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Irregular-Time Bayesian Networks | cs.AI cs.LG stat.ML | In many fields observations are performed irregularly along time, due to
either measurement limitations or lack of a constant immanent rate. While
discrete-time Markov models (as Dynamic Bayesian Networks) introduce either
inefficient computation or an information loss to reasoning about such
processes, continuous-time Markov models assume either a discrete state space
(as Continuous-Time Bayesian Networks), or a flat continuous state space (as
stochastic differential equations). To address these problems, we present a new
modeling class called Irregular-Time Bayesian Networks (ITBNs), generalizing
Dynamic Bayesian Networks, allowing substantially more compact representations,
and increasing the expressivity of the temporal dynamics. In addition, a
globally optimal solution is guaranteed when learning temporal systems,
provided that they are fully observed at the same irregularly spaced
time-points, and a semiparametric subclass of ITBNs is introduced to allow
further adaptation to the irregular nature of the available data.
| Michael Ramati, Yuval Shahar | null | 1203.3510 | null | null |
Inference by Minimizing Size, Divergence, or their Sum | cs.LG cs.CL stat.ML | We speed up marginal inference by ignoring factors that do not significantly
contribute to overall accuracy. In order to pick a suitable subset of factors
to ignore, we propose three schemes: minimizing the number of model factors
under a bound on the KL divergence between pruned and full models; minimizing
the KL divergence under a bound on factor count; and minimizing the weighted
sum of KL divergence and factor count. All three problems are solved using an
approximation of the KL divergence than can be calculated in terms of marginals
computed on a simple seed graph. Applied to synthetic image denoising and to
three different types of NLP parsing models, this technique performs marginal
inference up to 11 times faster than loopy BP, with graph sizes reduced up to
98%-at comparable error in marginals and parsing accuracy. We also show that
minimizing the weighted sum of divergence and size is substantially faster than
minimizing either of the other objectives based on the approximation to
divergence presented here.
| Sebastian Riedel, David A. Smith, Andrew McCallum | null | 1203.3511 | null | null |
Modeling Events with Cascades of Poisson Processes | cs.LG cs.AI stat.ML | We present a probabilistic model of events in continuous time in which each
event triggers a Poisson process of successor events. The ensemble of observed
events is thereby modeled as a superposition of Poisson processes. Efficient
inference is feasible under this model with an EM algorithm. Moreover, the EM
algorithm can be implemented as a distributed algorithm, permitting the model
to be applied to very large datasets. We apply these techniques to the modeling
of Twitter messages and the revision history of Wikipedia.
| Aleksandr Simma, Michael I. Jordan | null | 1203.3516 | null | null |
A Bayesian Matrix Factorization Model for Relational Data | cs.LG stat.ML | Relational learning can be used to augment one data source with other
correlated sources of information, to improve predictive accuracy. We frame a
large class of relational learning problems as matrix factorization problems,
and propose a hierarchical Bayesian model. Training our Bayesian model using
random-walk Metropolis-Hastings is impractically slow, and so we develop a
block Metropolis-Hastings sampler which uses the gradient and Hessian of the
likelihood to dynamically tune the proposal. We demonstrate that a predictive
model of brain response to stimuli can be improved by augmenting it with side
information about the stimuli.
| Ajit P. Singh, Geoffrey Gordon | null | 1203.3517 | null | null |
Variance-Based Rewards for Approximate Bayesian Reinforcement Learning | cs.LG cs.AI stat.ML | The explore{exploit dilemma is one of the central challenges in Reinforcement
Learning (RL). Bayesian RL solves the dilemma by providing the agent with
information in the form of a prior distribution over environments; however,
full Bayesian planning is intractable. Planning with the mean MDP is a common
myopic approximation of Bayesian planning. We derive a novel reward bonus that
is a function of the posterior distribution over environments, which, when
added to the reward in planning with the mean MDP, results in an agent which
explores efficiently and effectively. Although our method is similar to
existing methods when given an uninformative or unstructured prior, unlike
existing methods, our method can exploit structured priors. We prove that our
method results in a polynomial sample complexity and empirically demonstrate
its advantages in a structured exploration task.
| Jonathan Sorg, Satinder Singh, Richard L. Lewis | null | 1203.3518 | null | null |
Bayesian Inference in Monte-Carlo Tree Search | cs.LG cs.AI stat.ML | Monte-Carlo Tree Search (MCTS) methods are drawing great interest after
yielding breakthrough results in computer Go. This paper proposes a Bayesian
approach to MCTS that is inspired by distributionfree approaches such as UCT
[13], yet significantly differs in important respects. The Bayesian framework
allows potentially much more accurate (Bayes-optimal) estimation of node values
and node uncertainties from a limited number of simulation trials. We further
propose propagating inference in the tree via fast analytic Gaussian
approximation methods: this can make the overhead of Bayesian inference
manageable in domains such as Go, while preserving high accuracy of
expected-value estimates. We find substantial empirical outperformance of UCT
in an idealized bandit-tree test environment, where we can obtain valuable
insights by comparing with known ground truth. Additionally we rigorously prove
on-policy and off-policy convergence of the proposed methods.
| Gerald Tesauro, V T Rajan, Richard Segal | null | 1203.3519 | null | null |
Bayesian Model Averaging Using the k-best Bayesian Network Structures | cs.LG cs.AI stat.ML | We study the problem of learning Bayesian network structures from data. We
develop an algorithm for finding the k-best Bayesian network structures. We
propose to compute the posterior probabilities of hypotheses of interest by
Bayesian model averaging over the k-best Bayesian networks. We present
empirical results on structural discovery over several real and synthetic data
sets and show that the method outperforms the model selection method and the
state of-the-art MCMC methods.
| Jin Tian, Ru He, Lavanya Ram | null | 1203.3520 | null | null |
Learning networks determined by the ratio of prior and data | cs.LG stat.ML | Recent reports have described that the equivalent sample size (ESS) in a
Dirichlet prior plays an important role in learning Bayesian networks. This
paper provides an asymptotic analysis of the marginal likelihood score for a
Bayesian network. Results show that the ratio of the ESS and sample size
determine the penalty of adding arcs in learning Bayesian networks. The number
of arcs increases monotonically as the ESS increases; the number of arcs
monotonically decreases as the ESS decreases. Furthermore, the marginal
likelihood score provides a unified expression of various score metrics by
changing prior knowledge.
| Maomi Ueno | null | 1203.3521 | null | null |
Online Semi-Supervised Learning on Quantized Graphs | cs.LG stat.ML | In this paper, we tackle the problem of online semi-supervised learning
(SSL). When data arrive in a stream, the dual problems of computation and data
storage arise for any SSL method. We propose a fast approximate online SSL
algorithm that solves for the harmonic solution on an approximate graph. We
show, both empirically and theoretically, that good behavior can be achieved by
collapsing nearby points into a set of local "representative points" that
minimize distortion. Moreover, we regularize the harmonic solution to achieve
better stability properties. We apply our algorithm to face recognition and
optical character recognition applications to show that we can take advantage
of the manifold structure to outperform the previous methods. Unlike previous
heuristic approaches, we show that our method yields provable performance
bounds.
| Michal Valko, Branislav Kveton, Ling Huang, Daniel Ting | null | 1203.3522 | null | null |
Speeding up the binary Gaussian process classification | stat.ML cs.LG | Gaussian processes (GP) are attractive building blocks for many probabilistic
models. Their drawbacks, however, are the rapidly increasing inference time and
memory requirement alongside increasing data. The problem can be alleviated
with compactly supported (CS) covariance functions, which produce sparse
covariance matrices that are fast in computations and cheap to store. CS
functions have previously been used in GP regression but here the focus is in a
classification problem. This brings new challenges since the posterior
inference has to be done approximately. We utilize the expectation propagation
algorithm and show how its standard implementation has to be modified to obtain
computational benefits from the sparse covariance matrices. We study four CS
covariance functions and show that they may lead to substantial speed up in the
inference time compared to globally supported functions.
| Jarno Vanhatalo, Aki Vehtari | null | 1203.3524 | null | null |
Primal View on Belief Propagation | cs.LG cs.AI stat.ML | It is known that fixed points of loopy belief propagation (BP) correspond to
stationary points of the Bethe variational problem, where we minimize the Bethe
free energy subject to normalization and marginalization constraints.
Unfortunately, this does not entirely explain BP because BP is a dual rather
than primal algorithm to solve the Bethe variational problem -- beliefs are
infeasible before convergence. Thus, we have no better understanding of BP than
as an algorithm to seek for a common zero of a system of non-linear functions,
not explicitly related to each other. In this theoretical paper, we show that
these functions are in fact explicitly related -- they are the partial
derivatives of a single function of reparameterizations. That means, BP seeks
for a stationary point of a single function, without any constraints. This
function has a very natural form: it is a linear combination of local
log-partition functions, exactly as the Bethe entropy is the same linear
combination of local entropies.
| Tomas Werner | null | 1203.3526 | null | null |
Modeling Multiple Annotator Expertise in the Semi-Supervised Learning
Scenario | cs.LG cs.AI stat.ML | Learning algorithms normally assume that there is at most one annotation or
label per data point. However, in some scenarios, such as medical diagnosis and
on-line collaboration,multiple annotations may be available. In either case,
obtaining labels for data points can be expensive and time-consuming (in some
circumstances ground-truth may not exist). Semi-supervised learning approaches
have shown that utilizing the unlabeled data is often beneficial in these
cases. This paper presents a probabilistic semi-supervised model and algorithm
that allows for learning from both unlabeled and labeled data in the presence
of multiple annotators. We assume that it is known what annotator labeled which
data points. The proposed approach produces annotator models that allow us to
provide (1) estimates of the true label and (2) annotator variable expertise
for both labeled and unlabeled data. We provide numerical comparisons under
various scenarios and with respect to standard semi-supervised learning.
Experiments showed that the presented approach provides clear advantages over
multi-annotator methods that do not use the unlabeled data and over methods
that do not use multi-labeler information.
| Yan Yan, Romer Rosales, Glenn Fung, Jennifer Dy | null | 1203.3529 | null | null |
Hybrid Generative/Discriminative Learning for Automatic Image Annotation | cs.LG cs.CV stat.ML | Automatic image annotation (AIA) raises tremendous challenges to machine
learning as it requires modeling of data that are both ambiguous in input and
output, e.g., images containing multiple objects and labeled with multiple
semantic tags. Even more challenging is that the number of candidate tags is
usually huge (as large as the vocabulary size) yet each image is only related
to a few of them. This paper presents a hybrid generative-discriminative
classifier to simultaneously address the extreme data-ambiguity and
overfitting-vulnerability issues in tasks such as AIA. Particularly: (1) an
Exponential-Multinomial Mixture (EMM) model is established to capture both the
input and output ambiguity and in the meanwhile to encourage prediction
sparsity; and (2) the prediction ability of the EMM model is explicitly
maximized through discriminative learning that integrates variational inference
of graphical models and the pairwise formulation of ordinal regression.
Experiments show that our approach achieves both superior annotation
performance and better tag scalability.
| Shuang Hong Yang, Jiang Bian, Hongyuan Zha | null | 1203.3530 | null | null |
Learning Structural Changes of Gaussian Graphical Models in Controlled
Experiments | cs.LG stat.ML | Graphical models are widely used in scienti fic and engineering research to
represent conditional independence structures between random variables. In many
controlled experiments, environmental changes or external stimuli can often
alter the conditional dependence between the random variables, and potentially
produce significant structural changes in the corresponding graphical models.
