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Efficient Probabilistic Inference with Partial Ranking Queries | cs.LG cs.AI stat.ML | Distributions over rankings are used to model data in various settings such
as preference analysis and political elections. The factorial size of the space
of rankings, however, typically forces one to make structural assumptions, such
as smoothness, sparsity, or probabilistic independence about these underlying
distributions. We approach the modeling problem from the computational
principle that one should make structural assumptions which allow for efficient
calculation of typical probabilistic queries. For ranking models, "typical"
queries predominantly take the form of partial ranking queries (e.g., given a
user's top-k favorite movies, what are his preferences over remaining movies?).
In this paper, we argue that riffled independence factorizations proposed in
recent literature [7, 8] are a natural structural assumption for ranking
distributions, allowing for particularly efficient processing of partial
ranking queries.
| Jonathan Huang, Ashish Kapoor, Carlos E. Guestrin | null | 1202.3734 | null | null |
Noisy-OR Models with Latent Confounding | cs.LG stat.ML | Given a set of experiments in which varying subsets of observed variables are
subject to intervention, we consider the problem of identifiability of causal
models exhibiting latent confounding. While identifiability is trivial when
each experiment intervenes on a large number of variables, the situation is
more complicated when only one or a few variables are subject to intervention
per experiment. For linear causal models with latent variables Hyttinen et al.
(2010) gave precise conditions for when such data are sufficient to identify
the full model. While their result cannot be extended to discrete-valued
variables with arbitrary cause-effect relationships, we show that a similar
result can be obtained for the class of causal models whose conditional
probability distributions are restricted to a `noisy-OR' parameterization. We
further show that identification is preserved under an extension of the model
that allows for negative influences, and present learning algorithms that we
test for accuracy, scalability and robustness.
| Antti Hyttinen, Frederick Eberhardt, Patrik O. Hoyer | null | 1202.3735 | null | null |
Discovering causal structures in binary exclusive-or skew acyclic models | cs.LG stat.ML | Discovering causal relations among observed variables in a given data set is
a main topic in studies of statistics and artificial intelligence. Recently,
some techniques to discover an identifiable causal structure have been explored
based on non-Gaussianity of the observed data distribution. However, most of
these are limited to continuous data. In this paper, we present a novel causal
model for binary data and propose a new approach to derive an identifiable
causal structure governing the data based on skew Bernoulli distributions of
external noise. Experimental evaluation shows excellent performance for both
artificial and real world data sets.
| Takanori Inazumi, Takashi Washio, Shohei Shimizu, Joe Suzuki, Akihiro
Yamamoto, Yoshinobu Kawahara | null | 1202.3736 | null | null |
Detecting low-complexity unobserved causes | cs.LG stat.ML | We describe a method that infers whether statistical dependences between two
observed variables X and Y are due to a "direct" causal link or only due to a
connecting causal path that contains an unobserved variable of low complexity,
e.g., a binary variable. This problem is motivated by statistical genetics.
Given a genetic marker that is correlated with a phenotype of interest, we want
to detect whether this marker is causal or it only correlates with a causal
one. Our method is based on the analysis of the location of the conditional
distributions P(Y|x) in the simplex of all distributions of Y. We report
encouraging results on semi-empirical data.
| Dominik Janzing, Eleni Sgouritsa, Oliver Stegle, Jonas Peters,
Bernhard Schoelkopf | null | 1202.3737 | null | null |
Learning Determinantal Point Processes | cs.LG cs.AI stat.ML | Determinantal point processes (DPPs), which arise in random matrix theory and
quantum physics, are natural models for subset selection problems where
diversity is preferred. Among many remarkable properties, DPPs offer tractable
algorithms for exact inference, including computing marginal probabilities and
sampling; however, an important open question has been how to learn a DPP from
labeled training data. In this paper we propose a natural feature-based
parameterization of conditional DPPs, and show how it leads to a convex and
efficient learning formulation. We analyze the relationship between our model
and binary Markov random fields with repulsive potentials, which are
qualitatively similar but computationally intractable. Finally, we apply our
approach to the task of extractive summarization, where the goal is to choose a
small subset of sentences conveying the most important information from a set
of documents. In this task there is a fundamental tradeoff between sentences
that are highly relevant to the collection as a whole, and sentences that are
diverse and not repetitive. Our parameterization allows us to naturally balance
these two characteristics. We evaluate our system on data from the DUC 2003/04
multi-document summarization task, achieving state-of-the-art results.
| Alex Kulesza, Ben Taskar | null | 1202.3738 | null | null |
Variational Algorithms for Marginal MAP | cs.LG cs.AI cs.IT math.IT stat.ML | Marginal MAP problems are notoriously difficult tasks for graphical models.
We derive a general variational framework for solving marginal MAP problems, in
which we apply analogues of the Bethe, tree-reweighted, and mean field
approximations. We then derive a "mixed" message passing algorithm and a
convergent alternative using CCCP to solve the BP-type approximations.
Theoretically, we give conditions under which the decoded solution is a global
or local optimum, and obtain novel upper bounds on solutions. Experimentally we
demonstrate that our algorithms outperform related approaches. We also show
that EM and variational EM comprise a special case of our framework.
| Qiang Liu, Alexander T. Ihler | null | 1202.3742 | null | null |
Asymptotic Efficiency of Deterministic Estimators for Discrete
Energy-Based Models: Ratio Matching and Pseudolikelihood | cs.LG stat.ML | Standard maximum likelihood estimation cannot be applied to discrete
energy-based models in the general case because the computation of exact model
probabilities is intractable. Recent research has seen the proposal of several
new estimators designed specifically to overcome this intractability, but
virtually nothing is known about their theoretical properties. In this paper,
we present a generalized estimator that unifies many of the classical and
recently proposed estimators. We use results from the standard asymptotic
theory for M-estimators to derive a generic expression for the asymptotic
covariance matrix of our generalized estimator. We apply these results to study
the relative statistical efficiency of classical pseudolikelihood and the
recently-proposed ratio matching estimator.
| Benjamin Marlin, Nando de Freitas | null | 1202.3746 | null | null |
Reconstructing Pompeian Households | cs.LG stat.ML | A database of objects discovered in houses in the Roman city of Pompeii
provides a unique view of ordinary life in an ancient city. Experts have used
this collection to study the structure of Roman households, exploring the
distribution and variability of tasks in architectural spaces, but such
approaches are necessarily affected by modern cultural assumptions. In this
study we present a data-driven approach to household archeology, treating it as
an unsupervised labeling problem. This approach scales to large data sets and
provides a more objective complement to human interpretation.
| David Mimno | null | 1202.3747 | null | null |
Conditional Restricted Boltzmann Machines for Structured Output
Prediction | cs.LG stat.ML | Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic
models that have recently been applied to a wide range of problems, including
collaborative filtering, classification, and modeling motion capture data.
While much progress has been made in training non-conditional RBMs, these
algorithms are not applicable to conditional models and there has been almost
no work on training and generating predictions from conditional RBMs for
structured output problems. We first argue that standard Contrastive
Divergence-based learning may not be suitable for training CRBMs. We then
identify two distinct types of structured output prediction problems and
propose an improved learning algorithm for each. The first problem type is one
where the output space has arbitrary structure but the set of likely output
configurations is relatively small, such as in multi-label classification. The
second problem is one where the output space is arbitrarily structured but
where the output space variability is much greater, such as in image denoising
or pixel labeling. We show that the new learning algorithms can work much
better than Contrastive Divergence on both types of problems.
| Volodymyr Mnih, Hugo Larochelle, Geoffrey E. Hinton | null | 1202.3748 | null | null |
Fractional Moments on Bandit Problems | cs.LG stat.ML | Reinforcement learning addresses the dilemma between exploration to find
profitable actions and exploitation to act according to the best observations
already made. Bandit problems are one such class of problems in stateless
environments that represent this explore/exploit situation. We propose a
learning algorithm for bandit problems based on fractional expectation of
rewards acquired. The algorithm is theoretically shown to converge on an
eta-optimal arm and achieve O(n) sample complexity. Experimental results show
the algorithm incurs substantially lower regrets than parameter-optimized
eta-greedy and SoftMax approaches and other low sample complexity
state-of-the-art techniques.
| Ananda Narayanan B, Balaraman Ravindran | null | 1202.3750 | null | null |
Multidimensional counting grids: Inferring word order from disordered
bags of words | cs.IR cs.CL cs.LG stat.ML | Models of bags of words typically assume topic mixing so that the words in a
single bag come from a limited number of topics. We show here that many sets of
bag of words exhibit a very different pattern of variation than the patterns
that are efficiently captured by topic mixing. In many cases, from one bag of
words to the next, the words disappear and new ones appear as if the theme
slowly and smoothly shifted across documents (providing that the documents are
somehow ordered). Examples of latent structure that describe such ordering are
easily imagined. For example, the advancement of the date of the news stories
is reflected in a smooth change over the theme of the day as certain evolving
news stories fall out of favor and new events create new stories. Overlaps
among the stories of consecutive days can be modeled by using windows over
linearly arranged tight distributions over words. We show here that such
strategy can be extended to multiple dimensions and cases where the ordering of
data is not readily obvious. We demonstrate that this way of modeling
covariation in word occurrences outperforms standard topic models in
classification and prediction tasks in applications in biology, text modeling
and computer vision.
| Nebojsa Jojic, Alessandro Perina | null | 1202.3752 | null | null |
Partial Order MCMC for Structure Discovery in Bayesian Networks | cs.LG stat.ML | We present a new Markov chain Monte Carlo method for estimating posterior
probabilities of structural features in Bayesian networks. The method draws
samples from the posterior distribution of partial orders on the nodes; for
each sampled partial order, the conditional probabilities of interest are
computed exactly. We give both analytical and empirical results that suggest
the superiority of the new method compared to previous methods, which sample
either directed acyclic graphs or linear orders on the nodes.
| Teppo Niinimaki, Pekka Parviainen, Mikko Koivisto | null | 1202.3753 | null | null |
Identifiability of Causal Graphs using Functional Models | cs.LG stat.ML | This work addresses the following question: Under what assumptions on the
data generating process can one infer the causal graph from the joint
distribution? The approach taken by conditional independence-based causal
discovery methods is based on two assumptions: the Markov condition and
faithfulness. It has been shown that under these assumptions the causal graph
can be identified up to Markov equivalence (some arrows remain undirected)
using methods like the PC algorithm. In this work we propose an alternative by
defining Identifiable Functional Model Classes (IFMOCs). As our main theorem we
prove that if the data generating process belongs to an IFMOC, one can identify
the complete causal graph. To the best of our knowledge this is the first
identifiability result of this kind that is not limited to linear functional
relationships. We discuss how the IFMOC assumption and the Markov and
faithfulness assumptions relate to each other and explain why we believe that
the IFMOC assumption can be tested more easily on given data. We further
provide a practical algorithm that recovers the causal graph from finitely many
data; experiments on simulated data support the theoretical findings.
| Jonas Peters, Joris Mooij, Dominik Janzing, Bernhard Schoelkopf | null | 1202.3757 | null | null |
Nonparametric Divergence Estimation with Applications to Machine
Learning on Distributions | cs.LG stat.ML | Low-dimensional embedding, manifold learning, clustering, classification, and
anomaly detection are among the most important problems in machine learning.
