arbitrary bounded rewards, the KL-UCB algorithm
satisfies a uniformly better regret bound than UCB or UCB2; second, in the
special case of Bernoulli rewards, it reaches the lower bound of Lai and
Robbins. Furthermore, we show that simple adaptations of the KL-UCB algorithm
are also optimal for specific classes of (possibly unbounded) rewards,
including those generated from exponential families of distributions. A
large-scale numerical study comparing KL-UCB with its main competitors (UCB,
UCB2, UCB-Tuned, UCB-V, DMED) shows that KL-UCB is remarkably efficient and
stable, including for short time horizons. KL-UCB is also the only method that
always performs better than the basic UCB policy. Our regret bounds rely on
deviations results of independent interest which are stated and proved in the
Appendix. As a by-product, we also obtain an improved regret bound for the
standard UCB algorithm.
| Aur\'elien Garivier and Olivier Capp\'e | null | 1102.2490 | null | null |
A General Framework for Development of the Cortex-like Visual Object
Recognition System: Waves of Spikes, Predictive Coding and Universal
Dictionary of Features | cs.CV cs.AI cs.LG cs.NE | This study is focused on the development of the cortex-like visual object
recognition system. We propose a general framework, which consists of three
hierarchical levels (modules). These modules functionally correspond to the V1,
V4 and IT areas. Both bottom-up and top-down connections between the
hierarchical levels V4 and IT are employed. The higher the degree of matching
between the input and the preferred stimulus, the shorter the response time of
the neuron. Therefore information about a single stimulus is distributed in
time and is transmitted by the waves of spikes. The reciprocal connections and
waves of spikes implement predictive coding: an initial hypothesis is generated
on the basis of information delivered by the first wave of spikes and is tested
with the information carried by the consecutive waves. The development is
considered as extraction and accumulation of features in V4 and objects in IT.
Once stored a feature can be disposed, if rarely activated. This cause update
of feature repository. Consequently, objects in IT are also updated. This
illustrates the growing process and dynamical change of topological structures
of V4, IT and connections between these areas.
| Sergey S. Tarasenko | null | 1102.2739 | null | null |
Transductive Ordinal Regression | cs.LG | Ordinal regression is commonly formulated as a multi-class problem with
ordinal constraints. The challenge of designing accurate classifiers for
ordinal regression generally increases with the number of classes involved, due
to the large number of labeled patterns that are needed. The availability of
ordinal class labels, however, is often costly to calibrate or difficult to
obtain. Unlabeled patterns, on the other hand, often exist in much greater
abundance and are freely available. To take benefits from the abundance of
unlabeled patterns, we present a novel transductive learning paradigm for
ordinal regression in this paper, namely Transductive Ordinal Regression (TOR).
The key challenge of the present study lies in the precise estimation of both
the ordinal class label of the unlabeled data and the decision functions of the
ordinal classes, simultaneously. The core elements of the proposed TOR include
an objective function that caters to several commonly used loss functions
casted in transductive settings, for general ordinal regression. A label
swapping scheme that facilitates a strictly monotonic decrease in the objective
function value is also introduced. Extensive numerical studies on commonly used
benchmark datasets including the real world sentiment prediction problem are
then presented to showcase the characteristics and efficacies of the proposed
transductive ordinal regression. Further, comparisons to recent
state-of-the-art ordinal regression methods demonstrate the introduced
transductive learning paradigm for ordinal regression led to the robust and
improved performance.
| Chun-Wei Seah, Ivor W. Tsang, Yew-Soon Ong | 10.1109/TNNLS.2012.2198240 | 1102.2808 | null | null |
Decentralized Restless Bandit with Multiple Players and Unknown Dynamics | math.OC cs.LG cs.SY math.PR | We consider decentralized restless multi-armed bandit problems with unknown
dynamics and multiple players. The reward state of each arm transits according
to an unknown Markovian rule when it is played and evolves according to an
arbitrary unknown random process when it is passive. Players activating the
same arm at the same time collide and suffer from reward loss. The objective is
to maximize the long-term reward by designing a decentralized arm selection
policy to address unknown reward models and collisions among players. A
decentralized policy is constructed that achieves a regret with logarithmic
order when an arbitrary nontrivial bound on certain system parameters is known.
When no knowledge about the system is available, we extend the policy to
achieve a regret arbitrarily close to the logarithmic order. The result finds
applications in communication networks, financial investment, and industrial
engineering.
| Haoyang Liu, Keqin Liu, Qing Zhao | null | 1102.2975 | null | null |
Selecting the rank of truncated SVD by Maximum Approximation Capacity | cs.IT cs.LG math.IT stat.ML | Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$
approximation of a given input matrix. Selecting the appropriate rank $k$
defines a critical model order choice in most applications of SVD. To obtain a
principled cut-off criterion for the spectrum, we convert the underlying
optimization problem into a noisy channel coding problem. The optimal
approximation capacity of this channel controls the appropriate strength of
regularization to suppress noise. In simulation experiments, this information
theoretic method to determine the optimal rank competes with state-of-the art
model selection techniques.
| Mario Frank and Joachim M. Buhmann | 10.1109/ISIT.2011.6033687 | 1102.3176 | null | null |
Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy
Data | physics.data-an cond-mat.stat-mech cs.LG q-bio.NC q-bio.QM | We introduce a procedure to infer the interactions among a set of binary
variables, based on their sampled frequencies and pairwise correlations. The
algorithm builds the clusters of variables contributing most to the entropy of
the inferred Ising model, and rejects the small contributions due to the
sampling noise. Our procedure successfully recovers benchmark Ising models even
at criticality and in the low temperature phase, and is applied to
neurobiological data.
| Simona Cocco (LPS), R\'emi Monasson (LPTENS) | 10.1103/PhysRevLett.106.090601 | 1102.3260 | null | null |
Online Learning of Rested and Restless Bandits | math.OC cs.LG | In this paper we study the online learning problem involving rested and
restless multiarmed bandits with multiple plays. The system consists of a
single player/user and a set of K finite-state discrete-time Markov chains
(arms) with unknown state spaces and statistics. At each time step the player
can play M arms. The objective of the user is to decide for each step which M
of the K arms to play over a sequence of trials so as to maximize its long term
reward. The restless multiarmed bandit is particularly relevant to the
application of opportunistic spectrum access (OSA), where a (secondary) user
has access to a set of K channels, each of time-varying condition as a result
of random fading and/or certain primary users' activities.
| Cem Tekin and Mingyan Liu | 10.1109/TIT.2012.2198613 | 1102.3508 | null | null |
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