Therefore, it is of great importance to be able to detect such structural
changes from data, so as to gain novel insights into where and how the
structural changes take place and help the system adapt to the new environment.
Here we report an effective learning strategy to extract structural changes in
Gaussian graphical model using l1-regularization based convex optimization. We
discuss the properties of the problem formulation and introduce an efficient
implementation by the block coordinate descent algorithm. We demonstrate the
principle of the approach on a numerical simulation experiment, and we then
apply the algorithm to the modeling of gene regulatory networks under different
conditions and obtain promising yet biologically plausible results.
| Bai Zhang, Yue Wang | null | 1203.3532 | null | null |
Source Separation and Higher-Order Causal Analysis of MEG and EEG | cs.LG stat.ML | Separation of the sources and analysis of their connectivity have been an
important topic in EEG/MEG analysis. To solve this problem in an automatic
manner, we propose a two-layer model, in which the sources are conditionally
uncorrelated from each other, but not independent; the dependence is caused by
the causality in their time-varying variances (envelopes). The model is
identified in two steps. We first propose a new source separation technique
which takes into account the autocorrelations (which may be time-varying) and
time-varying variances of the sources. The causality in the envelopes is then
discovered by exploiting a special kind of multivariate GARCH (generalized
autoregressive conditional heteroscedasticity) model. The resulting causal
diagram gives the effective connectivity between the separated sources; in our
experimental results on MEG data, sources with similar functions are grouped
together, with negative influences between groups, and the groups are connected
via some interesting sources.
| Kun Zhang, Aapo Hyvarinen | null | 1203.3533 | null | null |
Invariant Gaussian Process Latent Variable Models and Application in
Causal Discovery | cs.LG stat.ML | In nonlinear latent variable models or dynamic models, if we consider the
latent variables as confounders (common causes), the noise dependencies imply
further relations between the observed variables. Such models are then closely
related to causal discovery in the presence of nonlinear confounders, which is
a challenging problem. However, generally in such models the observation noise
is assumed to be independent across data dimensions, and consequently the noise
dependencies are ignored. In this paper we focus on the Gaussian process latent
variable model (GPLVM), from which we develop an extended model called
invariant GPLVM (IGPLVM), which can adapt to arbitrary noise covariances. With
the Gaussian process prior put on a particular transformation of the latent
nonlinear functions, instead of the original ones, the algorithm for IGPLVM
involves almost the same computational loads as that for the original GPLVM.
Besides its potential application in causal discovery, IGPLVM has the advantage
that its estimated latent nonlinear manifold is invariant to any nonsingular
linear transformation of the data. Experimental results on both synthetic and
realworld data show its encouraging performance in nonlinear manifold learning
and causal discovery.
| Kun Zhang, Bernhard Schoelkopf, Dominik Janzing | null | 1203.3534 | null | null |
A Convex Formulation for Learning Task Relationships in Multi-Task
Learning | cs.LG cs.AI stat.ML | Multi-task learning is a learning paradigm which seeks to improve the
generalization performance of a learning task with the help of some other
related tasks. In this paper, we propose a regularization formulation for
learning the relationships between tasks in multi-task learning. This
formulation can be viewed as a novel generalization of the regularization
framework for single-task learning. Besides modeling positive task correlation,
our method, called multi-task relationship learning (MTRL), can also describe
negative task correlation and identify outlier tasks based on the same
underlying principle. Under this regularization framework, the objective
function of MTRL is convex. For efficiency, we use an alternating method to
learn the optimal model parameters for each task as well as the relationships
between tasks. We study MTRL in the symmetric multi-task learning setting and
then generalize it to the asymmetric setting as well. We also study the
relationships between MTRL and some existing multi-task learning methods.
Experiments conducted on a toy problem as well as several benchmark data sets
demonstrate the effectiveness of MTRL.
| Yu Zhang, Dit-Yan Yeung | null | 1203.3536 | null | null |
Automatic Tuning of Interactive Perception Applications | cs.LG cs.CV stat.ML | Interactive applications incorporating high-data rate sensing and computer
vision are becoming possible due to novel runtime systems and the use of
parallel computation resources. To allow interactive use, such applications
require careful tuning of multiple application parameters to meet required
fidelity and latency bounds. This is a nontrivial task, often requiring expert
knowledge, which becomes intractable as resources and application load
characteristics change. This paper describes a method for automatic performance
tuning that learns application characteristics and effects of tunable
parameters online, and constructs models that are used to maximize fidelity for
a given latency constraint. The paper shows that accurate latency models can be
learned online, knowledge of application structure can be used to reduce the
complexity of the learning task, and operating points can be found that achieve
90% of the optimal fidelity by exploring the parameter space only 3% of the
time.
| Qian Zhu, Branislav Kveton, Lily Mummert, Padmanabhan Pillai | null | 1203.3537 | null | null |
Learning Feature Hierarchies with Centered Deep Boltzmann Machines | stat.ML cs.AI cs.LG | Deep Boltzmann machines are in principle powerful models for extracting the
hierarchical structure of data. Unfortunately, attempts to train layers jointly
(without greedy layer-wise pretraining) have been largely unsuccessful. We
propose a modification of the learning algorithm that initially recenters the
output of the activation functions to zero. This modification leads to a better
conditioned Hessian and thus makes learning easier. We test the algorithm on
real data and demonstrate that our suggestion, the centered deep Boltzmann
machine, learns a hierarchy of increasingly abstract representations and a
better generative model of data.
| Gr\'egoire Montavon and Klaus-Robert M\"uller | 10.1007/978-3-642-35289-8_33 | 1203.3783 | null | null |
Data Mining: A Prediction for Performance Improvement of Engineering
Students using Classification | cs.LG | Now-a-days the amount of data stored in educational database increasing
rapidly. These databases contain hidden information for improvement of
students' performance. Educational data mining is used to study the data
available in the educational field and bring out the hidden knowledge from it.
Classification methods like decision trees, Bayesian network etc can be applied
on the educational data for predicting the student's performance in
examination. This prediction will help to identify the weak students and help
them to score better marks. The C4.5, ID3 and CART decision tree algorithms are
applied on engineering student's data to predict their performance in the final
exam. The outcome of the decision tree predicted the number of students who are
likely to pass, fail or promoted to next year. The results provide steps to
improve the performance of the students who were predicted to fail or promoted.
After the declaration of the results in the final examination the marks
obtained by the students are fed into the system and the results were analyzed
for the next session. The comparative analysis of the results states that the
prediction has helped the weaker students to improve and brought out betterment
in the result.
| Surjeet Kumar Yadav and Saurabh Pal | null | 1203.3832 | null | null |
Learning loopy graphical models with latent variables: Efficient methods
and guarantees | stat.ML cs.AI cs.LG math.ST stat.TH | The problem of structure estimation in graphical models with latent variables
is considered. We characterize conditions for tractable graph estimation and
develop efficient methods with provable guarantees. We consider models where
the underlying Markov graph is locally tree-like, and the model is in the
regime of correlation decay. For the special case of the Ising model, the
number of samples $n$ required for structural consistency of our method scales
as $n=\Omega(\theta_{\min}^{-\delta\eta(\eta+1)-2}\log p)$, where p is the
number of variables, $\theta_{\min}$ is the minimum edge potential, $\delta$ is
the depth (i.e., distance from a hidden node to the nearest observed nodes),
and $\eta$ is a parameter which depends on the bounds on node and edge
potentials in the Ising model. Necessary conditions for structural consistency
under any algorithm are derived and our method nearly matches the lower bound
on sample requirements. Further, the proposed method is practical to implement
and provides flexibility to control the number of latent variables and the
cycle lengths in the output graph.
| Animashree Anandkumar, Ragupathyraj Valluvan | 10.1214/12-AOS1070 | 1203.3887 | null | null |
Distributed Cooperative Q-learning for Power Allocation in Cognitive
Femtocell Networks | cs.LG cs.GT | In this paper, we propose a distributed reinforcement learning (RL) technique
called distributed power control using Q-learning (DPC-Q) to manage the
interference caused by the femtocells on macro-users in the downlink. The DPC-Q
leverages Q-Learning to identify the sub-optimal pattern of power allocation,
which strives to maximize femtocell capacity, while guaranteeing macrocell
capacity level in an underlay cognitive setting. We propose two different
approaches for the DPC-Q algorithm: namely, independent, and cooperative. In
the former, femtocells learn independently from each other while in the latter,
femtocells share some information during learning in order to enhance their
performance. Simulation results show that the independent approach is capable
of mitigating the interference generated by the femtocells on macro-users.
Moreover, the results show that cooperation enhances the performance of the
femtocells in terms of speed of convergence, fairness and aggregate femtocell
capacity.
| Hussein Saad, Amr Mohamed and Tamer ElBatt | null | 1203.3935 | null | null |
On Training Deep Boltzmann Machines | cs.NE cs.AI cs.LG | The deep Boltzmann machine (DBM) has been an important development in the
quest for powerful "deep" probabilistic models. To date, simultaneous or joint
training of all layers of the DBM has been largely unsuccessful with existing
training methods. We introduce a simple regularization scheme that encourages
the weight vectors associated with each hidden unit to have similar norms. We
demonstrate that this regularization can be easily combined with standard
stochastic maximum likelihood to yield an effective training strategy for the
simultaneous training of all layers of the deep Boltzmann machine.
| Guillaume Desjardins and Aaron Courville and Yoshua Bengio | null | 1203.4416 | null | null |
Semi-Supervised Single- and Multi-Domain Regression with Multi-Domain
Training | stat.ML cs.LG | We address the problems of multi-domain and single-domain regression based on
distinct and unpaired labeled training sets for each of the domains and a large
unlabeled training set from all domains. We formulate these problems as a
Bayesian estimation with partial knowledge of statistical relations. We propose
a worst-case design strategy and study the resulting estimators. Our analysis
explicitly accounts for the cardinality of the labeled sets and includes the
special cases in which one of the labeled sets is very large or, in the other
extreme, completely missing. We demonstrate our estimators in the context of
removing expressions from facial images and in the context of audio-visual word
recognition, and provide comparisons to several recently proposed multi-modal
learning algorithms.
| Tomer Michaeli, Yonina C. Eldar, Guillermo Sapiro | null | 1203.4422 | null | null |
On the Equivalence between Herding and Conditional Gradient Algorithms | cs.LG math.OC stat.ML | We show that the herding procedure of Welling (2009) takes exactly the form
of a standard convex optimization algorithm--namely a conditional gradient
algorithm minimizing a quadratic moment discrepancy. This link enables us to
invoke convergence results from convex optimization and to consider faster
alternatives for the task of approximating integrals in a reproducing kernel
Hilbert space. We study the behavior of the different variants through
numerical simulations. The experiments indicate that while we can improve over
herding on the task of approximating integrals, the original herding algorithm
tends to approach more often the maximum entropy distribution, shedding more
light on the learning bias behind herding.