The existing methods usually consider the case when each instance has a fixed,
finite-dimensional feature representation. Here we consider a different
setting. We assume that each instance corresponds to a continuous probability
distribution. These distributions are unknown, but we are given some i.i.d.
samples from each distribution. Our goal is to estimate the distances between
these distributions and use these distances to perform low-dimensional
embedding, clustering/classification, or anomaly detection for the
distributions. We present estimation algorithms, describe how to apply them for
machine learning tasks on distributions, and show empirical results on
synthetic data, real word images, and astronomical data sets.
| Barnabas Poczos, Liang Xiong, Jeff Schneider | null | 1202.3758 | null | null |
Fast MCMC sampling for Markov jump processes and continuous time
Bayesian networks | stat.ME cs.LG stat.ML | Markov jump processes and continuous time Bayesian networks are important
classes of continuous time dynamical systems. In this paper, we tackle the
problem of inferring unobserved paths in these models by introducing a fast
auxiliary variable Gibbs sampler. Our approach is based on the idea of
uniformization, and sets up a Markov chain over paths by sampling a finite set
of virtual jump times and then running a standard hidden Markov model forward
filtering-backward sampling algorithm over states at the set of extant and
virtual jump times. We demonstrate significant computational benefits over a
state-of-the-art Gibbs sampler on a number of continuous time Bayesian
networks.
| Vinayak Rao, Yee Whye Teh | null | 1202.3760 | null | null |
New Probabilistic Bounds on Eigenvalues and Eigenvectors of Random
Kernel Matrices | cs.LG stat.ML | Kernel methods are successful approaches for different machine learning
problems. This success is mainly rooted in using feature maps and kernel
matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel
matrix, while for other methods the spectral information can be used to
estimate the excess risk. An important question remains on how close the sample
eigenvalues/eigenvectors are to the population values. In this paper, we
improve earlier results on concentration bounds for eigenvalues of general
kernel matrices. For distance and inner product kernel functions, e.g. radial
basis functions, we provide new concentration bounds, which are characterized
by the eigenvalues of the sample covariance matrix. Meanwhile, the obstacles
for sharper bounds are accounted for and partially addressed. As a case study,
we derive a concentration inequality for sample kernel target-alignment.
| Nima Reyhani, Hideitsu Hino, Ricardo Vigario | null | 1202.3761 | null | null |
An Efficient Algorithm for Computing Interventional Distributions in
Latent Variable Causal Models | cs.LG stat.ML | Probabilistic inference in graphical models is the task of computing marginal
and conditional densities of interest from a factorized representation of a
joint probability distribution. Inference algorithms such as variable
elimination and belief propagation take advantage of constraints embedded in
this factorization to compute such densities efficiently. In this paper, we
propose an algorithm which computes interventional distributions in latent
variable causal models represented by acyclic directed mixed graphs(ADMGs). To
compute these distributions efficiently, we take advantage of a recursive
factorization which generalizes the usual Markov factorization for DAGs and the
more recent factorization for ADMGs. Our algorithm can be viewed as a
generalization of variable elimination to the mixed graph case. We show our
algorithm is exponential in the mixed graph generalization of treewidth.
| Ilya Shpitser, Thomas S. Richardson, James M. Robins | null | 1202.3763 | null | null |
Learning mixed graphical models from data with p larger than n | stat.ME cs.LG stat.ML | Structure learning of Gaussian graphical models is an extensively studied
problem in the classical multivariate setting where the sample size n is larger
than the number of random variables p, as well as in the more challenging
setting when p>>n. However, analogous approaches for learning the structure of
graphical models with mixed discrete and continuous variables when p>>n remain
largely unexplored. Here we describe a statistical learning procedure for this
problem based on limited-order correlations and assess its performance with
synthetic and real data.
| Inma Tur, Robert Castelo | null | 1202.3765 | null | null |
Robust learning Bayesian networks for prior belief | cs.LG stat.ML | Recent reports have described that learning Bayesian networks are highly
sensitive to the chosen equivalent sample size (ESS) in the Bayesian Dirichlet
equivalence uniform (BDeu). This sensitivity often engenders some unstable or
undesirable results. This paper describes some asymptotic analyses of BDeu to
explain the reasons for the sensitivity and its effects. Furthermore, this
paper presents a proposal for a robust learning score for ESS by eliminating
the sensitive factors from the approximation of log-BDeu.
| Maomi Ueno | null | 1202.3766 | null | null |
Sparse matrix-variate Gaussian process blockmodels for network modeling | cs.LG stat.ML | We face network data from various sources, such as protein interactions and
online social networks. A critical problem is to model network interactions and
identify latent groups of network nodes. This problem is challenging due to
many reasons. For example, the network nodes are interdependent instead of
independent of each other, and the data are known to be very noisy (e.g.,
missing edges). To address these challenges, we propose a new relational model
for network data, Sparse Matrix-variate Gaussian process Blockmodel (SMGB). Our
model generalizes popular bilinear generative models and captures nonlinear
network interactions using a matrix-variate Gaussian process with latent
membership variables. We also assign sparse prior distributions on the latent
membership variables to learn sparse group assignments for individual network
nodes. To estimate the latent variables efficiently from data, we develop an
efficient variational expectation maximization method. We compared our
approaches with several state-of-the-art network models on both synthetic and
real-world network datasets. Experimental results demonstrate SMGBs outperform
the alternative approaches in terms of discovering latent classes or predicting
unknown interactions.
| Feng Yan, Zenglin Xu, Yuan (Alan) Qi | null | 1202.3769 | null | null |
Hierarchical Maximum Margin Learning for Multi-Class Classification | cs.LG stat.ML | Due to myriads of classes, designing accurate and efficient classifiers
becomes very challenging for multi-class classification. Recent research has
shown that class structure learning can greatly facilitate multi-class
learning. In this paper, we propose a novel method to learn the class structure
for multi-class classification problems. The class structure is assumed to be a
binary hierarchical tree. To learn such a tree, we propose a maximum separating
margin method to determine the child nodes of any internal node. The proposed
method ensures that two classgroups represented by any two sibling nodes are
most separable. In the experiments, we evaluate the accuracy and efficiency of
the proposed method over other multi-class classification methods on real world
large-scale problems. The results show that the proposed method outperforms
benchmark methods in terms of accuracy for most datasets and performs
comparably with other class structure learning methods in terms of efficiency
for all datasets.
| Jian-Bo Yang, Ivor W. Tsang | null | 1202.3770 | null | null |
Tightening MRF Relaxations with Planar Subproblems | cs.LG stat.ML | We describe a new technique for computing lower-bounds on the minimum energy
configuration of a planar Markov Random Field (MRF). Our method successively
adds large numbers of constraints and enforces consistency over binary
projections of the original problem state space. These constraints are
represented in terms of subproblems in a dual-decomposition framework that is
optimized using subgradient techniques. The complete set of constraints we
consider enforces cycle consistency over the original graph. In practice we
find that the method converges quickly on most problems with the addition of a
few subproblems and outperforms existing methods for some interesting classes
of hard potentials.
| Julian Yarkony, Ragib Morshed, Alexander T. Ihler, Charless C. Fowlkes | null | 1202.3771 | null | null |
Rank/Norm Regularization with Closed-Form Solutions: Application to
Subspace Clustering | cs.LG cs.NA stat.ML | When data is sampled from an unknown subspace, principal component analysis
(PCA) provides an effective way to estimate the subspace and hence reduce the
dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem,
which characterizes the best rank k approximation of a matrix. In this paper,
we prove a generalization of the Eckart-Young-Mirsky theorem under all
unitarily invariant norms. Using this result, we obtain closed-form solutions
for a set of rank/norm regularized problems, and derive closed-form solutions
for a general class of subspace clustering problems (where data is modelled by
unions of unknown subspaces). From these results we obtain new theoretical
insights and promising experimental results.
| Yao-Liang Yu, Dale Schuurmans | null | 1202.3772 | null | null |
Risk Bounds for Infinitely Divisible Distribution | stat.ML cs.LG | In this paper, we study the risk bounds for samples independently drawn from
an infinitely divisible (ID) distribution. In particular, based on a martingale
method, we develop two deviation inequalities for a sequence of random
variables of an ID distribution with zero Gaussian component. By applying the
deviation inequalities, we obtain the risk bounds based on the covering number
for the ID distribution. Finally, we analyze the asymptotic convergence of the
risk bound derived from one of the two deviation inequalities and show that the
convergence rate of the bound is faster than the result for the generic i.i.d.
empirical process (Mendelson, 2003).
| Chao Zhang, Dacheng Tao | null | 1202.3774 | null | null |
Kernel-based Conditional Independence Test and Application in Causal
Discovery | cs.LG stat.ML | Conditional independence testing is an important problem, especially in
Bayesian network learning and causal discovery. Due to the curse of
dimensionality, testing for conditional independence of continuous variables is
particularly challenging. We propose a Kernel-based Conditional Independence
test (KCI-test), by constructing an appropriate test statistic and deriving its
asymptotic distribution under the null hypothesis of conditional independence.
The proposed method is computationally efficient and easy to implement.
Experimental results show that it outperforms other methods, especially when
the conditioning set is large or the sample size is not very large, in which
case other methods encounter difficulties.
| Kun Zhang, Jonas Peters, Dominik Janzing, Bernhard Schoelkopf | null | 1202.3775 | null | null |
Smoothing Multivariate Performance Measures | cs.LG stat.ML | A Support Vector Method for multivariate performance measures was recently
introduced by Joachims (2005). The underlying optimization problem is currently
solved using cutting plane methods such as SVM-Perf and BMRM. One can show that
these algorithms converge to an eta accurate solution in O(1/Lambda*e)
iterations, where lambda is the trade-off parameter between the regularizer and
the loss function. We present a smoothing strategy for multivariate performance
scores, in particular precision/recall break-even point and ROCArea. When
combined with Nesterov's accelerated gradient algorithm our smoothing strategy
yields an optimization algorithm which converges to an eta accurate solution in
O(min{1/e,1/sqrt(lambda*e)}) iterations. Furthermore, the cost per iteration of
our scheme is the same as that of SVM-Perf and BMRM. Empirical evaluation on a
number of publicly available datasets shows that our method converges
significantly faster than cutting plane methods without sacrificing
generalization ability.
| Xinhua Zhang, Ankan Saha, S. V.N. Vishwanatan | null | 1202.3776 | null | null |
Sparse Topical Coding | cs.LG stat.ML | We present sparse topical coding (STC), a non-probabilistic formulation of
topic models for discovering latent representations of large collections of
data. Unlike probabilistic topic models, STC relaxes the normalization
constraint of admixture proportions and the constraint of defining a normalized
likelihood function. Such relaxations make STC amenable to: 1) directly control
the sparsity of inferred representations by using sparsity-inducing
regularizers; 2) be seamlessly integrated with a convex error function (e.g.,
SVM hinge loss) for supervised learning; and 3) be efficiently learned with a
simply structured coordinate descent algorithm. Our results demonstrate the
advantages of STC and supervised MedSTC on identifying topical meanings of
words and improving classification accuracy and time efficiency.
| Jun Zhu, Eric P. Xing | null | 1202.3778 | null | null |
Testing whether linear equations are causal: A free probability theory
approach | cs.LG stat.ML | We propose a method that infers whether linear relations between two
high-dimensional variables X and Y are due to a causal influence from X to Y or
from Y to X. The earlier proposed so-called Trace Method is extended to the
regime where the dimension of the observed variables exceeds the sample size.
Based on previous work, we postulate conditions that characterize a causal
relation between X and Y. Moreover, we describe a statistical test and argue
that both causal directions are typically rejected if there is a common cause.