| Francis Bach (INRIA Paris - Rocquencourt, LIENS), Simon Lacoste-Julien
(INRIA Paris - Rocquencourt, LIENS), Guillaume Obozinski (INRIA Paris -
Rocquencourt, LIENS) | null | 1203.4523 | null | null |
A Novel Training Algorithm for HMMs with Partial and Noisy Access to the
States | cs.LG stat.ML | This paper proposes a new estimation algorithm for the parameters of an HMM
as to best account for the observed data. In this model, in addition to the
observation sequence, we have \emph{partial} and \emph{noisy} access to the
hidden state sequence as side information. This access can be seen as "partial
labeling" of the hidden states. Furthermore, we model possible mislabeling in
the side information in a joint framework and derive the corresponding EM
updates accordingly. In our simulations, we observe that using this side
information, we considerably improve the state recognition performance, up to
70%, with respect to the "achievable margin" defined by the baseline
algorithms. Moreover, our algorithm is shown to be robust to the training
conditions.
| Huseyin Ozkan, Arda Akman, Suleyman S. Kozat | null | 1203.4597 | null | null |
Adaptive Mixture Methods Based on Bregman Divergences | cs.LG | We investigate adaptive mixture methods that linearly combine outputs of $m$
constituent filters running in parallel to model a desired signal. We use
"Bregman divergences" and obtain certain multiplicative updates to train the
linear combination weights under an affine constraint or without any
constraints. We use unnormalized relative entropy and relative entropy to
define two different Bregman divergences that produce an unnormalized
exponentiated gradient update and a normalized exponentiated gradient update on
the mixture weights, respectively. We then carry out the mean and the
mean-square transient analysis of these adaptive algorithms when they are used
to combine outputs of $m$ constituent filters. We illustrate the accuracy of
our results and demonstrate the effectiveness of these updates for sparse
mixture systems.
| Mehmet A. Donmez, Huseyin A. Inan, Suleyman S. Kozat | 10.1016/j.dsp.2012.09.006 | 1203.4598 | null | null |
Very Short Literature Survey From Supervised Learning To Surrogate
Modeling | cs.LG | The past century was era of linear systems. Either systems (especially
industrial ones) were simple (quasi)linear or linear approximations were
accurate enough. In addition, just at the ending decades of the century
profusion of computing devices were available, before then due to lack of
computational resources it was not easy to evaluate available nonlinear system
studies. At the moment both these two conditions changed, systems are highly
complex and also pervasive amount of computation strength is cheap and easy to
achieve. For recent era, a new branch of supervised learning well known as
surrogate modeling (meta-modeling, surface modeling) has been devised which
aimed at answering new needs of modeling realm. This short literature survey is
on to introduce surrogate modeling to whom is familiar with the concepts of
supervised learning. Necessity, challenges and visions of the topic are
considered.
| Altay Brusan | null | 1203.4788 | null | null |
Parallel Matrix Factorization for Binary Response | cs.LG stat.AP | Predicting user affinity to items is an important problem in applications
like content optimization, computational advertising, and many more. While
bilinear random effect models (matrix factorization) provide state-of-the-art
performance when minimizing RMSE through a Gaussian response model on explicit
ratings data, applying it to imbalanced binary response data presents
additional challenges that we carefully study in this paper. Data in many
applications usually consist of users' implicit response that are often binary
-- clicking an item or not; the goal is to predict click rates, which is often
combined with other measures to calculate utilities to rank items at runtime of
the recommender systems. Because of the implicit nature, such data are usually
much larger than explicit rating data and often have an imbalanced distribution
with a small fraction of click events, making accurate click rate prediction
difficult. In this paper, we address two problems. First, we show previous
techniques to estimate bilinear random effect models with binary data are less
accurate compared to our new approach based on adaptive rejection sampling,
especially for imbalanced response. Second, we develop a parallel bilinear
random effect model fitting framework using Map-Reduce paradigm that scales to
massive datasets. Our parallel algorithm is based on a "divide and conquer"
strategy coupled with an ensemble approach. Through experiments on the
benchmark MovieLens data, a small Yahoo! Front Page data set, and a large
Yahoo! Front Page data set that contains 8M users and 1B binary observations,
we show that careful handling of binary response as well as identifiability
issues are needed to achieve good performance for click rate prediction, and
that the proposed adaptive rejection sampler and the partitioning as well as
ensemble techniques significantly improve model performance.
| Rajiv Khanna, Liang Zhang, Deepak Agarwal, Beechung Chen | null | 1203.5124 | null | null |
$k$-MLE: A fast algorithm for learning statistical mixture models | cs.LG stat.ML | We describe $k$-MLE, a fast and efficient local search algorithm for learning
finite statistical mixtures of exponential families such as Gaussian mixture
models. Mixture models are traditionally learned using the
expectation-maximization (EM) soft clustering technique that monotonically
increases the incomplete (expected complete) likelihood. Given prescribed
mixture weights, the hard clustering $k$-MLE algorithm iteratively assigns data
to the most likely weighted component and update the component models using
Maximum Likelihood Estimators (MLEs). Using the duality between exponential
families and Bregman divergences, we prove that the local convergence of the
complete likelihood of $k$-MLE follows directly from the convergence of a dual
additively weighted Bregman hard clustering. The inner loop of $k$-MLE can be
implemented using any $k$-means heuristic like the celebrated Lloyd's batched
or Hartigan's greedy swap updates. We then show how to update the mixture
weights by minimizing a cross-entropy criterion that implies to update weights
by taking the relative proportion of cluster points, and reiterate the mixture
parameter update and mixture weight update processes until convergence. Hard EM
is interpreted as a special case of $k$-MLE when both the component update and
the weight update are performed successively in the inner loop. To initialize
$k$-MLE, we propose $k$-MLE++, a careful initialization of $k$-MLE guaranteeing
probabilistically a global bound on the best possible complete likelihood.
| Frank Nielsen | 10.1109/ICASSP.2012.6288022 | 1203.5181 | null | null |
Distribution Free Prediction Bands | stat.ME cs.LG math.ST stat.TH | We study distribution free, nonparametric prediction bands with a special
focus on their finite sample behavior. First we investigate and develop
different notions of finite sample coverage guarantees. Then we give a new
prediction band estimator by combining the idea of "conformal prediction" (Vovk
et al. 2009) with nonparametric conditional density estimation. The proposed
estimator, called COPS (Conformal Optimized Prediction Set), always has finite
sample guarantee in a stronger sense than the original conformal prediction
estimator. Under regularity conditions the estimator converges to an oracle
band at a minimax optimal rate. A fast approximation algorithm and a data
driven method for selecting the bandwidth are developed. The method is
illustrated first in simulated data. Then, an application shows that the
proposed method gives desirable prediction intervals in an automatic way, as
compared to the classical linear regression modeling.
| Jing Lei and Larry Wasserman | null | 1203.5422 | null | null |
A Regularization Approach for Prediction of Edges and Node Features in
Dynamic Graphs | cs.LG stat.ML | We consider the two problems of predicting links in a dynamic graph sequence
and predicting functions defined at each node of the graph. In many
applications, the solution of one problem is useful for solving the other.
Indeed, if these functions reflect node features, then they are related through
the graph structure. In this paper, we formulate a hybrid approach that
simultaneously learns the structure of the graph and predicts the values of the
node-related functions. Our approach is based on the optimization of a joint
regularization objective. We empirically test the benefits of the proposed
method with both synthetic and real data. The results indicate that joint
regularization improves prediction performance over the graph evolution and the
node features.
| Emile Richard, Andreas Argyriou, Theodoros Evgeniou and Nicolas
Vayatis | null | 1203.5438 | null | null |
Transfer Learning, Soft Distance-Based Bias, and the Hierarchical BOA | cs.NE cs.AI cs.LG | An automated technique has recently been proposed to transfer learning in the
hierarchical Bayesian optimization algorithm (hBOA) based on distance-based
statistics. The technique enables practitioners to improve hBOA efficiency by
collecting statistics from probabilistic models obtained in previous hBOA runs
and using the obtained statistics to bias future hBOA runs on similar problems.
The purpose of this paper is threefold: (1) test the technique on several
classes of NP-complete problems, including MAXSAT, spin glasses and minimum
vertex cover; (2) demonstrate that the technique is effective even when
previous runs were done on problems of different size; (3) provide empirical
evidence that combining transfer learning with other efficiency enhancement
techniques can often yield nearly multiplicative speedups.
| Martin Pelikan, Mark W. Hauschild, and Pier Luca Lanzi | null | 1203.5443 | null | null |
A Bayesian Model Committee Approach to Forecasting Global Solar
Radiation | stat.AP cs.LG | This paper proposes to use a rather new modelling approach in the realm of
solar radiation forecasting. In this work, two forecasting models:
Autoregressive Moving Average (ARMA) and Neural Network (NN) models are
combined to form a model committee. The Bayesian inference is used to affect a
probability to each model in the committee. Hence, each model's predictions are
weighted by their respective probability. The models are fitted to one year of
hourly Global Horizontal Irradiance (GHI) measurements. Another year (the test
set) is used for making genuine one hour ahead (h+1) out-of-sample forecast
comparisons. The proposed approach is benchmarked against the persistence
model. The very first results show an improvement brought by this approach.
| Philippe Lauret (PIMENT), Auline Rodler (SPE), Marc Muselli (SPE),
Mathieu David (PIMENT), Hadja Diagne (PIMENT), Cyril Voyant (SPE, CHD
Castellucio) | null | 1203.5446 | null | null |
Credal Classification based on AODE and compression coefficients | cs.LG | Bayesian model averaging (BMA) is an approach to average over alternative
models; yet, it usually gets excessively concentrated around the single most
probable model, therefore achieving only sub-optimal classification
performance. The compression-based approach (Boulle, 2007) overcomes this
problem, averaging over the different models by applying a logarithmic
smoothing over the models' posterior probabilities. This approach has shown
excellent performances when applied to ensembles of naive Bayes classifiers.
AODE is another ensemble of models with high performance (Webb, 2005), based on
a collection of non-naive classifiers (called SPODE) whose probabilistic
predictions are aggregated by simple arithmetic mean. Aggregating the SPODEs
via BMA rather than by arithmetic mean deteriorates the performance; instead,
we aggregate the SPODEs via the compression coefficients and we show that the
resulting classifier obtains a slight but consistent improvement over AODE.
However, an important issue in any Bayesian ensemble of models is the
arbitrariness in the choice of the prior over the models. We address this
problem by the paradigm of credal classification, namely by substituting the
unique prior with a set of priors. Credal classifier automatically recognize
the prior-dependent instances, namely the instances whose most probable class
varies, when different priors are considered; in these cases, credal
classifiers remain reliable by returning a set of classes rather than a single
class. We thus develop the credal version of both the BMA-based and the
compression-based ensemble of SPODEs, substituting the single prior over the
models by a set of priors. Experiments show that both credal classifiers
provide higher classification reliability than their determinate counterparts;
moreover the compression-based credal classifier compares favorably to previous
credal classifiers.
| Giorgio Corani and Alessandro Antonucci | null | 1203.5716 | null | null |
Spectral dimensionality reduction for HMMs | stat.ML cs.LG | Hidden Markov Models (HMMs) can be accurately approximated using
co-occurrence frequencies of pairs and triples of observations by using a fast
spectral method in contrast to the usual slow methods like EM or Gibbs
sampling. We provide a new spectral method which significantly reduces the
number of model parameters that need to be estimated, and generates a sample
complexity that does not depend on the size of the observation vocabulary. We
present an elementary proof giving bounds on the relative accuracy of
probability estimates from our model. (Correlaries show our bounds can be
weakened to provide either L1 bounds or KL bounds which provide easier direct
comparisons to previous work.) Our theorem uses conditions that are checkable
from the data, instead of putting conditions on the unobservable Markov
transition matrix.
| Dean P. Foster, Jordan Rodu, Lyle H. Ungar | null | 1203.6130 | null | null |
Statistical Mechanics of Dictionary Learning | cond-mat.dis-nn cond-mat.stat-mech cs.IT cs.LG math.IT | Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations.
| Ayaka Sakata and Yoshiyuki Kabashima | 10.1209/0295-5075/103/28008 | 1203.6178 | null | null |
Transforming Graph Representations for Statistical Relational Learning | stat.ML cs.AI cs.LG cs.SI | Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed.
| Ryan A. Rossi, Luke K. McDowell, David W. Aha and Jennifer Neville | null | 1204.0033 | null | null |
A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization | cs.LG stat.ML | The problem of optimizing unknown costly-to-evaluate functions has been
studied for a long time in the context of Bayesian Optimization. Algorithms in
this field aim to find the optimizer of the function by asking only a few
function evaluations at locations carefully selected based on a posterior
model. In this paper, we assume the unknown function is Lipschitz continuous.