A full theoretical analysis is presented for the deterministic case but our
approach seems to be valid for the noisy case, too, for which we additionally
present an approach based on a sparsity constraint. The discussed method yields
promising results for both simulated and real world data.
| Jakob Zscheischler, Dominik Janzing, Kun Zhang | null | 1202.3779 | null | null |
Graphical Models for Bandit Problems | cs.LG cs.AI stat.ML | We introduce a rich class of graphical models for multi-armed bandit problems
that permit both the state or context space and the action space to be very
large, yet succinctly specify the payoffs for any context-action pair. Our main
result is an algorithm for such models whose regret is bounded by the number of
parameters and whose running time depends only on the treewidth of the graph
substructure induced by the action space.
| Kareem Amin, Michael Kearns, Umar Syed | null | 1202.3782 | null | null |
PAC Bounds for Discounted MDPs | cs.LG | We study upper and lower bounds on the sample-complexity of learning
near-optimal behaviour in finite-state discounted Markov Decision Processes
(MDPs). For the upper bound we make the assumption that each action leads to at
most two possible next-states and prove a new bound for a UCRL-style algorithm
on the number of time-steps when it is not Probably Approximately Correct
(PAC). The new lower bound strengthens previous work by being both more general
(it applies to all policies) and tighter. The upper and lower bounds match up
to logarithmic factors.
| Tor Lattimore and Marcus Hutter | null | 1202.3890 | null | null |
Generalized Principal Component Analysis (GPCA) | cs.CV cs.LG | This paper presents an algebro-geometric solution to the problem of
segmenting an unknown number of subspaces of unknown and varying dimensions
from sample data points. We represent the subspaces with a set of homogeneous
polynomials whose degree is the number of subspaces and whose derivatives at a
data point give normal vectors to the subspace passing through the point. When
the number of subspaces is known, we show that these polynomials can be
estimated linearly from data; hence, subspace segmentation is reduced to
classifying one point per subspace. We select these points optimally from the
data set by minimizing certain distance function, thus dealing automatically
with moderate noise in the data. A basis for the complement of each subspace is
then recovered by applying standard PCA to the collection of derivatives
(normal vectors). Extensions of GPCA that deal with data in a high- dimensional
space and with an unknown number of subspaces are also presented. Our
experiments on low-dimensional data show that GPCA outperforms existing
algebraic algorithms based on polynomial factorization and provides a good
initialization to iterative techniques such as K-subspaces and Expectation
Maximization. We also present applications of GPCA to computer vision problems
such as face clustering, temporal video segmentation, and 3D motion
segmentation from point correspondences in multiple affine views.
| Rene Vidal, Yi Ma, Shankar Sastry | null | 1202.4002 | null | null |
On the Sample Complexity of Predictive Sparse Coding | cs.LG stat.ML | The goal of predictive sparse coding is to learn a representation of examples
as sparse linear combinations of elements from a dictionary, such that a
learned hypothesis linear in the new representation performs well on a
predictive task. Predictive sparse coding algorithms recently have demonstrated
impressive performance on a variety of supervised tasks, but their
generalization properties have not been studied. We establish the first
generalization error bounds for predictive sparse coding, covering two
settings: 1) the overcomplete setting, where the number of features k exceeds
the original dimensionality d; and 2) the high or infinite-dimensional setting,
where only dimension-free bounds are useful. Both learning bounds intimately
depend on stability properties of the learned sparse encoder, as measured on
the training sample. Consequently, we first present a fundamental stability
result for the LASSO, a result characterizing the stability of the sparse codes
with respect to perturbations to the dictionary. In the overcomplete setting,
we present an estimation error bound that decays as \tilde{O}(sqrt(d k/m)) with
respect to d and k. In the high or infinite-dimensional setting, we show a
dimension-free bound that is \tilde{O}(sqrt(k^2 s / m)) with respect to k and
s, where s is an upper bound on the number of non-zeros in the sparse code for
any training data point.
| Nishant A. Mehta and Alexander G. Gray | null | 1202.4050 | null | null |
The best of both worlds: stochastic and adversarial bandits | cs.LG cs.DS | We present a new bandit algorithm, SAO (Stochastic and Adversarial Optimal),
whose regret is, essentially, optimal both for adversarial rewards and for
stochastic rewards. Specifically, SAO combines the square-root worst-case
regret of Exp3 (Auer et al., SIAM J. on Computing 2002) and the
(poly)logarithmic regret of UCB1 (Auer et al., Machine Learning 2002) for
stochastic rewards. Adversarial rewards and stochastic rewards are the two main
settings in the literature on (non-Bayesian) multi-armed bandits. Prior work on
multi-armed bandits treats them separately, and does not attempt to jointly
optimize for both. Our result falls into a general theme of achieving good
worst-case performance while also taking advantage of "nice" problem instances,
an important issue in the design of algorithms with partially known inputs.
| Sebastien Bubeck and Aleksandrs Slivkins | null | 1202.4473 | null | null |
(weak) Calibration is Computationally Hard | cs.GT cs.AI cs.LG stat.ML | We show that the existence of a computationally efficient calibration
algorithm, with a low weak calibration rate, would imply the existence of an
efficient algorithm for computing approximate Nash equilibria - thus implying
the unlikely conclusion that every problem in PPAD is solvable in polynomial
time.
| Elad Hazan, Sham Kakade | null | 1202.4478 | null | null |
Metabolic cost as an organizing principle for cooperative learning | q-bio.NC cs.LG nlin.AO | This paper investigates how neurons can use metabolic cost to facilitate
learning at a population level. Although decision-making by individual neurons
has been extensively studied, questions regarding how neurons should behave to
cooperate effectively remain largely unaddressed. Under assumptions that
capture a few basic features of cortical neurons, we show that constraining
reward maximization by metabolic cost aligns the information content of actions
with their expected reward. Thus, metabolic cost provides a mechanism whereby
neurons encode expected reward into their outputs. Further, aside from reducing
energy expenditures, imposing a tight metabolic constraint also increases the
accuracy of empirical estimates of rewards, increasing the robustness of
distributed learning. Finally, we present two implementations of metabolically
constrained learning that confirm our theoretical finding. These results
suggest that metabolic cost may be an organizing principle underlying the
neural code, and may also provide a useful guide to the design and analysis of
other cooperating populations.
| David Balduzzi, Pedro A Ortega, Michel Besserve | null | 1202.4482 | null | null |
Min Max Generalization for Two-stage Deterministic Batch Mode
Reinforcement Learning: Relaxation Schemes | cs.SY cs.LG | We study the minmax optimization problem introduced in [22] for computing
policies for batch mode reinforcement learning in a deterministic setting.
First, we show that this problem is NP-hard. In the two-stage case, we provide
two relaxation schemes. The first relaxation scheme works by dropping some
constraints in order to obtain a problem that is solvable in polynomial time.
The second relaxation scheme, based on a Lagrangian relaxation where all
constraints are dualized, leads to a conic quadratic programming problem. We
also theoretically prove and empirically illustrate that both relaxation
schemes provide better results than those given in [22].
| Raphael Fonteneau, Damien Ernst, Bernard Boigelot and Quentin Louveaux | null | 1202.5298 | null | null |
Classification approach based on association rules mining for unbalanced
data | stat.ML cs.LG | This paper deals with the binary classification task when the target class
has the lower probability of occurrence. In such situation, it is not possible
to build a powerful classifier by using standard methods such as logistic
regression, classification tree, discriminant analysis, etc. To overcome this
short-coming of these methods which yield classifiers with low sensibility, we
tackled the classification problem here through an approach based on the
association rules learning. This approach has the advantage of allowing the
identification of the patterns that are well correlated with the target class.
Association rules learning is a well known method in the area of data-mining.
It is used when dealing with large database for unsupervised discovery of local
patterns that expresses hidden relationships between input variables. In
considering association rules from a supervised learning point of view, a
relevant set of weak classifiers is obtained from which one derives a
classifier that performs well.
| Cheikh Ndour (1,2,3), Aliou Diop (1), Simplice Dossou-Gb\'et\'e (2)
((1) Universit\'e Gaston Berger, Saint-Louis, S\'en\'egal (2) Universit\'e de
Pau et des Pays de l 'Adour, Pau, France (3) Universit\'e de Bordeaux,
Bordeaux, France) | null | 1202.5514 | null | null |
Hybrid Batch Bayesian Optimization | cs.AI cs.LG | Bayesian Optimization aims at optimizing an unknown non-convex/concave
function that is costly to evaluate. We are interested in application scenarios
where concurrent function evaluations are possible. Under such a setting, BO
could choose to either sequentially evaluate the function, one input at a time
and wait for the output of the function before making the next selection, or
evaluate the function at a batch of multiple inputs at once. These two
different settings are commonly referred to as the sequential and batch
settings of Bayesian Optimization. In general, the sequential setting leads to
better optimization performance as each function evaluation is selected with
more information, whereas the batch setting has an advantage in terms of the
total experimental time (the number of iterations). In this work, our goal is
to combine the strength of both settings. Specifically, we systematically
analyze Bayesian optimization using Gaussian process as the posterior estimator
and provide a hybrid algorithm that, based on the current state, dynamically
switches between a sequential policy and a batch policy with variable batch
sizes. We provide theoretical justification for our algorithm and present
experimental results on eight benchmark BO problems. The results show that our
method achieves substantial speedup (up to %78) compared to a pure sequential
policy, without suffering any significant performance loss.
| Javad Azimi, Ali Jalali and Xiaoli Fern | null | 1202.5597 | null | null |
Clustering using Max-norm Constrained Optimization | cs.LG stat.ML | We suggest using the max-norm as a convex surrogate constraint for
clustering. We show how this yields a better exact cluster recovery guarantee
than previously suggested nuclear-norm relaxation, and study the effectiveness
of our method, and other related convex relaxations, compared to other
clustering approaches.
| Ali Jalali and Nathan Srebro | null | 1202.5598 | null | null |
Training Restricted Boltzmann Machines on Word Observations | cs.LG stat.ML | The restricted Boltzmann machine (RBM) is a flexible tool for modeling
complex data, however there have been significant computational difficulties in
using RBMs to model high-dimensional multinomial observations. In natural
language processing applications, words are naturally modeled by K-ary discrete
distributions, where K is determined by the vocabulary size and can easily be
in the hundreds of thousands. The conventional approach to training RBMs on
word observations is limited because it requires sampling the states of K-way
softmax visible units during block Gibbs updates, an operation that takes time
linear in K. In this work, we address this issue by employing a more general
class of Markov chain Monte Carlo operators on the visible units, yielding
updates with computational complexity independent of K. We demonstrate the
success of our approach by training RBMs on hundreds of millions of word
n-grams using larger vocabularies than previously feasible and using the
learned features to improve performance on chunking and sentiment
classification tasks, achieving state-of-the-art results on the latter.
| George E. Dahl, Ryan P. Adams and Hugo Larochelle | null | 1202.5695 | null | null |
Efficiently Sampling Multiplicative Attribute Graphs Using a
Ball-Dropping Process | stat.ML cs.LG | We introduce a novel and efficient sampling algorithm for the Multiplicative
Attribute Graph Model (MAGM - Kim and Leskovec (2010)}). Our algorithm is
\emph{strictly} more efficient than the algorithm proposed by Yun and
Vishwanathan (2012), in the sense that our method extends the \emph{best} time
complexity guarantee of their algorithm to a larger fraction of parameter
space. Both in theory and in empirical evaluation on sparse graphs, our new
algorithm outperforms the previous one. To design our algorithm, we first
define a stochastic \emph{ball-dropping process} (BDP). Although a special case
of this process was introduced as an efficient approximate sampling algorithm
for the Kronecker Product Graph Model (KPGM - Leskovec et al. (2010)}), neither
\emph{why} such an approximation works nor \emph{what} is the actual
distribution this process is sampling from has been addressed so far to the
best of our knowledge. Our rigorous treatment of the BDP enables us to clarify
the rational behind a BDP approximation of KPGM, and design an efficient
sampling algorithm for the MAGM.
| Hyokun Yun and S. V. N. Vishwanathan | null | 1202.6001 | null | null |
Protocols for Learning Classifiers on Distributed Data | stat.ML cs.LG | We consider the problem of learning classifiers for labeled data that has
been distributed across several nodes. Our goal is to find a single classifier,
with small approximation error, across all datasets while minimizing the
communication between nodes. This setting models real-world communication
bottlenecks in the processing of massive distributed datasets. We present
several very general sampling-based solutions as well as some two-way protocols
which have a provable exponential speed-up over any one-way protocol. We focus
on core problems for noiseless data distributed across two or more nodes. The
techniques we introduce are reminiscent of active learning, but rather than
actively probing labels, nodes actively communicate with each other, each node
simultaneously learning the important data from another node.
| Hal Daume III, Jeff M. Phillips, Avishek Saha, Suresh
Venkatasubramanian | null | 1202.6078 | null | null |
Nonlinear Laplacian spectral analysis: Capturing intermittent and
low-frequency spatiotemporal patterns in high-dimensional data | physics.data-an cs.LG | We present a technique for spatiotemporal data analysis called nonlinear
Laplacian spectral analysis (NLSA), which generalizes singular spectrum
analysis (SSA) to take into account the nonlinear manifold structure of complex
data sets. The key principle underlying NLSA is that the functions used to
represent temporal patterns should exhibit a degree of smoothness on the
nonlinear data manifold M; a constraint absent from classical SSA. NLSA
enforces such a notion of smoothness by requiring that temporal patterns belong
in low-dimensional Hilbert spaces V_l spanned by the leading l Laplace-Beltrami
eigenfunctions on M. These eigenfunctions can be evaluated efficiently in high
ambient-space dimensions using sparse graph-theoretic algorithms. Moreover,
they provide orthonormal bases to expand a family of linear maps, whose
singular value decomposition leads to sets of spatiotemporal patterns at
progressively finer resolution on the data manifold. The Riemannian measure of
M and an adaptive graph kernel width enhances the capability of NLSA to detect
important nonlinear processes, including intermittency and rare events. The
minimum dimension of V_l required to capture these features while avoiding
overfitting is estimated here using spectral entropy criteria.
| Dimitrios Giannakis and Andrew J. Majda | null | 1202.6103 | null | null |
Distributed Power Allocation with SINR Constraints Using Trial and Error
Learning | cs.GT cs.AI cs.LG | In this paper, we address the problem of global transmit power minimization
in a self-congiguring network where radio devices are subject to operate at a
minimum signal to interference plus noise ratio (SINR) level. We model the
network as a parallel Gaussian interference channel and we introduce a fully
decentralized algorithm (based on trial and error) able to statistically
achieve a congiguration where the performance demands are met. Contrary to
existing solutions, our algorithm requires only local information and can learn
stable and efficient working points by using only one bit feedback. We model
the network under two different game theoretical frameworks: normal form and
satisfaction form. We show that the converging points correspond to equilibrium
points, namely Nash and satisfaction equilibrium. Similarly, we provide
sufficient conditions for the algorithm to converge in both formulations.
Moreover, we provide analytical results to estimate the algorithm's
performance, as a function of the network parameters. Finally, numerical
results are provided to validate our theoretical conclusions. Keywords:
Learning, power control, trial and error, Nash equilibrium, spectrum sharing.
| Luca Rose, Samir M. Perlaza, M\'erouane Debbah, Christophe J. Le
Martret | null | 1202.6157 | null | null |
Confusion Matrix Stability Bounds for Multiclass Classification | cs.LG | In this paper, we provide new theoretical results on the generalization
properties of learning algorithms for multiclass classification problems. The
originality of our work is that we propose to use the confusion matrix of a
classifier as a measure of its quality; our contribution is in the line of work
which attempts to set up and study the statistical properties of new evaluation
measures such as, e.g. ROC curves. In the confusion-based learning framework we
propose, we claim that a targetted objective is to minimize the size of the
confusion matrix C, measured through its operator norm ||C||. We derive
generalization bounds on the (size of the) confusion matrix in an extended
framework of uniform stability, adapted to the case of matrix valued loss.
Pivotal to our study is a very recent matrix concentration inequality that
generalizes McDiarmid's inequality. As an illustration of the relevance of our
theoretical results, we show how two SVM learning procedures can be proved to
be confusion-friendly. To the best of our knowledge, the present paper is the
first that focuses on the confusion matrix from a theoretical point of view.
| Pierre Machart (LIF, LSIS), Liva Ralaivola (LIF) | null | 1202.6221 | null | null |
PAC-Bayesian Generalization Bound on Confusion Matrix for Multi-Class
Classification | stat.ML cs.LG | In this work, we propose a PAC-Bayes bound for the generalization risk of the
Gibbs classifier in the multi-class classification framework. The novelty of
our work is the critical use of the confusion matrix of a classifier as an
error measure; this puts our contribution in the line of work aiming at dealing
with performance measure that are richer than mere scalar criterion such as the
misclassification rate. Thanks to very recent and beautiful results on matrix
concentration inequalities, we derive two bounds showing that the true
confusion risk of the Gibbs classifier is upper-bounded by its empirical risk
plus a term depending on the number of training examples in each class. To the
best of our knowledge, this is the first PAC-Bayes bounds based on confusion
matrices.
| Emilie Morvant (LIF), Sokol Ko\c{c}o (LIF), Liva Ralaivola (LIF) | null | 1202.6228 | null | null |
A Stochastic Gradient Method with an Exponential Convergence Rate for
Finite Training Sets | math.OC cs.LG | We propose a new stochastic gradient method for optimizing the sum of a
finite set of smooth functions, where the sum is strongly convex. While
standard stochastic gradient methods converge at sublinear rates for this
problem, the proposed method incorporates a memory of previous gradient values
in order to achieve a linear convergence rate. In a machine learning context,
numerical experiments indicate that the new algorithm can dramatically
outperform standard algorithms, both in terms of optimizing the training error
and reducing the test error quickly.
| Nicolas Le Roux (INRIA Paris - Rocquencourt, LIENS), Mark Schmidt
(INRIA Paris - Rocquencourt, LIENS), Francis Bach (INRIA Paris -
Rocquencourt, LIENS) | null | 1202.6258 | null | null |
Learning from Distributions via Support Measure Machines | stat.ML cs.LG | This paper presents a kernel-based discriminative learning framework on
probability measures. Rather than relying on large collections of vectorial
training examples, our framework learns using a collection of probability
distributions that have been constructed to meaningfully represent training
data. By representing these probability distributions as mean embeddings in the
reproducing kernel Hilbert space (RKHS), we are able to apply many standard
kernel-based learning techniques in straightforward fashion. To accomplish
this, we construct a generalization of the support vector machine (SVM) called
a support measure machine (SMM). Our analyses of SMMs provides several insights
into their relationship to traditional SVMs. Based on such insights, we propose
a flexible SVM (Flex-SVM) that places different kernel functions on each
training example. Experimental results on both synthetic and real-world data
demonstrate the effectiveness of our proposed framework.
| Krikamol Muandet, Kenji Fukumizu, Francesco Dinuzzo, Bernhard
Sch\"olkopf | null | 1202.6504 | null | null |
mlpy: Machine Learning Python | cs.MS cs.LG stat.ML | mlpy is a Python Open Source Machine Learning library built on top of
NumPy/SciPy and the GNU Scientific Libraries. mlpy provides a wide range of
state-of-the-art machine learning methods for supervised and unsupervised
problems and it is aimed at finding a reasonable compromise among modularity,
maintainability, reproducibility, usability and efficiency. mlpy is
multiplatform, it works with Python 2 and 3 and it is distributed under GPL3 at
the website http://mlpy.fbk.eu.
| Davide Albanese and Roberto Visintainer and Stefano Merler and
Samantha Riccadonna and Giuseppe Jurman and Cesare Furlanello | null | 1202.6548 | null | null |
Inference in Hidden Markov Models with Explicit State Duration
Distributions | stat.ML cs.LG | In this letter we borrow from the inference techniques developed for
unbounded state-cardinality (nonparametric) variants of the HMM and use them to
develop a tuning-parameter free, black-box inference procedure for
Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have
latent states consisting of both discrete state-indicator and discrete
state-duration random variables. In contrast to the implicit geometric state
duration distribution possessed by the standard HMM, EDHMMs allow the direct
parameterisation and estimation of per-state duration distributions. As most
duration distributions are defined over the positive integers, truncation or
other approximations are usually required to perform EDHMM inference.
| Michael Dewar, Chris Wiggins, Frank Wood | 10.1109/LSP.2012.2184795 | 1203.0038 | null | null |
A Bayesian Approach to Discovering Truth from Conflicting Sources for
Data Integration | cs.DB cs.LG | In practical data integration systems, it is common for the data sources
being integrated to provide conflicting information about the same entity.
Consequently, a major challenge for data integration is to derive the most
complete and accurate integrated records from diverse and sometimes conflicting
sources. We term this challenge the truth finding problem. We observe that some
sources are generally more reliable than others, and therefore a good model of
source quality is the key to solving the truth finding problem. In this work,
we propose a probabilistic graphical model that can automatically infer true
records and source quality without any supervision. In contrast to previous
methods, our principled approach leverages a generative process of two types of
errors (false positive and false negative) by modeling two different aspects of
source quality. In so doing, ours is also the first approach designed to merge
multi-valued attribute types. Our method is scalable, due to an efficient
sampling-based inference algorithm that needs very few iterations in practice
and enjoys linear time complexity, with an even faster incremental variant.