Leveraging the Lipschitz property, we propose an algorithm with a distinct
exploration phase followed by an exploitation phase. The exploration phase aims
to select samples that shrink the search space as much as possible. The
exploitation phase then focuses on the reduced search space and selects samples
closest to the optimizer. Considering the Expected Improvement (EI) as a
baseline, we empirically show that the proposed algorithm significantly
outperforms EI.
| Ali Jalali, Javad Azimi, Xiaoli Fern and Ruofei Zhang | null | 1204.0047 | null | null |
Near-Optimal Algorithms for Online Matrix Prediction | cs.LG cs.DS | In several online prediction problems of recent interest the comparison class
is composed of matrices with bounded entries. For example, in the online
max-cut problem, the comparison class is matrices which represent cuts of a
given graph and in online gambling the comparison class is matrices which
represent permutations over n teams. Another important example is online
collaborative filtering in which a widely used comparison class is the set of
matrices with a small trace norm. In this paper we isolate a property of
matrices, which we call (beta,tau)-decomposability, and derive an efficient
online learning algorithm, that enjoys a regret bound of O*(sqrt(beta tau T))
for all problems in which the comparison class is composed of
(beta,tau)-decomposable matrices. By analyzing the decomposability of cut
matrices, triangular matrices, and low trace-norm matrices, we derive near
optimal regret bounds for online max-cut, online gambling, and online
collaborative filtering. In particular, this resolves (in the affirmative) an
open problem posed by Abernethy (2010); Kleinberg et al (2010). Finally, we
derive lower bounds for the three problems and show that our upper bounds are
optimal up to logarithmic factors. In particular, our lower bound for the
online collaborative filtering problem resolves another open problem posed by
Shamir and Srebro (2011).
| Elad Hazan, Satyen Kale, Shai Shalev-Shwartz | null | 1204.0136 | null | null |
A New Approach to Speeding Up Topic Modeling | cs.LG cs.IR | Latent Dirichlet allocation (LDA) is a widely-used probabilistic topic
modeling paradigm, and recently finds many applications in computer vision and
computational biology. In this paper, we propose a fast and accurate batch
algorithm, active belief propagation (ABP), for training LDA. Usually batch LDA
algorithms require repeated scanning of the entire corpus and searching the
complete topic space. To process massive corpora having a large number of
topics, the training iteration of batch LDA algorithms is often inefficient and
time-consuming. To accelerate the training speed, ABP actively scans the subset
of corpus and searches the subset of topic space for topic modeling, therefore
saves enormous training time in each iteration. To ensure accuracy, ABP selects
only those documents and topics that contribute to the largest residuals within
the residual belief propagation (RBP) framework. On four real-world corpora,
ABP performs around $10$ to $100$ times faster than state-of-the-art batch LDA
algorithms with a comparable topic modeling accuracy.
| Jia Zeng, Zhi-Qiang Liu and Xiao-Qin Cao | null | 1204.0170 | null | null |
A New Fuzzy Stacked Generalization Technique and Analysis of its
Performance | cs.LG cs.CV | In this study, a new Stacked Generalization technique called Fuzzy Stacked
Generalization (FSG) is proposed to minimize the difference between N -sample
and large-sample classification error of the Nearest Neighbor classifier. The
proposed FSG employs a new hierarchical distance learning strategy to minimize
the error difference. For this purpose, we first construct an ensemble of
base-layer fuzzy k- Nearest Neighbor (k-NN) classifiers, each of which receives
a different feature set extracted from the same sample set. The fuzzy
membership values computed at the decision space of each fuzzy k-NN classifier
are concatenated to form the feature vectors of a fusion space. Finally, the
feature vectors are fed to a meta-layer classifier to learn the degree of
accuracy of the decisions of the base-layer classifiers for meta-layer
classification. Rather than the power of the individual base layer-classifiers,
diversity and cooperation of the classifiers become an important issue to
improve the overall performance of the proposed FSG. A weak base-layer
classifier may boost the overall performance more than a strong classifier, if
it is capable of recognizing the samples, which are not recognized by the rest
of the classifiers, in its own feature space. The experiments explore the type
of the collaboration among the individual classifiers required for an improved
performance of the suggested architecture. Experiments on multiple feature
real-world datasets show that the proposed FSG performs better than the state
of the art ensemble learning algorithms such as Adaboost, Random Subspace and
Rotation Forest. On the other hand, compatible performances are observed in the
experiments on single feature multi-attribute datasets.
| Mete Ozay, Fatos T. Yarman Vural | null | 1204.0171 | null | null |
The Kernelized Stochastic Batch Perceptron | cs.LG | We present a novel approach for training kernel Support Vector Machines,
establish learning runtime guarantees for our method that are better then those
of any other known kernelized SVM optimization approach, and show that our
method works well in practice compared to existing alternatives.
| Andrew Cotter, Shai Shalev-Shwartz, Nathan Srebro | null | 1204.0566 | null | null |
Validation of nonlinear PCA | cs.LG cs.AI cs.CV stat.ML | Linear principal component analysis (PCA) can be extended to a nonlinear PCA
by using artificial neural networks. But the benefit of curved components
requires a careful control of the model complexity. Moreover, standard
techniques for model selection, including cross-validation and more generally
the use of an independent test set, fail when applied to nonlinear PCA because
of its inherent unsupervised characteristics. This paper presents a new
approach for validating the complexity of nonlinear PCA models by using the
error in missing data estimation as a criterion for model selection. It is
motivated by the idea that only the model of optimal complexity is able to
predict missing values with the highest accuracy. While standard test set
validation usually favours over-fitted nonlinear PCA models, the proposed model
validation approach correctly selects the optimal model complexity.
| Matthias Scholz | 10.1007/s11063-012-9220-6 | 1204.0684 | null | null |
Relax and Localize: From Value to Algorithms | cs.LG cs.GT stat.ML | We show a principled way of deriving online learning algorithms from a
minimax analysis. Various upper bounds on the minimax value, previously thought
to be non-constructive, are shown to yield algorithms. This allows us to
seamlessly recover known methods and to derive new ones. Our framework also
captures such "unorthodox" methods as Follow the Perturbed Leader and the R^2
forecaster. We emphasize that understanding the inherent complexity of the
learning problem leads to the development of algorithms.
We define local sequential Rademacher complexities and associated algorithms
that allow us to obtain faster rates in online learning, similarly to
statistical learning theory. Based on these localized complexities we build a
general adaptive method that can take advantage of the suboptimality of the
observed sequence.
We present a number of new algorithms, including a family of randomized
methods that use the idea of a "random playout". Several new versions of the
Follow-the-Perturbed-Leader algorithms are presented, as well as methods based
on the Littlestone's dimension, efficient methods for matrix completion with
trace norm, and algorithms for the problems of transductive learning and
prediction with static experts.
| Alexander Rakhlin, Ohad Shamir, Karthik Sridharan | null | 1204.0870 | null | null |
PID Parameters Optimization by Using Genetic Algorithm | cs.SY cs.LG cs.NE | Time delays are components that make time-lag in systems response. They arise
in physical, chemical, biological and economic systems, as well as in the
process of measurement and computation. In this work, we implement Genetic
Algorithm (GA) in determining PID controller parameters to compensate the delay
in First Order Lag plus Time Delay (FOLPD) and compare the results with
Iterative Method and Ziegler-Nichols rule results.
| Andri Mirzal, Shinichiro Yoshii, Masashi Furukawa | null | 1204.0885 | null | null |
Fast ALS-based tensor factorization for context-aware recommendation
from implicit feedback | cs.LG cs.IR cs.NA | Albeit, the implicit feedback based recommendation problem - when only the
user history is available but there are no ratings - is the most typical
setting in real-world applications, it is much less researched than the
explicit feedback case. State-of-the-art algorithms that are efficient on the
explicit case cannot be straightforwardly transformed to the implicit case if
scalability should be maintained. There are few if any implicit feedback
benchmark datasets, therefore new ideas are usually experimented on explicit
benchmarks. In this paper, we propose a generic context-aware implicit feedback
recommender algorithm, coined iTALS. iTALS apply a fast, ALS-based tensor
factorization learning method that scales linearly with the number of non-zero
elements in the tensor. The method also allows us to incorporate diverse
context information into the model while maintaining its computational
efficiency. In particular, we present two such context-aware implementation
variants of iTALS. The first incorporates seasonality and enables to
distinguish user behavior in different time intervals. The other views the user
history as sequential information and has the ability to recognize usage
pattern typical to certain group of items, e.g. to automatically tell apart
product types or categories that are typically purchased repetitively
(collectibles, grocery goods) or once (household appliances). Experiments
performed on three implicit datasets (two proprietary ones and an implicit
variant of the Netflix dataset) show that by integrating context-aware
information with our factorization framework into the state-of-the-art implicit
recommender algorithm the recommendation quality improves significantly.
| Bal\'azs Hidasi, Domonkos Tikk | 10.1007/978-3-642-33486-3_5 | 1204.1259 | null | null |
Distribution-Dependent Sample Complexity of Large Margin Learning | stat.ML cs.LG | We obtain a tight distribution-specific characterization of the sample
complexity of large-margin classification with L2 regularization: We introduce
the margin-adapted dimension, which is a simple function of the second order
statistics of the data distribution, and show distribution-specific upper and
lower bounds on the sample complexity, both governed by the margin-adapted
dimension of the data distribution. The upper bounds are universal, and the
lower bounds hold for the rich family of sub-Gaussian distributions with
independent features. We conclude that this new quantity tightly characterizes
the true sample complexity of large-margin classification. To prove the lower
bound, we develop several new tools of independent interest. These include new
connections between shattering and hardness of learning, new properties of
shattering with linear classifiers, and a new lower bound on the smallest
eigenvalue of a random Gram matrix generated by sub-Gaussian variables. Our
results can be used to quantitatively compare large margin learning to other
learning rules, and to improve the effectiveness of methods that use sample
complexity bounds, such as active learning.
| Sivan Sabato, Nathan Srebro and Naftali Tishby | null | 1204.1276 | null | null |
Fast projections onto mixed-norm balls with applications | stat.ML cs.LG math.OC | Joint sparsity offers powerful structural cues for feature selection,
especially for variables that are expected to demonstrate a "grouped" behavior.