Experiments on two real world datasets show that our new method outperforms
existing state-of-the-art approaches to the truth finding problem.
| Bo Zhao, Benjamin I. P. Rubinstein, Jim Gemmell, Jiawei Han | null | 1203.0058 | null | null |
Scaling Datalog for Machine Learning on Big Data | cs.DB cs.LG cs.PF | In this paper, we present the case for a declarative foundation for
data-intensive machine learning systems. Instead of creating a new system for
each specific flavor of machine learning task, or hardcoding new optimizations,
we argue for the use of recursive queries to program a variety of machine
learning systems. By taking this approach, database query optimization
techniques can be utilized to identify effective execution plans, and the
resulting runtime plans can be executed on a single unified data-parallel query
processing engine. As a proof of concept, we consider two programming
models--Pregel and Iterative Map-Reduce-Update---from the machine learning
domain, and show how they can be captured in Datalog, tuned for a specific
task, and then compiled into an optimized physical plan. Experiments performed
on a large computing cluster with real data demonstrate that this declarative
approach can provide very good performance while offering both increased
generality and programming ease.
| Yingyi Bu, Vinayak Borkar, Michael J. Carey, Joshua Rosen, Neoklis
Polyzotis, Tyson Condie, Markus Weimer, Raghu Ramakrishnan | null | 1203.0160 | null | null |
Fast Reinforcement Learning with Large Action Sets using
Error-Correcting Output Codes for MDP Factorization | cs.LG stat.ML | The use of Reinforcement Learning in real-world scenarios is strongly limited
by issues of scale. Most RL learning algorithms are unable to deal with
problems composed of hundreds or sometimes even dozens of possible actions, and
therefore cannot be applied to many real-world problems. We consider the RL
problem in the supervised classification framework where the optimal policy is
obtained through a multiclass classifier, the set of classes being the set of
actions of the problem. We introduce error-correcting output codes (ECOCs) in
this setting and propose two new methods for reducing complexity when using
rollouts-based approaches. The first method consists in using an ECOC-based
classifier as the multiclass classifier, reducing the learning complexity from
O(A2) to O(Alog(A)). We then propose a novel method that profits from the
ECOC's coding dictionary to split the initial MDP into O(log(A)) seperate
two-action MDPs. This second method reduces learning complexity even further,
from O(A2) to O(log(A)), thus rendering problems with large action sets
tractable. We finish by experimentally demonstrating the advantages of our
approach on a set of benchmark problems, both in speed and performance.
| Gabriel Dulac-Arnold, Ludovic Denoyer, Philippe Preux, Patrick
Gallinari | null | 1203.0203 | null | null |
Application of Gist SVM in Cancer Detection | cs.LG | In this paper, we study the application of GIST SVM in disease prediction
(detection of cancer). Pattern classification problems can be effectively
solved by Support vector machines. Here we propose a classifier which can
differentiate patients having benign and malignant cancer cells. To improve the
accuracy of classification, we propose to determine the optimal size of the
training set and perform feature selection. To find the optimal size of the
training set, different sizes of training sets are experimented and the one
with highest classification rate is selected. The optimal features are selected
through their F-Scores.
| S. Aruna, S. P. Rajagopalan and L. V. Nandakishore | null | 1203.0298 | null | null |
Change-Point Detection in Time-Series Data by Relative Density-Ratio
Estimation | stat.ML cs.LG stat.ME | The objective of change-point detection is to discover abrupt property
changes lying behind time-series data. In this paper, we present a novel
statistical change-point detection algorithm based on non-parametric divergence
estimation between time-series samples from two retrospective segments. Our
method uses the relative Pearson divergence as a divergence measure, and it is
accurately and efficiently estimated by a method of direct density-ratio
estimation. Through experiments on artificial and real-world datasets including
human-activity sensing, speech, and Twitter messages, we demonstrate the
usefulness of the proposed method.
| Song Liu, Makoto Yamada, Nigel Collier, Masashi Sugiyama | 10.1016/j.neunet.2013.01.012 | 1203.0453 | null | null |
Algorithms for Learning Kernels Based on Centered Alignment | cs.LG cs.AI | This paper presents new and effective algorithms for learning kernels. In
particular, as shown by our empirical results, these algorithms consistently
outperform the so-called uniform combination solution that has proven to be
difficult to improve upon in the past, as well as other algorithms for learning
kernels based on convex combinations of base kernels in both classification and
regression. Our algorithms are based on the notion of centered alignment which
is used as a similarity measure between kernels or kernel matrices. We present
a number of novel algorithmic, theoretical, and empirical results for learning
kernels based on our notion of centered alignment. In particular, we describe
efficient algorithms for learning a maximum alignment kernel by showing that
the problem can be reduced to a simple QP and discuss a one-stage algorithm for
learning both a kernel and a hypothesis based on that kernel using an
alignment-based regularization. Our theoretical results include a novel
concentration bound for centered alignment between kernel matrices, the proof
of the existence of effective predictors for kernels with high alignment, both
for classification and for regression, and the proof of stability-based
generalization bounds for a broad family of algorithms for learning kernels
based on centered alignment. We also report the results of experiments with our
centered alignment-based algorithms in both classification and regression.
| Corinna Cortes, Mehryar Mohri, Afshin Rostamizadeh | null | 1203.0550 | null | null |
Learning DNF Expressions from Fourier Spectrum | cs.LG cs.CC cs.DS | Since its introduction by Valiant in 1984, PAC learning of DNF expressions
remains one of the central problems in learning theory. We consider this
problem in the setting where the underlying distribution is uniform, or more
generally, a product distribution. Kalai, Samorodnitsky and Teng (2009) showed
that in this setting a DNF expression can be efficiently approximated from its
"heavy" low-degree Fourier coefficients alone. This is in contrast to previous
approaches where boosting was used and thus Fourier coefficients of the target
function modified by various distributions were needed. This property is
crucial for learning of DNF expressions over smoothed product distributions, a
learning model introduced by Kalai et al. (2009) and inspired by the seminal
smoothed analysis model of Spielman and Teng (2001).
We introduce a new approach to learning (or approximating) a polynomial
threshold functions which is based on creating a function with range [-1,1]
that approximately agrees with the unknown function on low-degree Fourier
coefficients. We then describe conditions under which this is sufficient for
learning polynomial threshold functions. Our approach yields a new, simple
algorithm for approximating any polynomial-size DNF expression from its "heavy"
low-degree Fourier coefficients alone. Our algorithm greatly simplifies the
proof of learnability of DNF expressions over smoothed product distributions.
We also describe an application of our algorithm to learning monotone DNF
expressions over product distributions. Building on the work of Servedio
(2001), we give an algorithm that runs in time $\poly((s \cdot
\log{(s/\eps)})^{\log{(s/\eps)}}, n)$, where $s$ is the size of the target DNF
expression and $\eps$ is the accuracy. This improves on $\poly((s \cdot
\log{(ns/\eps)})^{\log{(s/\eps)} \cdot \log{(1/\eps)}}, n)$ bound of Servedio
(2001).
| Vitaly Feldman | null | 1203.0594 | null | null |
Checking Tests for Read-Once Functions over Arbitrary Bases | cs.DM cs.CC cs.LG | A Boolean function is called read-once over a basis B if it can be expressed
by a formula over B where no variable appears more than once. A checking test
for a read-once function f over B depending on all its variables is a set of
input vectors distinguishing f from all other read-once functions of the same
variables. We show that every read-once function f over B has a checking test
containing O(n^l) vectors, where n is the number of relevant variables of f and
l is the largest arity of functions in B. For some functions, this bound cannot
be improved by more than a constant factor. The employed technique involves
reconstructing f from its l-variable projections and provides a stronger form
of Kuznetsov's classic theorem on read-once representations.
| Dmitry V. Chistikov | null | 1203.0631 | null | null |
A Method of Moments for Mixture Models and Hidden Markov Models | cs.LG stat.ML | Mixture models are a fundamental tool in applied statistics and machine
learning for treating data taken from multiple subpopulations. The current
practice for estimating the parameters of such models relies on local search
heuristics (e.g., the EM algorithm) which are prone to failure, and existing
consistent methods are unfavorable due to their high computational and sample
complexity which typically scale exponentially with the number of mixture
components. This work develops an efficient method of moments approach to
parameter estimation for a broad class of high-dimensional mixture models with
many components, including multi-view mixtures of Gaussians (such as mixtures
of axis-aligned Gaussians) and hidden Markov models. The new method leads to
rigorous unsupervised learning results for mixture models that were not
achieved by previous works; and, because of its simplicity, it offers a viable
alternative to EM for practical deployment.
| Animashree Anandkumar, Daniel Hsu, Sham M. Kakade | null | 1203.0683 | null | null |
Learning High-Dimensional Mixtures of Graphical Models | stat.ML cs.AI cs.LG | We consider unsupervised estimation of mixtures of discrete graphical models,
where the class variable corresponding to the mixture components is hidden and
each mixture component over the observed variables can have a potentially
different Markov graph structure and parameters. We propose a novel approach
for estimating the mixture components, and our output is a tree-mixture model
which serves as a good approximation to the underlying graphical model mixture.
Our method is efficient when the union graph, which is the union of the Markov
graphs of the mixture components, has sparse vertex separators between any pair
of observed variables. This includes tree mixtures and mixtures of bounded
degree graphs. For such models, we prove that our method correctly recovers the
union graph structure and the tree structures corresponding to
maximum-likelihood tree approximations of the mixture components. The sample
and computational complexities of our method scale as $\poly(p, r)$, for an
$r$-component mixture of $p$-variate graphical models. We further extend our
results to the case when the union graph has sparse local separators between
any pair of observed variables, such as mixtures of locally tree-like graphs,
and the mixture components are in the regime of correlation decay.
| A. Anandkumar, D. Hsu, F. Huang and S. M. Kakade | null | 1203.0697 | null | null |
Infinite Shift-invariant Grouped Multi-task Learning for Gaussian
Processes | cs.LG astro-ph.IM stat.ML | Multi-task learning leverages shared information among data sets to improve
the learning performance of individual tasks. The paper applies this framework
for data where each task is a phase-shifted periodic time series. In
particular, we develop a novel Bayesian nonparametric model capturing a mixture
of Gaussian processes where each task is a sum of a group-specific function and
a component capturing individual variation, in addition to each task being
phase shifted. We develop an efficient \textsc{em} algorithm to learn the
parameters of the model. As a special case we obtain the Gaussian mixture model
and \textsc{em} algorithm for phased-shifted periodic time series. Furthermore,
we extend the proposed model by using a Dirichlet Process prior and thereby
leading to an infinite mixture model that is capable of doing automatic model
selection. A Variational Bayesian approach is developed for inference in this
model. Experiments in regression, classification and class discovery
demonstrate the performance of the proposed models using both synthetic data
and real-world time series data from astrophysics. Our methods are particularly
useful when the time series are sparsely and non-synchronously sampled.
| Yuyang Wang, Roni Khardon, Pavlos Protopapas | null | 1203.0970 | null | null |
Sparse Subspace Clustering: Algorithm, Theory, and Applications | cs.CV cs.IR cs.IT cs.LG math.IT math.OC stat.ML | In many real-world problems, we are dealing with collections of
high-dimensional data, such as images, videos, text and web documents, DNA
microarray data, and more. Often, high-dimensional data lie close to
low-dimensional structures corresponding to several classes or categories the
data belongs to. In this paper, we propose and study an algorithm, called
Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of
low-dimensional subspaces. The key idea is that, among infinitely many possible
representations of a data point in terms of other points, a sparse
representation corresponds to selecting a few points from the same subspace.
This motivates solving a sparse optimization program whose solution is used in
a spectral clustering framework to infer the clustering of data into subspaces.
Since solving the sparse optimization program is in general NP-hard, we
consider a convex relaxation and show that, under appropriate conditions on the
arrangement of subspaces and the distribution of data, the proposed
minimization program succeeds in recovering the desired sparse representations.