Such behavior is commonly modeled via group-lasso, multitask lasso, and related
methods where feature selection is effected via mixed-norms. Several mixed-norm
based sparse models have received substantial attention, and for some cases
efficient algorithms are also available. Surprisingly, several constrained
sparse models seem to be lacking scalable algorithms. We address this
deficiency by presenting batch and online (stochastic-gradient) optimization
methods, both of which rely on efficient projections onto mixed-norm balls. We
illustrate our methods by applying them to the multitask lasso. We conclude by
mentioning some open problems.
| Suvrit Sra | null | 1204.1437 | null | null |
Learning Fuzzy {\beta}-Certain and {\beta}-Possible rules from
incomplete quantitative data by rough sets | cs.DS cs.LG | The rough-set theory proposed by Pawlak, has been widely used in dealing with
data classification problems. The original rough-set model is, however, quite
sensitive to noisy data. Tzung thus proposed deals with the problem of
producing a set of fuzzy certain and fuzzy possible rules from quantitative
data with a predefined tolerance degree of uncertainty and misclassification.
This model allowed, which combines the variable precision rough-set model and
the fuzzy set theory, is thus proposed to solve this problem. This paper thus
deals with the problem of producing a set of fuzzy certain and fuzzy possible
rules from incomplete quantitative data with a predefined tolerance degree of
uncertainty and misclassification. A new method, incomplete quantitative data
for rough-set model and the fuzzy set theory, is thus proposed to solve this
problem. It first transforms each quantitative value into a fuzzy set of
linguistic terms using membership functions and then finding incomplete
quantitative data with lower and the fuzzy upper approximations. It second
calculates the fuzzy {\beta}-lower and the fuzzy {\beta}-upper approximations.
The certain and possible rules are then generated based on these fuzzy
approximations. These rules can then be used to classify unknown objects.
| Ali Soltan Mohammadi and L. Asadzadeh and D. D. Rezaee | null | 1204.1467 | null | null |
Minimal model of associative learning for cross-situational lexicon
acquisition | q-bio.NC cs.LG | An explanation for the acquisition of word-object mappings is the associative
learning in a cross-situational scenario. Here we present analytical results of
the performance of a simple associative learning algorithm for acquiring a
one-to-one mapping between $N$ objects and $N$ words based solely on the
co-occurrence between objects and words. In particular, a learning trial in our
learning scenario consists of the presentation of $C + 1 < N$ objects together
with a target word, which refers to one of the objects in the context. We find
that the learning times are distributed exponentially and the learning rates
are given by $\ln{[\frac{N(N-1)}{C + (N-1)^{2}}]}$ in the case the $N$ target
words are sampled randomly and by $\frac{1}{N} \ln [\frac{N-1}{C}] $ in the
case they follow a deterministic presentation sequence. This learning
performance is much superior to those exhibited by humans and more realistic
learning algorithms in cross-situational experiments. We show that introduction
of discrimination limitations using Weber's law and forgetting reduce the
performance of the associative algorithm to the human level.
| Paulo F. C. Tilles and Jose F. Fontanari | 10.1016/j.jmp.2012.11.002 | 1204.1564 | null | null |
UCB Algorithm for Exponential Distributions | stat.ML cs.LG | We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB)
problems. A machine learning paradigm popular within Cognitive Network related
topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the
rewards are exponentially distributed, which is common when dealing with
Rayleigh fading channels. This strategy, named Multiplicative Upper Confidence
Bound (MUCB), associates a utility index to every available arm, and then
selects the arm with the highest index. For every arm, the associated index is
equal to the product of a multiplicative factor by the sample mean of the
rewards collected by this arm. We show that the MUCB policy has a low
complexity and is order optimal.
| Wassim Jouini and Christophe Moy | null | 1204.1624 | null | null |
The threshold EM algorithm for parameter learning in bayesian network
with incomplete data | cs.AI cs.LG stat.ML | Bayesian networks (BN) are used in a big range of applications but they have
one issue concerning parameter learning. In real application, training data are
always incomplete or some nodes are hidden. To deal with this problem many
learning parameter algorithms are suggested foreground EM, Gibbs sampling and
RBE algorithms. In order to limit the search space and escape from local maxima
produced by executing EM algorithm, this paper presents a learning parameter
algorithm that is a fusion of EM and RBE algorithms. This algorithm
incorporates the range of a parameter into the EM algorithm. This range is
calculated by the first step of RBE algorithm allowing a regularization of each
parameter in bayesian network after the maximization step of the EM algorithm.
The threshold EM algorithm is applied in brain tumor diagnosis and show some
advantages and disadvantages over the EM algorithm.
| Fradj Ben Lamine, Karim Kalti, Mohamed Ali Mahjoub | null | 1204.1681 | null | null |
Density-sensitive semisupervised inference | math.ST cs.LG stat.ML stat.TH | Semisupervised methods are techniques for using labeled data
$(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$
to make predictions. These methods invoke some assumptions that link the
marginal distribution $P_X$ of X to the regression function f(x). For example,
it is common to assume that f is very smooth over high density regions of
$P_X$. Many of the methods are ad-hoc and have been shown to work in specific
examples but are lacking a theoretical foundation. We provide a minimax
framework for analyzing semisupervised methods. In particular, we study methods
based on metrics that are sensitive to the distribution $P_X$. Our model
includes a parameter $\alpha$ that controls the strength of the semisupervised
assumption. We then use the data to adapt to $\alpha$.
| Martin Azizyan, Aarti Singh, Larry Wasserman | 10.1214/13-AOS1092 | 1204.1685 | null | null |
The asymptotics of ranking algorithms | math.ST cs.LG stat.ML stat.TH | We consider the predictive problem of supervised ranking, where the task is
to rank sets of candidate items returned in response to queries. Although there
exist statistical procedures that come with guarantees of consistency in this
setting, these procedures require that individuals provide a complete ranking
of all items, which is rarely feasible in practice. Instead, individuals
routinely provide partial preference information, such as pairwise comparisons
of items, and more practical approaches to ranking have aimed at modeling this
partial preference data directly. As we show, however, such an approach raises
serious theoretical challenges. Indeed, we demonstrate that many commonly used
surrogate losses for pairwise comparison data do not yield consistency;
surprisingly, we show inconsistency even in low-noise settings. With these
negative results as motivation, we present a new approach to supervised ranking
based on aggregation of partial preferences, and we develop $U$-statistic-based
empirical risk minimization procedures. We present an asymptotic analysis of
these new procedures, showing that they yield consistency results that parallel
those available for classification. We complement our theoretical results with
an experiment studying the new procedures in a large-scale web-ranking task.
| John C. Duchi, Lester Mackey, Michael I. Jordan | 10.1214/13-AOS1142 | 1204.1688 | null | null |
On Power-law Kernels, corresponding Reproducing Kernel Hilbert Space and
Applications | cs.LG cs.IT math.IT stat.ML | The role of kernels is central to machine learning. Motivated by the
importance of power-law distributions in statistical modeling, in this paper,
we propose the notion of power-law kernels to investigate power-laws in
learning problem. We propose two power-law kernels by generalizing Gaussian and
Laplacian kernels. This generalization is based on distributions, arising out
of maximization of a generalized information measure known as nonextensive
entropy that is very well studied in statistical mechanics. We prove that the
proposed kernels are positive definite, and provide some insights regarding the
corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical
significance of both kernels in classification and regression, and present some
simulation results.
| Debarghya Ghoshdastidar and Ambedkar Dukkipati | null | 1204.1800 | null | null |
Knapsack based Optimal Policies for Budget-Limited Multi-Armed Bandits | cs.AI cs.LG | In budget-limited multi-armed bandit (MAB) problems, the learner's actions
are costly and constrained by a fixed budget. Consequently, an optimal
exploitation policy may not be to pull the optimal arm repeatedly, as is the
case in other variants of MAB, but rather to pull the sequence of different
arms that maximises the agent's total reward within the budget. This difference
from existing MABs means that new approaches to maximising the total reward are
required. Given this, we develop two pulling policies, namely: (i) KUBE; and
(ii) fractional KUBE. Whereas the former provides better performance up to 40%
in our experimental settings, the latter is computationally less expensive. We
also prove logarithmic upper bounds for the regret of both policies, and show
that these bounds are asymptotically optimal (i.e. they only differ from the
best possible regret by a constant factor).
| Long Tran-Thanh, Archie Chapman, Alex Rogers, Nicholas R. Jennings | null | 1204.1909 | null | null |
Learning Topic Models - Going beyond SVD | cs.LG cs.DS cs.IR | Topic Modeling is an approach used for automatic comprehension and
classification of data in a variety of settings, and perhaps the canonical
application is in uncovering thematic structure in a corpus of documents. A
number of foundational works both in machine learning and in theory have
suggested a probabilistic model for documents, whereby documents arise as a
convex combination of (i.e. distribution on) a small number of topic vectors,
each topic vector being a distribution on words (i.e. a vector of
word-frequencies). Similar models have since been used in a variety of
application areas; the Latent Dirichlet Allocation or LDA model of Blei et al.
is especially popular.
Theoretical studies of topic modeling focus on learning the model's
parameters assuming the data is actually generated from it. Existing approaches
for the most part rely on Singular Value Decomposition(SVD), and consequently
have one of two limitations: these works need to either assume that each
document contains only one topic, or else can only recover the span of the
topic vectors instead of the topic vectors themselves.
This paper formally justifies Nonnegative Matrix Factorization(NMF) as a main
tool in this context, which is an analog of SVD where all vectors are
nonnegative. Using this tool we give the first polynomial-time algorithm for
learning topic models without the above two limitations. The algorithm uses a
fairly mild assumption about the underlying topic matrix called separability,
which is usually found to hold in real-life data. A compelling feature of our
algorithm is that it generalizes to models that incorporate topic-topic
correlations, such as the Correlated Topic Model and the Pachinko Allocation
Model.
We hope that this paper will motivate further theoretical results that use
NMF as a replacement for SVD - just as NMF has come to replace SVD in many
applications.
| Sanjeev Arora, Rong Ge, Ankur Moitra | null | 1204.1956 | null | null |
A technical study and analysis on fuzzy similarity based models for text
classification | cs.IR cs.LG | In this new and current era of technology, advancements and techniques,
efficient and effective text document classification is becoming a challenging
and highly required area to capably categorize text documents into mutually
exclusive categories. Fuzzy similarity provides a way to find the similarity of
features among various documents. In this paper, a technical review on various
fuzzy similarity based models is given. These models are discussed and compared
to frame out their use and necessity. A tour of different methodologies is
provided which is based upon fuzzy similarity related concerns. It shows that
how text and web documents are categorized efficiently into different
categories. Various experimental results of these models are also discussed.
The technical comparisons among each model's parameters are shown in the form
of a 3-D chart. Such study and technical review provide a strong base of
research work done on fuzzy similarity based text document categorization.
| Shalini Puri and Sona Kaushik | 10.5121/ijdkp.2012.2201 | 1204.2058 | null | null |
A Fuzzy Similarity Based Concept Mining Model for Text Classification | cs.IR cs.LG | Text Classification is a challenging and a red hot field in the current
scenario and has great importance in text categorization applications. A lot of
research work has been done in this field but there is a need to categorize a
collection of text documents into mutually exclusive categories by extracting
the concepts or features using supervised learning paradigm and different
classification algorithms. In this paper, a new Fuzzy Similarity Based Concept
Mining Model (FSCMM) is proposed to classify a set of text documents into pre -
defined Category Groups (CG) by providing them training and preparing on the
sentence, document and integrated corpora levels along with feature reduction,
ambiguity removal on each level to achieve high system performance. Fuzzy
Feature Category Similarity Analyzer (FFCSA) is used to analyze each extracted
feature of Integrated Corpora Feature Vector (ICFV) with the corresponding
categories or classes. This model uses Support Vector Machine Classifier (SVMC)
to classify correctly the training data patterns into two groups; i. e., + 1
and - 1, thereby producing accurate and correct results. The proposed model
works efficiently and effectively with great performance and high - accuracy
results.
| Shalini Puri | null | 1204.2061 | null | null |
Asymptotic Accuracy of Distribution-Based Estimation for Latent
Variables | stat.ML cs.LG | Hierarchical statistical models are widely employed in information science
and data engineering. The models consist of two types of variables: observable
variables that represent the given data and latent variables for the
unobservable labels. An asymptotic analysis of the models plays an important
role in evaluating the learning process; the result of the analysis is applied
not only to theoretical but also to practical situations, such as optimal model
selection and active learning. There are many studies of generalization errors,
which measure the prediction accuracy of the observable variables. However, the
accuracy of estimating the latent variables has not yet been elucidated. For a
quantitative evaluation of this, the present paper formulates
distribution-based functions for the errors in the estimation of the latent
variables. The asymptotic behavior is analyzed for both the maximum likelihood
and the Bayes methods.
| Keisuke Yamazaki | null | 1204.2069 | null | null |
Robust Nonnegative Matrix Factorization via $L_1$ Norm Regularization | cs.LG cs.CV stat.ML | Nonnegative Matrix Factorization (NMF) is a widely used technique in many
applications such as face recognition, motion segmentation, etc. It
approximates the nonnegative data in an original high dimensional space with a
linear representation in a low dimensional space by using the product of two
nonnegative matrices. In many applications data are often partially corrupted
with large additive noise. When the positions of noise are known, some existing
variants of NMF can be applied by treating these corrupted entries as missing
values. However, the positions are often unknown in many real world
applications, which prevents the usage of traditional NMF or other existing
variants of NMF. This paper proposes a Robust Nonnegative Matrix Factorization
(RobustNMF) algorithm that explicitly models the partial corruption as large
additive noise without requiring the information of positions of noise. In
practice, large additive noise can be used to model outliers. In particular,
the proposed method jointly approximates the clean data matrix with the product
of two nonnegative matrices and estimates the positions and values of
outliers/noise. An efficient iterative optimization algorithm with a solid
theoretical justification has been proposed to learn the desired matrix
factorization. Experimental results demonstrate the advantages of the proposed
algorithm.
| Bin Shen, Luo Si, Rongrong Ji, Baodi Liu | null | 1204.2311 | null | null |
A Simple Explanation of A Spectral Algorithm for Learning Hidden Markov
Models | stat.ME cs.LG stat.ML | A simple linear algebraic explanation of the algorithm in "A Spectral
Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content
is in Figure 2; the text just makes everything precise in four nearly-trivial
claims.
| Matthew James Johnson | null | 1204.2477 | null | null |
Concept Modeling with Superwords | stat.ML cs.CL cs.IR cs.LG | In information retrieval, a fundamental goal is to transform a document into
concepts that are representative of its content. The term "representative" is
in itself challenging to define, and various tasks require different
granularities of concepts. In this paper, we aim to model concepts that are
sparse over the vocabulary, and that flexibly adapt their content based on
other relevant semantic information such as textual structure or associated
image features. We explore a Bayesian nonparametric model based on nested beta
processes that allows for inferring an unknown number of strictly sparse
concepts. The resulting model provides an inherently different representation
of concepts than a standard LDA (or HDP) based topic model, and allows for
direct incorporation of semantic features. We demonstrate the utility of this
representation on multilingual blog data and the Congressional Record.
| Khalid El-Arini, Emily B. Fox, Carlos Guestrin | null | 1204.2523 | null | null |
Modeling Relational Data via Latent Factor Blockmodel | cs.DS cs.LG stat.ML | In this paper we address the problem of modeling relational data, which
appear in many applications such as social network analysis, recommender
systems and bioinformatics. Previous studies either consider latent feature
based models but disregarding local structure in the network, or focus
exclusively on capturing local structure of objects based on latent blockmodels
without coupling with latent characteristics of objects. To combine the
benefits of the previous work, we propose a novel model that can simultaneously
incorporate the effect of latent features and covariates if any, as well as the
effect of latent structure that may exist in the data. To achieve this, we
model the relation graph as a function of both latent feature factors and
latent cluster memberships of objects to collectively discover globally
predictive intrinsic properties of objects and capture latent block structure
in the network to improve prediction performance. We also develop an
optimization transfer algorithm based on the generalized EM-style strategy to
learn the latent factors. We prove the efficacy of our proposed model through
the link prediction task and cluster analysis task, and extensive experiments
on the synthetic data and several real world datasets suggest that our proposed
LFBM model outperforms the other state of the art approaches in the evaluated
tasks.
| Sheng Gao and Ludovic Denoyer and Patrick Gallinari | null | 1204.2581 | null | null |
Probabilistic Latent Tensor Factorization Model for Link Pattern
Prediction in Multi-relational Networks | cs.SI cs.LG stat.ML | This paper aims at the problem of link pattern prediction in collections of
objects connected by multiple relation types, where each type may play a
distinct role. While common link analysis models are limited to single-type
link prediction, we attempt here to capture the correlations among different
relation types and reveal the impact of various relation types on performance
quality. For that, we define the overall relations between object pairs as a
\textit{link pattern} which consists in interaction pattern and connection
structure in the network, and then use tensor formalization to jointly model
and predict the link patterns, which we refer to as \textit{Link Pattern
Prediction} (LPP) problem. To address the issue, we propose a Probabilistic
Latent Tensor Factorization (PLTF) model by introducing another latent factor
for multiple relation types and furnish the Hierarchical Bayesian treatment of
the proposed probabilistic model to avoid overfitting for solving the LPP
problem. To learn the proposed model we develop an efficient Markov Chain Monte
Carlo sampling method. Extensive experiments are conducted on several real
world datasets and demonstrate significant improvements over several existing
state-of-the-art methods.
| Sheng Gao and Ludovic Denoyer and Patrick Gallinari | null | 1204.2588 | null | null |
Stochastic Feature Mapping for PAC-Bayes Classification | cs.LG | Probabilistic generative modeling of data distributions can potentially
exploit hidden information which is useful for discriminative classification.
This observation has motivated the development of approaches that couple
generative and discriminative models for classification. In this paper, we
propose a new approach to couple generative and discriminative models in an
unified framework based on PAC-Bayes risk theory. We first derive the
model-parameter-independent stochastic feature mapping from a practical MAP
classifier operating on generative models. Then we construct a linear
stochastic classifier equipped with the feature mapping, and derive the
explicit PAC-Bayes risk bounds for such classifier for both supervised and
semi-supervised learning. Minimizing the risk bound, using an EM-like iterative
procedure, results in a new posterior over hidden variables (E-step) and the
update rules of model parameters (M-step). The derivation of the posterior is
always feasible due to the way of equipping feature mapping and the explicit
form of bounding risk. The derived posterior allows the tuning of generative
models and subsequently the feature mappings for better classification. The
derived update rules of the model parameters are same to those of the uncoupled
models as the feature mapping is model-parameter-independent. Our experiments
show that the coupling between data modeling generative model and the
discriminative classifier via a stochastic feature mapping in this framework
leads to a general classification tool with state-of-the-art performance.
| Xiong Li and Tai Sing Lee and Yuncai Liu | null | 1204.2609 | null | null |
Plug-in martingales for testing exchangeability on-line | cs.LG stat.ME | A standard assumption in machine learning is the exchangeability of data,
which is equivalent to assuming that the examples are generated from the same
probability distribution independently. This paper is devoted to testing the
assumption of exchangeability on-line: the examples arrive one by one, and
after receiving each example we would like to have a valid measure of the
degree to which the assumption of exchangeability has been falsified. Such
measures are provided by exchangeability martingales. We extend known
techniques for constructing exchangeability martingales and show that our new
method is competitive with the martingales introduced before. Finally we
investigate the performance of our testing method on two benchmark datasets,
USPS and Statlog Satellite data; for the former, the known techniques give
satisfactory results, but for the latter our new more flexible method becomes
necessary.
| Valentina Fedorova, Alex Gammerman, Ilia Nouretdinov, and Vladimir
Vovk | null | 1204.3251 | null | null |
Distributed Learning, Communication Complexity and Privacy | cs.LG cs.DS | We consider the problem of PAC-learning from distributed data and analyze
fundamental communication complexity questions involved. We provide general
upper and lower bounds on the amount of communication needed to learn well,
showing that in addition to VC-dimension and covering number, quantities such
as the teaching-dimension and mistake-bound of a class play an important role.
We also present tight results for a number of common concept classes including
conjunctions, parity functions, and decision lists. For linear separators, we
show that for non-concentrated distributions, we can use a version of the
Perceptron algorithm to learn with much less communication than the number of
updates given by the usual margin bound. We also show how boosting can be
performed in a generic manner in the distributed setting to achieve
communication with only logarithmic dependence on 1/epsilon for any concept
class, and demonstrate how recent work on agnostic learning from
class-conditional queries can be used to achieve low communication in agnostic
settings as well. We additionally present an analysis of privacy, considering
both differential privacy and a notion of distributional privacy that is
especially appealing in this context.
| Maria-Florina Balcan, Avrim Blum, Shai Fine, and Yishay Mansour | null | 1204.3514 | null | null |
Efficient Protocols for Distributed Classification and Optimization | cs.LG stat.ML | In distributed learning, the goal is to perform a learning task over data
distributed across multiple nodes with minimal (expensive) communication. Prior
work (Daume III et al., 2012) proposes a general model that bounds the
communication required for learning classifiers while allowing for $\eps$
training error on linearly separable data adversarially distributed across
nodes.
In this work, we develop key improvements and extensions to this basic model.
Our first result is a two-party multiplicative-weight-update based protocol
that uses $O(d^2 \log{1/\eps})$ words of communication to classify distributed
data in arbitrary dimension $d$, $\eps$-optimally. This readily extends to
classification over $k$ nodes with $O(kd^2 \log{1/\eps})$ words of
communication. Our proposed protocol is simple to implement and is considerably
more efficient than baselines compared, as demonstrated by our empirical
results.
In addition, we illustrate general algorithm design paradigms for doing
efficient learning over distributed data. We show how to solve
fixed-dimensional and high dimensional linear programming efficiently in a
distributed setting where constraints may be distributed across nodes. Since
many learning problems can be viewed as convex optimization problems where
constraints are generated by individual points, this models many typical
distributed learning scenarios. Our techniques make use of a novel connection
from multipass streaming, as well as adapting the multiplicative-weight-update
framework more generally to a distributed setting. As a consequence, our
methods extend to the wide range of problems solvable using these techniques.
| Hal Daume III, Jeff M. Phillips, Avishek Saha, Suresh
Venkatasubramanian | null | 1204.3523 | null | null |
Learning to Predict the Wisdom of Crowds | cs.SI cs.LG | The problem of "approximating the crowd" is that of estimating the crowd's
majority opinion by querying only a subset of it. Algorithms that approximate
the crowd can intelligently stretch a limited budget for a crowdsourcing task.