The proposed algorithm can be solved efficiently and can handle data points
near the intersections of subspaces. Another key advantage of the proposed
algorithm with respect to the state of the art is that it can deal with data
nuisances, such as noise, sparse outlying entries, and missing entries,
directly by incorporating the model of the data into the sparse optimization
program. We demonstrate the effectiveness of the proposed algorithm through
experiments on synthetic data as well as the two real-world problems of motion
segmentation and face clustering.
| Ehsan Elhamifar and Rene Vidal | null | 1203.1005 | null | null |
Agnostic System Identification for Model-Based Reinforcement Learning | cs.LG cs.AI cs.SY stat.ML | A fundamental problem in control is to learn a model of a system from
observations that is useful for controller synthesis. To provide good
performance guarantees, existing methods must assume that the real system is in
the class of models considered during learning. We present an iterative method
with strong guarantees even in the agnostic case where the system is not in the
class. In particular, we show that any no-regret online learning algorithm can
be used to obtain a near-optimal policy, provided some model achieves low
training error and access to a good exploration distribution. Our approach
applies to both discrete and continuous domains. We demonstrate its efficacy
and scalability on a challenging helicopter domain from the literature.
| Stephane Ross, J. Andrew Bagnell | null | 1203.1007 | null | null |
Learning Random Kernel Approximations for Object Recognition | cs.CV cs.LG | Approximations based on random Fourier features have recently emerged as an
efficient and formally consistent methodology to design large-scale kernel
machines. By expressing the kernel as a Fourier expansion, features are
generated based on a finite set of random basis projections, sampled from the
Fourier transform of the kernel, with inner products that are Monte Carlo
approximations of the original kernel. Based on the observation that different
kernel-induced Fourier sampling distributions correspond to different kernel
parameters, we show that an optimization process in the Fourier domain can be
used to identify the different frequency bands that are useful for prediction
on training data. Moreover, the application of group Lasso to random feature
vectors corresponding to a linear combination of multiple kernels, leads to
efficient and scalable reformulations of the standard multiple kernel learning
model \cite{Varma09}. In this paper we develop the linear Fourier approximation
methodology for both single and multiple gradient-based kernel learning and
show that it produces fast and accurate predictors on a complex dataset such as
the Visual Object Challenge 2011 (VOC2011).
| Eduard Gabriel B\u{a}z\u{a}van, Fuxin Li and Cristian Sminchisescu | null | 1203.1483 | null | null |
Multiple Operator-valued Kernel Learning | stat.ML cs.LG | Positive definite operator-valued kernels generalize the well-known notion of
reproducing kernels, and are naturally adapted to multi-output learning
situations. This paper addresses the problem of learning a finite linear
combination of infinite-dimensional operator-valued kernels which are suitable
for extending functional data analysis methods to nonlinear contexts. We study
this problem in the case of kernel ridge regression for functional responses
with an lr-norm constraint on the combination coefficients. The resulting
optimization problem is more involved than those of multiple scalar-valued
kernel learning since operator-valued kernels pose more technical and
theoretical issues. We propose a multiple operator-valued kernel learning
algorithm based on solving a system of linear operator equations by using a
block coordinatedescent procedure. We experimentally validate our approach on a
functional regression task in the context of finger movement prediction in
brain-computer interfaces.
| Hachem Kadri (INRIA Lille - Nord Europe), Alain Rakotomamonjy (LITIS),
Francis Bach (INRIA Paris - Rocquencourt, LIENS), Philippe Preux (INRIA Lille
- Nord Europe) | null | 1203.1596 | null | null |
Graph partitioning advance clustering technique | cs.LG cs.DB | Clustering is a common technique for statistical data analysis, Clustering is
the process of grouping the data into classes or clusters so that objects
within a cluster have high similarity in comparison to one another, but are
very dissimilar to objects in other clusters. Dissimilarities are assessed
based on the attribute values describing the objects. Often, distance measures
are used. Clustering is an unsupervised learning technique, where interesting
patterns and structures can be found directly from very large data sets with
little or none of the background knowledge. This paper also considers the
partitioning of m-dimensional lattice graphs using Fiedler's approach, which
requires the determination of the eigenvector belonging to the second smallest
Eigenvalue of the Laplacian with K-means partitioning algorithm.
| T Soni Madhulatha | null | 1203.2002 | null | null |
Regret Bounds for Deterministic Gaussian Process Bandits | cs.LG stat.ML | This paper analyses the problem of Gaussian process (GP) bandits with
deterministic observations. The analysis uses a branch and bound algorithm that
is related to the UCB algorithm of (Srinivas et al., 2010). For GPs with
Gaussian observation noise, with variance strictly greater than zero, (Srinivas
et al., 2010) proved that the regret vanishes at the approximate rate of
$O(\frac{1}{\sqrt{t}})$, where t is the number of observations. To complement
their result, we attack the deterministic case and attain a much faster
exponential convergence rate. Under some regularity assumptions, we show that
the regret decreases asymptotically according to $O(e^{-\frac{\tau t}{(\ln
t)^{d/4}}})$ with high probability. Here, d is the dimension of the search
space and $\tau$ is a constant that depends on the behaviour of the objective
function near its global maximum.
| Nando de Freitas, Alex Smola, Masrour Zoghi | null | 1203.2177 | null | null |
Role-Dynamics: Fast Mining of Large Dynamic Networks | cs.SI cs.AI cs.LG stat.ML | To understand the structural dynamics of a large-scale social, biological or
technological network, it may be useful to discover behavioral roles
representing the main connectivity patterns present over time. In this paper,
we propose a scalable non-parametric approach to automatically learn the
structural dynamics of the network and individual nodes. Roles may represent
structural or behavioral patterns such as the center of a star, peripheral
nodes, or bridge nodes that connect different communities. Our novel approach
learns the appropriate structural role dynamics for any arbitrary network and
tracks the changes over time. In particular, we uncover the specific global
network dynamics and the local node dynamics of a technological, communication,
and social network. We identify interesting node and network patterns such as
stationary and non-stationary roles, spikes/steps in role-memberships (perhaps
indicating anomalies), increasing/decreasing role trends, among many others.
Our results indicate that the nodes in each of these networks have distinct
connectivity patterns that are non-stationary and evolve considerably over
time. Overall, the experiments demonstrate the effectiveness of our approach
for fast mining and tracking of the dynamics in large networks. Furthermore,
the dynamic structural representation provides a basis for building more
sophisticated models and tools that are fast for exploring large dynamic
networks.
| Ryan Rossi, Brian Gallagher, Jennifer Neville, Keith Henderson | null | 1203.2200 | null | null |
Decentralized, Adaptive, Look-Ahead Particle Filtering | stat.ML cs.LG stat.CO | The decentralized particle filter (DPF) was proposed recently to increase the
level of parallelism of particle filtering. Given a decomposition of the state
space into two nested sets of variables, the DPF uses a particle filter to
sample the first set and then conditions on this sample to generate a set of
samples for the second set of variables. The DPF can be understood as a variant
of the popular Rao-Blackwellized particle filter (RBPF), where the second step
is carried out using Monte Carlo approximations instead of analytical
inference. As a result, the range of applications of the DPF is broader than
the one for the RBPF. In this paper, we improve the DPF in two ways. First, we
derive a Monte Carlo approximation of the optimal proposal distribution and,
consequently, design and implement a more efficient look-ahead DPF. Although
the decentralized filters were initially designed to capitalize on parallel
implementation, we show that the look-ahead DPF can outperform the standard
particle filter even on a single machine. Second, we propose the use of bandit
algorithms to automatically configure the state space decomposition of the DPF.
| Mohamed Osama Ahmed, Pouyan T. Bibalan, Nando de Freitas and Simon
Fauvel | null | 1203.2394 | null | null |
Deviation optimal learning using greedy Q-aggregation | math.ST cs.LG stat.ML stat.TH | Given a finite family of functions, the goal of model selection aggregation
is to construct a procedure that mimics the function from this family that is
the closest to an unknown regression function. More precisely, we consider a
general regression model with fixed design and measure the distance between
functions by the mean squared error at the design points. While procedures
based on exponential weights are known to solve the problem of model selection
aggregation in expectation, they are, surprisingly, sub-optimal in deviation.
We propose a new formulation called Q-aggregation that addresses this
limitation; namely, its solution leads to sharp oracle inequalities that are
optimal in a minimax sense. Moreover, based on the new formulation, we design
greedy Q-aggregation procedures that produce sparse aggregation models
achieving the optimal rate. The convergence and performance of these greedy
procedures are illustrated and compared with other standard methods on
simulated examples.
| Dong Dai, Philippe Rigollet, Tong Zhang | 10.1214/12-AOS1025 | 1203.2507 | null | null |
A Simple Flood Forecasting Scheme Using Wireless Sensor Networks | cs.LG cs.CE cs.NI cs.SY stat.AP | This paper presents a forecasting model designed using WSNs (Wireless Sensor
Networks) to predict flood in rivers using simple and fast calculations to
provide real-time results and save the lives of people who may be affected by
the flood. Our prediction model uses multiple variable robust linear regression
which is easy to understand and simple and cost effective in implementation, is
speed efficient, but has low resource utilization and yet provides real time
predictions with reliable accuracy, thus having features which are desirable in
any real world algorithm. Our prediction model is independent of the number of
parameters, i.e. any number of parameters may be added or removed based on the
on-site requirements. When the water level rises, we represent it using a
polynomial whose nature is used to determine if the water level may exceed the
flood line in the near future. We compare our work with a contemporary
algorithm to demonstrate our improvements over it. Then we present our
simulation results for the predicted water level compared to the actual water
level.
| Victor Seal, Arnab Raha, Shovan Maity, Souvik Kr Mitra, Amitava
Mukherjee and Mrinal Kanti Naskar | 10.5121/ijasuc.2012.3105 | 1203.2511 | null | null |
On the Necessity of Irrelevant Variables | cs.LG | This work explores the effects of relevant and irrelevant boolean variables
on the accuracy of classifiers. The analysis uses the assumption that the
variables are conditionally independent given the class, and focuses on a
natural family of learning algorithms for such sources when the relevant
variables have a small advantage over random guessing. The main result is that
algorithms relying predominately on irrelevant variables have error
probabilities that quickly go to 0 in situations where algorithms that limit
the use of irrelevant variables have errors bounded below by a positive
constant. We also show that accurate learning is possible even when there are
so few examples that one cannot determine with high confidence whether or not
any individual variable is relevant.
| David P. Helmbold and Philip M. Long | null | 1203.2557 | null | null |
Differential Privacy for Functions and Functional Data | stat.ML cs.LG | Differential privacy is a framework for privately releasing summaries of a
database. Previous work has focused mainly on methods for which the output is a
finite dimensional vector, or an element of some discrete set. We develop
methods for releasing functions while preserving differential privacy.
Specifically, we show that adding an appropriate Gaussian process to the
function of interest yields differential privacy. When the functions lie in the
same RKHS as the Gaussian process, then the correct noise level is established
by measuring the "sensitivity" of the function in the RKHS norm. As examples we
consider kernel density estimation, kernel support vector machines, and
functions in reproducing kernel Hilbert spaces.
| Rob Hall, Alessandro Rinaldo, Larry Wasserman | null | 1203.2570 | null | null |
Graphlet decomposition of a weighted network | stat.ME cs.LG cs.SI physics.soc-ph | We introduce the graphlet decomposition of a weighted network, which encodes
a notion of social information based on social structure. We develop a scalable
inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion,
for estimating the parameters of the model underlying graphlets using one
network sample. We explore some theoretical properties of the graphlet
decomposition, including computational complexity, redundancy and expected
accuracy. We demonstrate graphlets on synthetic and real data. We analyze
messaging patterns on Facebook and criminal associations in the 19th century.
| Hossein Azari Soufiani, Edoardo M Airoldi | null | 1203.2821 | null | null |
Mining Education Data to Predict Student's Retention: A comparative
Study | cs.LG cs.DB | The main objective of higher education is to provide quality education to
students. One way to achieve highest level of quality in higher education
system is by discovering knowledge for prediction regarding enrolment of
students in a course. This paper presents a data mining project to generate
predictive models for student retention management. Given new records of
incoming students, these predictive models can produce short accurate
prediction lists identifying students who tend to need the support from the
student retention program most. This paper examines the quality of the
predictive models generated by the machine learning algorithms. The results
show that some of the machines learning algorithms are able to establish
effective predictive models from the existing student retention data.