We present an algorithm, "CrowdSense," that works in an online fashion to
dynamically sample subsets of labelers based on an exploration/exploitation
criterion. The algorithm produces a weighted combination of a subset of the
labelers' votes that approximates the crowd's opinion.
| Seyda Ertekin, Haym Hirsh, Cynthia Rudin | null | 1204.3611 | null | null |
Convolutional Neural Networks Applied to House Numbers Digit
Classification | cs.CV cs.LG cs.NE | We classify digits of real-world house numbers using convolutional neural
networks (ConvNets). ConvNets are hierarchical feature learning neural networks
whose structure is biologically inspired. Unlike many popular vision approaches
that are hand-designed, ConvNets can automatically learn a unique set of
features optimized for a given task. We augmented the traditional ConvNet
architecture by learning multi-stage features and by using Lp pooling and
establish a new state-of-the-art of 94.85% accuracy on the SVHN dataset (45.2%
error improvement). Furthermore, we analyze the benefits of different pooling
methods and multi-stage features in ConvNets. The source code and a tutorial
are available at eblearn.sf.net.
| Pierre Sermanet, Soumith Chintala, Yann LeCun | null | 1204.3968 | null | null |
EigenGP: Sparse Gaussian process models with data-dependent
eigenfunctions | cs.LG stat.CO stat.ML | Gaussian processes (GPs) provide a nonparametric representation of functions.
However, classical GP inference suffers from high computational cost and it is
difficult to design nonstationary GP priors in practice. In this paper, we
propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve
(KL) expansion of a GP prior. We use the Nystrom approximation to obtain data
dependent eigenfunctions and select these eigenfunctions by evidence
maximization. This selection reduces the number of eigenfunctions in our model
and provides a nonstationary covariance function. To handle nonlinear
likelihoods, we develop an efficient expectation propagation (EP) inference
algorithm, and couple it with expectation maximization for eigenfunction
selection. Because the eigenfunctions of a Gaussian kernel are associated with
clusters of samples - including both the labeled and unlabeled - selecting
relevant eigenfunctions enables EigenGP to conduct semi-supervised learning.
Our experimental results demonstrate improved predictive performance of EigenGP
over alternative state-of-the-art sparse GP and semisupervised learning methods
for regression, classification, and semisupervised classification.
| Yuan Qi and Bo Dai and Yao Zhu | null | 1204.3972 | null | null |
Learning From An Optimization Viewpoint | cs.LG cs.GT | In this dissertation we study statistical and online learning problems from
an optimization viewpoint.The dissertation is divided into two parts :
I. We first consider the question of learnability for statistical learning
problems in the general learning setting. The question of learnability is well
studied and fully characterized for binary classification and for real valued
supervised learning problems using the theory of uniform convergence. However
we show that for the general learning setting uniform convergence theory fails
to characterize learnability. To fill this void we use stability of learning
algorithms to fully characterize statistical learnability in the general
setting. Next we consider the problem of online learning. Unlike the
statistical learning framework there is a dearth of generic tools that can be
used to establish learnability and rates for online learning problems in
general. We provide online analogs to classical tools from statistical learning
theory like Rademacher complexity, covering numbers, etc. We further use these
tools to fully characterize learnability for online supervised learning
problems.
II. In the second part, for general classes of convex learning problems, we
provide appropriate mirror descent (MD) updates for online and statistical
learning of these problems. Further, we show that the the MD is near optimal
for online convex learning and for most cases, is also near optimal for
statistical convex learning. We next consider the problem of convex
optimization and show that oracle complexity can be lower bounded by the so
called fat-shattering dimension of the associated linear class. Thus we
establish a strong connection between offline convex optimization problems and
statistical learning problems. We also show that for a large class of high
dimensional optimization problems, MD is in fact near optimal even for convex
optimization.
| Karthik Sridharan | null | 1204.4145 | null | null |
Message passing with relaxed moment matching | cs.LG stat.CO stat.ML | Bayesian learning is often hampered by large computational expense. As a
powerful generalization of popular belief propagation, expectation propagation
(EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP
can be sensitive to outliers and suffer from divergence for difficult cases. To
address this issue, we propose a new approximate inference approach, relaxed
expectation propagation (REP). It relaxes the moment matching requirement of
expectation propagation by adding a relaxation factor into the KL minimization.
We penalize this relaxation with a $l_1$ penalty. As a result, when two
distributions in the relaxed KL divergence are similar, the relaxation factor
will be penalized to zero and, therefore, we obtain the original moment
matching; In the presence of outliers, these two distributions are
significantly different and the relaxation factor will be used to reduce the
contribution of the outlier. Based on this penalized KL minimization, REP is
robust to outliers and can greatly improve the posterior approximation quality
over EP. To examine the effectiveness of REP, we apply it to Gaussian process
classification, a task known to be suitable to EP. Our classification results
on synthetic and UCI benchmark datasets demonstrate significant improvement of
REP over EP and Power EP--in terms of algorithmic stability, estimation
accuracy and predictive performance.
| Yuan Qi and Yandong Guo | null | 1204.4166 | null | null |
Discrete Dynamical Genetic Programming in XCS | cs.AI cs.LG cs.NE cs.SY | A number of representation schemes have been presented for use within
Learning Classifier Systems, ranging from binary encodings to neural networks.
This paper presents results from an investigation into using a discrete
dynamical system representation within the XCS Learning Classifier System. In
particular, asynchronous random Boolean networks are used to represent the
traditional condition-action production system rules. It is shown possible to
use self-adaptive, open-ended evolution to design an ensemble of such discrete
dynamical systems within XCS to solve a number of well-known test problems.
| Richard J. Preen and Larry Bull | 10.1145/1569901.1570075 | 1204.4200 | null | null |
Fuzzy Dynamical Genetic Programming in XCSF | cs.AI cs.LG cs.NE cs.SY | A number of representation schemes have been presented for use within
Learning Classifier Systems, ranging from binary encodings to Neural Networks,
and more recently Dynamical Genetic Programming (DGP). This paper presents
results from an investigation into using a fuzzy DGP representation within the
XCSF Learning Classifier System. In particular, asynchronous Fuzzy Logic
Networks are used to represent the traditional condition-action production
system rules. It is shown possible to use self-adaptive, open-ended evolution
to design an ensemble of such fuzzy dynamical systems within XCSF to solve
several well-known continuous-valued test problems.
| Richard J. Preen and Larry Bull | 10.1145/2001858.2001952 | 1204.4202 | null | null |
Learning in Riemannian Orbifolds | cs.LG cs.AI cs.CV | Learning in Riemannian orbifolds is motivated by existing machine learning
algorithms that directly operate on finite combinatorial structures such as
point patterns, trees, and graphs. These methods, however, lack statistical
justification. This contribution derives consistency results for learning
problems in structured domains and thereby generalizes learning in vector
spaces and manifolds.
| Brijnesh J. Jain and Klaus Obermayer | null | 1204.4294 | null | null |
Supervised feature evaluation by consistency analysis: application to
measure sets used to characterise geographic objects | cs.LG | Nowadays, supervised learning is commonly used in many domains. Indeed, many
works propose to learn new knowledge from examples that translate the expected
behaviour of the considered system. A key issue of supervised learning concerns
the description language used to represent the examples. In this paper, we
propose a method to evaluate the feature set used to describe them. Our method
is based on the computation of the consistency of the example base. We carried
out a case study in the domain of geomatic in order to evaluate the sets of
measures used to characterise geographic objects. The case study shows that our
method allows to give relevant evaluations of measure sets.
| Patrick Taillandier (UMMISCO), Alexis Drogoul (UMMISCO, MSI) | null | 1204.4329 | null | null |
Designing generalisation evaluation function through human-machine
dialogue | cs.HC cs.LG | Automated generalisation has known important improvements these last few
years. However, an issue that still deserves more study concerns the automatic
evaluation of generalised data. Indeed, many automated generalisation systems
require the utilisation of an evaluation function to automatically assess
generalisation outcomes. In this paper, we propose a new approach dedicated to
the design of such a function. This approach allows an imperfectly defined
evaluation function to be revised through a man-machine dialogue. The user
gives its preferences to the system by comparing generalisation outcomes.
Machine Learning techniques are then used to improve the evaluation function.
An experiment carried out on buildings shows that our approach significantly
improves generalisation evaluation functions defined by users.
| Patrick Taillandier (UMMISCO), Julien Gaffuri (COGIT) | null | 1204.4332 | null | null |
A Privacy-Aware Bayesian Approach for Combining Classifier and Cluster
Ensembles | cs.LG cs.CV stat.ML | This paper introduces a privacy-aware Bayesian approach that combines
ensembles of classifiers and clusterers to perform semi-supervised and
transductive learning. We consider scenarios where instances and their
classification/clustering results are distributed across different data sites
and have sharing restrictions. As a special case, the privacy aware computation
of the model when instances of the target data are distributed across different
data sites, is also discussed. Experimental results show that the proposed
approach can provide good classification accuracies while adhering to the
data/model sharing constraints.
| Ayan Acharya, Eduardo R. Hruschka, Joydeep Ghosh | null | 1204.4521 | null | null |
Supervised Feature Selection in Graphs with Path Coding Penalties and
Network Flows | stat.ML cs.LG math.OC | We consider supervised learning problems where the features are embedded in a
graph, such as gene expressions in a gene network. In this context, it is of
much interest to automatically select a subgraph with few connected components;
by exploiting prior knowledge, one can indeed improve the prediction
performance or obtain results that are easier to interpret. Regularization or
penalty functions for selecting features in graphs have recently been proposed,
but they raise new algorithmic challenges. For example, they typically require
solving a combinatorially hard selection problem among all connected subgraphs.