| Surjeet Kumar Yadav, Brijesh Bharadwaj and Saurabh Pal | null | 1203.2987 | null | null |
Evolving Culture vs Local Minima | cs.LG cs.AI | We propose a theory that relates difficulty of learning in deep architectures
to culture and language. It is articulated around the following hypotheses: (1)
learning in an individual human brain is hampered by the presence of effective
local minima; (2) this optimization difficulty is particularly important when
it comes to learning higher-level abstractions, i.e., concepts that cover a
vast and highly-nonlinear span of sensory configurations; (3) such high-level
abstractions are best represented in brains by the composition of many levels
of representation, i.e., by deep architectures; (4) a human brain can learn
such high-level abstractions if guided by the signals produced by other humans,
which act as hints or indirect supervision for these high-level abstractions;
and (5), language and the recombination and optimization of mental concepts
provide an efficient evolutionary recombination operator, and this gives rise
to rapid search in the space of communicable ideas that help humans build up
better high-level internal representations of their world. These hypotheses put
together imply that human culture and the evolution of ideas have been crucial
to counter an optimization difficulty: this optimization difficulty would
otherwise make it very difficult for human brains to capture high-level
knowledge of the world. The theory is grounded in experimental observations of
the difficulties of training deep artificial neural networks. Plausible
consequences of this theory for the efficiency of cultural evolutions are
sketched.
| Yoshua Bengio | null | 1203.2990 | null | null |
Learning, Social Intelligence and the Turing Test - why an
"out-of-the-box" Turing Machine will not pass the Turing Test | cs.AI cs.LG nlin.AO | The Turing Test (TT) checks for human intelligence, rather than any putative
general intelligence. It involves repeated interaction requiring learning in
the form of adaption to the human conversation partner. It is a macro-level
post-hoc test in contrast to the definition of a Turing Machine (TM), which is
a prior micro-level definition. This raises the question of whether learning is
just another computational process, i.e. can be implemented as a TM. Here we
argue that learning or adaption is fundamentally different from computation,
though it does involve processes that can be seen as computations. To
illustrate this difference we compare (a) designing a TM and (b) learning a TM,
defining them for the purpose of the argument. We show that there is a
well-defined sequence of problems which are not effectively designable but are
learnable, in the form of the bounded halting problem. Some characteristics of
human intelligence are reviewed including it's: interactive nature, learning
abilities, imitative tendencies, linguistic ability and context-dependency. A
story that explains some of these is the Social Intelligence Hypothesis. If
this is broadly correct, this points to the necessity of a considerable period
of acculturation (social learning in context) if an artificial intelligence is
to pass the TT. Whilst it is always possible to 'compile' the results of
learning into a TM, this would not be a designed TM and would not be able to
continually adapt (pass future TTs). We conclude three things, namely that: a
purely "designed" TM will never pass the TT; that there is no such thing as a
general intelligence since it necessary involves learning; and that
learning/adaption and computation should be clearly distinguished.
| Bruce Edmonds and Carlos Gershenson | 10.1007/978-3-642-30870-3_18 | 1203.3376 | null | null |
Robust Metric Learning by Smooth Optimization | cs.LG stat.ML | Most existing distance metric learning methods assume perfect side
information that is usually given in pairwise or triplet constraints. Instead,
in many real-world applications, the constraints are derived from side
information, such as users' implicit feedbacks and citations among articles. As
a result, these constraints are usually noisy and contain many mistakes. In
this work, we aim to learn a distance metric from noisy constraints by robust
optimization in a worst-case scenario, to which we refer as robust metric
learning. We formulate the learning task initially as a combinatorial
optimization problem, and show that it can be elegantly transformed to a convex
programming problem. We present an efficient learning algorithm based on smooth
optimization [7]. It has a worst-case convergence rate of
O(1/{\surd}{\varepsilon}) for smooth optimization problems, where {\varepsilon}
is the desired error of the approximate solution. Finally, our empirical study
with UCI data sets demonstrate the effectiveness of the proposed method in
comparison to state-of-the-art methods.
| Kaizhu Huang, Rong Jin, Zenglin Xu, Cheng-Lin Liu | null | 1203.3461 | null | null |
Gaussian Process Topic Models | cs.LG stat.ML | We introduce Gaussian Process Topic Models (GPTMs), a new family of topic
models which can leverage a kernel among documents while extracting correlated
topics. GPTMs can be considered a systematic generalization of the Correlated
Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding.
Since GPTMs work with both a topic covariance matrix and a document kernel
matrix, learning GPTMs involves a novel component-solving a suitable Sylvester
equation capturing both topic and document dependencies. The efficacy of GPTMs
is demonstrated with experiments evaluating the quality of both topic modeling
and embedding.
| Amrudin Agovic, Arindam Banerjee | null | 1203.3462 | null | null |
Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering
Birth/Death and Evolution of Topics in Text Stream | cs.IR cs.LG stat.ML | Topic models have proven to be a useful tool for discovering latent
structures in document collections. However, most document collections often
come as temporal streams and thus several aspects of the latent structure such
as the number of topics, the topics' distribution and popularity are
time-evolving. Several models exist that model the evolution of some but not
all of the above aspects. In this paper we introduce infinite dynamic topic
models, iDTM, that can accommodate the evolution of all the aforementioned
aspects. Our model assumes that documents are organized into epochs, where the
documents within each epoch are exchangeable but the order between the
documents is maintained across epochs. iDTM allows for unbounded number of
topics: topics can die or be born at any epoch, and the representation of each
topic can evolve according to a Markovian dynamics. We use iDTM to analyze the
birth and evolution of topics in the NIPS community and evaluated the efficacy
of our model on both simulated and real datasets with favorable outcome.
| Amr Ahmed, Eric P. Xing | null | 1203.3463 | null | null |
Bayesian Rose Trees | cs.LG stat.ML | Hierarchical structure is ubiquitous in data across many domains. There are
many hierarchical clustering methods, frequently used by domain experts, which
strive to discover this structure. However, most of these methods limit
discoverable hierarchies to those with binary branching structure. This
limitation, while computationally convenient, is often undesirable. In this
paper we explore a Bayesian hierarchical clustering algorithm that can produce
trees with arbitrary branching structure at each node, known as rose trees. We
interpret these trees as mixtures over partitions of a data set, and use a
computationally efficient, greedy agglomerative algorithm to find the rose
trees which have high marginal likelihood given the data. Lastly, we perform
experiments which demonstrate that rose trees are better models of data than
the typical binary trees returned by other hierarchical clustering algorithms.
| Charles Blundell, Yee Whye Teh, Katherine A. Heller | null | 1203.3468 | null | null |
An Online Learning-based Framework for Tracking | cs.LG cs.AI stat.ML | We study the tracking problem, namely, estimating the hidden state of an
object over time, from unreliable and noisy measurements. The standard
framework for the tracking problem is the generative framework, which is the
basis of solutions such as the Bayesian algorithm and its approximation, the
particle filters. However, these solutions can be very sensitive to model
mismatches. In this paper, motivated by online learning, we introduce a new
framework for tracking. We provide an efficient tracking algorithm for this
framework. We provide experimental results comparing our algorithm to the
Bayesian algorithm on simulated data. Our experiments show that when there are
slight model mismatches, our algorithm outperforms the Bayesian algorithm.
| Kamalika Chaudhuri, Yoav Freund, Daniel Hsu | null | 1203.3471 | null | null |
Super-Samples from Kernel Herding | cs.LG stat.ML | We extend the herding algorithm to continuous spaces by using the kernel
trick. The resulting "kernel herding" algorithm is an infinite memory
deterministic process that learns to approximate a PDF with a collection of
samples. We show that kernel herding decreases the error of expectations of
functions in the Hilbert space at a rate O(1/T) which is much faster than the
usual O(1/pT) for iid random samples. We illustrate kernel herding by
approximating Bayesian predictive distributions.
| Yutian Chen, Max Welling, Alex Smola | null | 1203.3472 | null | null |
Inferring deterministic causal relations | cs.LG stat.ML | We consider two variables that are related to each other by an invertible
function. While it has previously been shown that the dependence structure of
the noise can provide hints to determine which of the two variables is the
cause, we presently show that even in the deterministic (noise-free) case,
there are asymmetries that can be exploited for causal inference. Our method is
based on the idea that if the function and the probability density of the cause
are chosen independently, then the distribution of the effect will, in a
certain sense, depend on the function. We provide a theoretical analysis of
this method, showing that it also works in the low noise regime, and link it to
information geometry. We report strong empirical results on various real-world
data sets from different domains.
| Povilas Daniusis, Dominik Janzing, Joris Mooij, Jakob Zscheischler,
Bastian Steudel, Kun Zhang, Bernhard Schoelkopf | null | 1203.3475 | null | null |
Inference-less Density Estimation using Copula Bayesian Networks | cs.LG stat.ML | We consider learning continuous probabilistic graphical models in the face of
missing data. For non-Gaussian models, learning the parameters and structure of
such models depends on our ability to perform efficient inference, and can be
prohibitive even for relatively modest domains. Recently, we introduced the
Copula Bayesian Network (CBN) density model - a flexible framework that
captures complex high-dimensional dependency structures while offering direct
control over the univariate marginals, leading to improved generalization. In
this work we show that the CBN model also offers significant computational
advantages when training data is partially observed. Concretely, we leverage on
the specialized form of the model to derive a computationally amenable learning
objective that is a lower bound on the log-likelihood function. Importantly,
our energy-like bound circumvents the need for costly inference of an auxiliary
distribution, thus facilitating practical learning of highdimensional
densities. We demonstrate the effectiveness of our approach for learning the
structure and parameters of a CBN model for two reallife continuous domains.
| Gal Elidan | null | 1203.3476 | null | null |
Real-Time Scheduling via Reinforcement Learning | cs.LG cs.AI stat.ML | Cyber-physical systems, such as mobile robots, must respond adaptively to
dynamic operating conditions. Effective operation of these systems requires
that sensing and actuation tasks are performed in a timely manner.
Additionally, execution of mission specific tasks such as imaging a room must
be balanced against the need to perform more general tasks such as obstacle
avoidance. This problem has been addressed by maintaining relative utilization
of shared resources among tasks near a user-specified target level. Producing
optimal scheduling strategies requires complete prior knowledge of task
behavior, which is unlikely to be available in practice. Instead, suitable
scheduling strategies must be learned online through interaction with the
system. We consider the sample complexity of reinforcement learning in this
domain, and demonstrate that while the problem state space is countably
infinite, we may leverage the problem's structure to guarantee efficient
learning.
| Robert Glaubius, Terry Tidwell, Christopher Gill, William D. Smart | null | 1203.3481 | null | null |
Regularized Maximum Likelihood for Intrinsic Dimension Estimation | cs.LG stat.ML | We propose a new method for estimating the intrinsic dimension of a dataset
by applying the principle of regularized maximum likelihood to the distances
between close neighbors. We propose a regularization scheme which is motivated
by divergence minimization principles. We derive the estimator by a Poisson
process approximation, argue about its convergence properties and apply it to a
number of simulated and real datasets. We also show it has the best overall
performance compared with two other intrinsic dimension estimators.
| Mithun Das Gupta, Thomas S. Huang | null | 1203.3483 | null | null |
The Hierarchical Dirichlet Process Hidden Semi-Markov Model | cs.LG stat.ML | There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the
traditional HMM. However, in many settings the HDP-HMM's strict Markovian
constraints are undesirable, particularly if we wish to learn or encode
non-geometric state durations. We can extend the HDP-HMM to capture such
structure by drawing upon explicit-duration semi-Markovianity, which has been
developed in the parametric setting to allow construction of highly
interpretable models that admit natural prior information on state durations.
In this paper we introduce the explicitduration HDP-HSMM and develop posterior
sampling algorithms for efficient inference in both the direct-assignment and
weak-limit approximation settings. We demonstrate the utility of the model and
our inference methods on synthetic data as well as experiments on a speaker
diarization problem and an example of learning the patterns in Morse code.
| Matthew J. Johnson, Alan Willsky | null | 1203.3485 | null | null |
Combining Spatial and Telemetric Features for Learning Animal Movement
Models | cs.LG stat.ML | We introduce a new graphical model for tracking radio-tagged animals and
learning their movement patterns. The model provides a principled way to
combine radio telemetry data with an arbitrary set of userdefined, spatial
features. We describe an efficient stochastic gradient algorithm for fitting
model parameters to data and demonstrate its effectiveness via asymptotic
analysis and synthetic experiments. We also apply our model to real datasets,
and show that it outperforms the most popular radio telemetry software package
used in ecology. We conclude that integration of different data sources under a
single statistical framework, coupled with appropriate parameter and state
estimation procedures, produces both accurate location estimates and an
interpretable statistical model of animal movement.
| Berk Kapicioglu, Robert E. Schapire, Martin Wikelski, Tamara Broderick | null | 1203.3486 | null | null |
Causal Conclusions that Flip Repeatedly and Their Justification | cs.LG cs.AI stat.ML | Over the past two decades, several consistent procedures have been designed
to infer causal conclusions from observational data. We prove that if the true
causal network might be an arbitrary, linear Gaussian network or a discrete
Bayes network, then every unambiguous causal conclusion produced by a
consistent method from non-experimental data is subject to reversal as the
sample size increases any finite number of times. That result, called the
causal flipping theorem, extends prior results to the effect that causal
discovery cannot be reliable on a given sample size. We argue that since
repeated flipping of causal conclusions is unavoidable in principle for
consistent methods, the best possible discovery methods are consistent methods
that retract their earlier conclusions no more than necessary. A series of
simulations of various methods across a wide range of sample sizes illustrates
concretely both the theorem and the principle of comparing methods in terms of
retractions.
| Kevin T. Kelly, Conor Mayo-Wilson | null | 1203.3488 | null | null |
Bayesian exponential family projections for coupled data sources | cs.LG stat.ML | Exponential family extensions of principal component analysis (EPCA) have
received a considerable amount of attention in recent years, demonstrating the
growing need for basic modeling tools that do not assume the squared loss or
Gaussian distribution. We extend the EPCA model toolbox by presenting the first
exponential family multi-view learning methods of the partial least squares and
canonical correlation analysis, based on a unified representation of EPCA as
matrix factorization of the natural parameters of exponential family. The
models are based on a new family of priors that are generally usable for all
such factorizations. We also introduce new inference strategies, and
demonstrate how the methods outperform earlier ones when the Gaussianity
assumption does not hold.
| Arto Klami, Seppo Virtanen, Samuel Kaski | null | 1203.3489 | null | null |
Robust LogitBoost and Adaptive Base Class (ABC) LogitBoost | cs.LG stat.ML | Logitboost is an influential boosting algorithm for classification. In this
paper, we develop robust logitboost to provide an explicit formulation of
tree-split criterion for building weak learners (regression trees) for
logitboost. This formulation leads to a numerically stable implementation of
logitboost. We then propose abc-logitboost for multi-class classification, by
combining robust logitboost with the prior work of abc-boost. Previously,
abc-boost was implemented as abc-mart using the mart algorithm. Our extensive
experiments on multi-class classification compare four algorithms: mart,
abcmart, (robust) logitboost, and abc-logitboost, and demonstrate the
superiority of abc-logitboost. Comparisons with other learning methods
including SVM and deep learning are also available through prior publications.
| Ping Li | null | 1203.3491 | null | null |
Approximating Higher-Order Distances Using Random Projections | cs.LG stat.ML | We provide a simple method and relevant theoretical analysis for efficiently
estimating higher-order lp distances. While the analysis mainly focuses on l4,
our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).
Distance-based methods are popular in machine learning. In large-scale
applications, storing, computing, and retrieving the distances can be both
space and time prohibitive. Efficient algorithms exist for estimating lp
distances if 0 < p <= 2. The task for p > 2 is known to be difficult. Our work
partially fills this gap.
| Ping Li, Michael W. Mahoney, Yiyuan She | null | 1203.3492 | null | null |
Negative Tree Reweighted Belief Propagation | cs.LG stat.ML | We introduce a new class of lower bounds on the log partition function of a
Markov random field which makes use of a reversed Jensen's inequality. In
particular, our method approximates the intractable distribution using a linear
combination of spanning trees with negative weights. This technique is a
lower-bound counterpart to the tree-reweighted belief propagation algorithm,
which uses a convex combination of spanning trees with positive weights to
provide corresponding upper bounds. We develop algorithms to optimize and
tighten the lower bounds over the non-convex set of valid parameter values. Our
algorithm generalizes mean field approaches (including naive and structured
mean field approximations), which it includes as a limiting case.
| Qiang Liu, Alexander T. Ihler | null | 1203.3494 | null | null |
Parameter-Free Spectral Kernel Learning | cs.LG stat.ML | Due to the growing ubiquity of unlabeled data, learning with unlabeled data
is attracting increasing attention in machine learning. In this paper, we
propose a novel semi-supervised kernel learning method which can seamlessly
combine manifold structure of unlabeled data and Regularized Least-Squares
(RLS) to learn a new kernel. Interestingly, the new kernel matrix can be
obtained analytically with the use of spectral decomposition of graph Laplacian
matrix. Hence, the proposed algorithm does not require any numerical
optimization solvers. Moreover, by maximizing kernel target alignment on
labeled data, we can also learn model parameters automatically with a
closed-form solution. For a given graph Laplacian matrix, our proposed method
does not need to tune any model parameter including the tradeoff parameter in
RLS and the balance parameter for unlabeled data. Extensive experiments on ten
benchmark datasets show that our proposed two-stage parameter-free spectral
kernel learning algorithm can obtain comparable performance with fine-tuned
manifold regularization methods in transductive setting, and outperform
multiple kernel learning in supervised setting.
| Qi Mao, Ivor W. Tsang | null | 1203.3495 | null | null |
Dirichlet Process Mixtures of Generalized Mallows Models | cs.LG stat.ML | We present a Dirichlet process mixture model over discrete incomplete
rankings and study two Gibbs sampling inference techniques for estimating
posterior clusterings. The first approach uses a slice sampling subcomponent
for estimating cluster parameters. The second approach marginalizes out several
cluster parameters by taking advantage of approximations to the conditional
posteriors. We empirically demonstrate (1) the effectiveness of this
approximation for improving convergence, (2) the benefits of the Dirichlet
process model over alternative clustering techniques for ranked data, and (3)
the applicability of the approach to exploring large realworld ranking
datasets.
| Marina Meila, Harr Chen | null | 1203.3496 | null | null |
Parametric Return Density Estimation for Reinforcement Learning | cs.LG stat.ML | Most conventional Reinforcement Learning (RL) algorithms aim to optimize
decision-making rules in terms of the expected returns. However, especially for
risk management purposes, other risk-sensitive criteria such as the
value-at-risk or the expected shortfall are sometimes preferred in real
applications. Here, we describe a parametric method for estimating density of
the returns, which allows us to handle various criteria in a unified manner. We
first extend the Bellman equation for the conditional expected return to cover
a conditional probability density of the returns. Then we derive an extension
of the TD-learning algorithm for estimating the return densities in an unknown
environment. As test instances, several parametric density estimation
algorithms are presented for the Gaussian, Laplace, and skewed Laplace
distributions. We show that these algorithms lead to risk-sensitive as well as
robust RL paradigms through numerical experiments.
| Tetsuro Morimura, Masashi Sugiyama, Hisashi Kashima, Hirotaka Hachiya,
Toshiyuki Tanaka | null | 1203.3497 | null | null |
Algorithms and Complexity Results for Exact Bayesian Structure Learning | cs.LG cs.DS stat.ML | Bayesian structure learning is the NP-hard problem of discovering a Bayesian
network that optimally represents a given set of training data. In this paper
we study the computational worst-case complexity of exact Bayesian structure
learning under graph theoretic restrictions on the super-structure. The
super-structure (a concept introduced by Perrier, Imoto, and Miyano, JMLR 2008)
is an undirected graph that contains as subgraphs the skeletons of solution
networks. Our results apply to several variants of score-based Bayesian
structure learning where the score of a network decomposes into local scores of
its nodes. Results: We show that exact Bayesian structure learning can be
carried out in non-uniform polynomial time if the super-structure has bounded
treewidth and in linear time if in addition the super-structure has bounded
maximum degree. We complement this with a number of hardness results. We show
that both restrictions (treewidth and degree) are essential and cannot be
dropped without loosing uniform polynomial time tractability (subject to a
complexity-theoretic assumption). Furthermore, we show that the restrictions
remain essential if we do not search for a globally optimal network but we aim
to improve a given network by means of at most k arc additions, arc deletions,
or arc reversals (k-neighborhood local search).
| Sebastian Ordyniak, Stefan Szeider | null | 1203.3501 | null | null |
A Family of Computationally Efficient and Simple Estimators for
Unnormalized Statistical Models | cs.LG stat.ML | We introduce a new family of estimators for unnormalized statistical models.
Our family of estimators is parameterized by two nonlinear functions and uses a
single sample from an auxiliary distribution, generalizing Maximum Likelihood
Monte Carlo estimation of Geyer and Thompson (1992). The family is such that we
can estimate the partition function like any other parameter in the model. The
estimation is done by optimizing an algebraically simple, well defined
objective function, which allows for the use of dedicated optimization methods.
We establish consistency of the estimator family and give an expression for the
asymptotic covariance matrix, which enables us to further analyze the influence
of the nonlinearities and the auxiliary density on estimation performance. Some
estimators in our family are particularly stable for a wide range of auxiliary
densities. Interestingly, a specific choice of the nonlinearity establishes a
connection between density estimation and classification by nonlinear logistic
regression. Finally, the optimal amount of auxiliary samples relative to the
given amount of the data is considered from the perspective of computational
efficiency.
| Miika Pihlaja, Michael Gutmann, Aapo Hyvarinen | null | 1203.3506 | null | null |
Sparse-posterior Gaussian Processes for general likelihoods | cs.LG stat.ML | Gaussian processes (GPs) provide a probabilistic nonparametric representation
of functions in regression, classification, and other problems. Unfortunately,
exact learning with GPs is intractable for large datasets. A variety of
approximate GP methods have been proposed that essentially map the large
dataset into a small set of basis points. Among them, two state-of-the-art
methods are sparse pseudo-input Gaussian process (SPGP) (Snelson and
Ghahramani, 2006) and variablesigma GP (VSGP) Walder et al. (2008), which
generalizes SPGP and allows each basis point to have its own length scale.
However, VSGP was only derived for regression. In this paper, we propose a new
sparse GP framework that uses expectation propagation to directly approximate
general GP likelihoods using a sparse and smooth basis. It includes both SPGP
and VSGP for regression as special cases. Plus as an EP algorithm, it inherits
the ability to process data online. As a particular choice of approximating
family, we blur each basis point with a Gaussian distribution that has a full
covariance matrix representing the data distribution around that basis point;
as a result, we can summarize local data manifold information with a small set
of basis points. Our experiments demonstrate that this framework outperforms
previous GP classification methods on benchmark datasets in terms of minimizing
divergence to the non-sparse GP solution as well as lower misclassification
rate.
| Yuan (Alan) Qi, Ahmed H. Abdel-Gawad, Thomas P. Minka | null | 1203.3507 | null | null |
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