In this paper, we propose computationally feasible strategies to select a
sparse and well-connected subset of features sitting on a directed acyclic
graph (DAG). We introduce structured sparsity penalties over paths on a DAG
called "path coding" penalties. Unlike existing regularization functions that
model long-range interactions between features in a graph, path coding
penalties are tractable. The penalties and their proximal operators involve
path selection problems, which we efficiently solve by leveraging network flow
optimization. We experimentally show on synthetic, image, and genomic data that
our approach is scalable and leads to more connected subgraphs than other
regularization functions for graphs.
| Julien Mairal and Bin Yu | null | 1204.4539 | null | null |
Regret in Online Combinatorial Optimization | cs.LG stat.ML | We address online linear optimization problems when the possible actions of
the decision maker are represented by binary vectors. The regret of the
decision maker is the difference between her realized loss and the best loss
she would have achieved by picking, in hindsight, the best possible action. Our
goal is to understand the magnitude of the best possible (minimax) regret. We
study the problem under three different assumptions for the feedback the
decision maker receives: full information, and the partial information models
of the so-called "semi-bandit" and "bandit" problems. Combining the Mirror
Descent algorithm and the INF (Implicitely Normalized Forecaster) strategy, we
are able to prove optimal bounds for the semi-bandit case. We also recover the
optimal bounds for the full information setting. In the bandit case we discuss
existing results in light of a new lower bound, and suggest a conjecture on the
optimal regret in that case. Finally we also prove that the standard
exponentially weighted average forecaster is provably suboptimal in the setting
of online combinatorial optimization.
| Jean-Yves Audibert, S\'ebastien Bubeck and G\'abor Lugosi | null | 1204.4710 | null | null |
Energy-Efficient Building HVAC Control Using Hybrid System LBMPC | math.OC cs.LG cs.SY | Improving the energy-efficiency of heating, ventilation, and air-conditioning
(HVAC) systems has the potential to realize large economic and societal
benefits. This paper concerns the system identification of a hybrid system
model of a building-wide HVAC system and its subsequent control using a hybrid
system formulation of learning-based model predictive control (LBMPC). Here,
the learning refers to model updates to the hybrid system model that
incorporate the heating effects due to occupancy, solar effects, outside air
temperature (OAT), and equipment, in addition to integrator dynamics inherently
present in low-level control. Though we make significant modeling
simplifications, our corresponding controller that uses this model is able to
experimentally achieve a large reduction in energy usage without any
degradations in occupant comfort. It is in this way that we justify the
modeling simplifications that we have made. We conclude by presenting results
from experiments on our building HVAC testbed, which show an average of 1.5MWh
of energy savings per day (p = 0.002) with a 95% confidence interval of 1.0MWh
to 2.1MWh of energy savings.
| Anil Aswani, Neal Master, Jay Taneja, Andrew Krioukov, David Culler,
Claire Tomlin | null | 1204.4717 | null | null |
Objective Function Designing Led by User Preferences Acquisition | cs.LG cs.AI cs.HC | Many real world problems can be defined as optimisation problems in which the
aim is to maximise an objective function. The quality of obtained solution is
directly linked to the pertinence of the used objective function. However,
designing such function, which has to translate the user needs, is usually
fastidious. In this paper, a method to help user objective functions designing
is proposed. Our approach, which is highly interactive, is based on man machine
dialogue and more particularly on the comparison of problem instance solutions
by the user. We propose an experiment in the domain of cartographic
generalisation that shows promising results.
| Patrick Taillandier (UMMISCO), Julien Gaffuri (COGIT) | null | 1204.4990 | null | null |
Knowledge revision in systems based on an informed tree search strategy
: application to cartographic generalisation | cs.AI cs.LG | Many real world problems can be expressed as optimisation problems. Solving
this kind of problems means to find, among all possible solutions, the one that
maximises an evaluation function. One approach to solve this kind of problem is
to use an informed search strategy. The principle of this kind of strategy is
to use problem-specific knowledge beyond the definition of the problem itself
to find solutions more efficiently than with an uninformed strategy. This kind
of strategy demands to define problem-specific knowledge (heuristics). The
efficiency and the effectiveness of systems based on it directly depend on the
used knowledge quality. Unfortunately, acquiring and maintaining such knowledge
can be fastidious. The objective of the work presented in this paper is to
propose an automatic knowledge revision approach for systems based on an
informed tree search strategy. Our approach consists in analysing the system
execution logs and revising knowledge based on these logs by modelling the
revision problem as a knowledge space exploration problem. We present an
experiment we carried out in an application domain where informed search
strategies are often used: cartographic generalisation.
| Patrick Taillandier (COGIT, UMMISCO), C\'ecile Duch\^ene (COGIT),
Alexis Drogoul (UMMISCO, MSI) | 10.1145/1456223.1456281 | 1204.4991 | null | null |
Sparse Prediction with the $k$-Support Norm | stat.ML cs.LG | We derive a novel norm that corresponds to the tightest convex relaxation of
sparsity combined with an $\ell_2$ penalty. We show that this new {\em
$k$-support norm} provides a tighter relaxation than the elastic net and is
thus a good replacement for the Lasso or the elastic net in sparse prediction
problems. Through the study of the $k$-support norm, we also bound the
looseness of the elastic net, thus shedding new light on it and providing
justification for its use.
| Andreas Argyriou and Rina Foygel and Nathan Srebro | null | 1204.5043 | null | null |
Analysis Operator Learning and Its Application to Image Reconstruction | cs.LG cs.CV | Exploiting a priori known structural information lies at the core of many
image reconstruction methods that can be stated as inverse problems. The
synthesis model, which assumes that images can be decomposed into a linear
combination of very few atoms of some dictionary, is now a well established
tool for the design of image reconstruction algorithms. An interesting
alternative is the analysis model, where the signal is multiplied by an
analysis operator and the outcome is assumed to be the sparse. This approach
has only recently gained increasing interest. The quality of reconstruction
methods based on an analysis model severely depends on the right choice of the
suitable operator.
In this work, we present an algorithm for learning an analysis operator from
training images. Our method is based on an $\ell_p$-norm minimization on the
set of full rank matrices with normalized columns. We carefully introduce the
employed conjugate gradient method on manifolds, and explain the underlying
geometry of the constraints. Moreover, we compare our approach to
state-of-the-art methods for image denoising, inpainting, and single image
super-resolution. Our numerical results show competitive performance of our
general approach in all presented applications compared to the specialized
state-of-the-art techniques.
| Simon Hawe, Martin Kleinsteuber, and Klaus Diepold | 10.1109/TIP.2013.2246175 | 1204.5309 | null | null |
Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit
Problems | cs.LG stat.ML | Multi-armed bandit problems are the most basic examples of sequential
decision problems with an exploration-exploitation trade-off. This is the
balance between staying with the option that gave highest payoffs in the past
and exploring new options that might give higher payoffs in the future.
Although the study of bandit problems dates back to the Thirties,
exploration-exploitation trade-offs arise in several modern applications, such
as ad placement, website optimization, and packet routing. Mathematically, a
multi-armed bandit is defined by the payoff process associated with each
option. In this survey, we focus on two extreme cases in which the analysis of
regret is particularly simple and elegant: i.i.d. payoffs and adversarial
payoffs. Besides the basic setting of finitely many actions, we also analyze
some of the most important variants and extensions, such as the contextual
bandit model.
| S\'ebastien Bubeck and Nicol\`o Cesa-Bianchi | null | 1204.5721 | null | null |
Quantitative Concept Analysis | cs.LG math.CT | Formal Concept Analysis (FCA) begins from a context, given as a binary
relation between some objects and some attributes, and derives a lattice of
concepts, where each concept is given as a set of objects and a set of
attributes, such that the first set consists of all objects that satisfy all
attributes in the second, and vice versa. Many applications, though, provide
contexts with quantitative information, telling not just whether an object
satisfies an attribute, but also quantifying this satisfaction. Contexts in
this form arise as rating matrices in recommender systems, as occurrence
matrices in text analysis, as pixel intensity matrices in digital image
processing, etc. Such applications have attracted a lot of attention, and
several numeric extensions of FCA have been proposed. We propose the framework
of proximity sets (proxets), which subsume partially ordered sets (posets) as
well as metric spaces. One feature of this approach is that it extracts from
quantified contexts quantified concepts, and thus allows full use of the
available information. Another feature is that the categorical approach allows
analyzing any universal properties that the classical FCA and the new versions
may have, and thus provides structural guidance for aligning and combining the
approaches.
| Dusko Pavlovic | null | 1204.5802 | null | null |
Geometry of Online Packing Linear Programs | cs.DS cs.LG | We consider packing LP's with $m$ rows where all constraint coefficients are
normalized to be in the unit interval. The n columns arrive in random order and
the goal is to set the corresponding decision variables irrevocably when they
arrive so as to obtain a feasible solution maximizing the expected reward.
Previous (1 - \epsilon)-competitive algorithms require the right-hand side of
the LP to be Omega((m/\epsilon^2) log (n/\epsilon)), a bound that worsens with
the number of columns and rows. However, the dependence on the number of
columns is not required in the single-row case and known lower bounds for the
general case are also independent of n.
Our goal is to understand whether the dependence on n is required in the
multi-row case, making it fundamentally harder than the single-row version. We
refute this by exhibiting an algorithm which is (1 - \epsilon)-competitive as
long as the right-hand sides are Omega((m^2/\epsilon^2) log (m/\epsilon)). Our
techniques refine previous PAC-learning based approaches which interpret the
online decisions as linear classifications of the columns based on sampled dual
prices. The key ingredient of our improvement comes from a non-standard
covering argument together with the realization that only when the columns of
the LP belong to few 1-d subspaces we can obtain small such covers; bounding
the size of the cover constructed also relies on the geometry of linear
classifiers. General packing LP's are handled by perturbing the input columns,
which can be seen as making the learning problem more robust.
| Marco Molinaro and R. Ravi | null | 1204.5810 | null | null |
Distributed GraphLab: A Framework for Machine Learning in the Cloud | cs.DB cs.LG | While high-level data parallel frameworks, like MapReduce, simplify the
design and implementation of large-scale data processing systems, they do not
naturally or efficiently support many important data mining and machine
learning algorithms and can lead to inefficient learning systems. To help fill
this critical void, we introduced the GraphLab abstraction which naturally
expresses asynchronous, dynamic, graph-parallel computation while ensuring data
consistency and achieving a high degree of parallel performance in the
shared-memory setting. In this paper, we extend the GraphLab framework to the
substantially more challenging distributed setting while preserving strong data
consistency guarantees. We develop graph based extensions to pipelined locking
and data versioning to reduce network congestion and mitigate the effect of
network latency. We also introduce fault tolerance to the GraphLab abstraction
using the classic Chandy-Lamport snapshot algorithm and demonstrate how it can
be easily implemented by exploiting the GraphLab abstraction itself. Finally,
we evaluate our distributed implementation of the GraphLab abstraction on a
large Amazon EC2 deployment and show 1-2 orders of magnitude performance gains
over Hadoop-based implementations.
| Yucheng Low, Joseph Gonzalez, Aapo Kyrola, Danny Bickson, Carlos
Guestrin, Joseph M. Hellerstein | null | 1204.6078 | null | null |
Feature Selection for Generator Excitation Neurocontroller Development
Using Filter Technique | cs.SY cs.LG | Essentially, motive behind using control system is to generate suitable
control signal for yielding desired response of a physical process. Control of
synchronous generator has always remained very critical in power system
operation and control. For certain well known reasons power generators are
normally operated well below their steady state stability limit. This raises
demand for efficient and fast controllers. Artificial intelligence has been
reported to give revolutionary outcomes in the field of control engineering.
Artificial Neural Network (ANN), a branch of artificial intelligence has been
used for nonlinear and adaptive control, utilizing its inherent observability.
The overall performance of neurocontroller is dependent upon input features
too. Selecting optimum features to train a neurocontroller optimally is very
critical. Both quality and size of data are of equal importance for better
performance. In this work filter technique is employed to select independent
factors for ANN training.
| Abdul Ghani Abro, Junita Mohamad Saleh | null | 1204.6250 | null | null |
CELL: Connecting Everyday Life in an archipeLago | cs.HC cs.LG | We explore the design of a seamless broadcast communication system that
brings together the distributed community of remote secondary education
schools. In contrast to higher education, primary and secondary education
establishments should remain distributed, in order to maintain a balance of
urban and rural life in the developing and the developed world. We plan to
deploy an ambient and social interactive TV platform (physical installation,
authoring tools, interactive content) that supports social communication in a
positive way. In particular, we present the physical design and the conceptual
model of the system.
| Konstantinos Chorianopoulos, Vassiliki Tsaknaki | null | 1204.6325 | null | null |
Dissimilarity Clustering by Hierarchical Multi-Level Refinement | stat.ML cs.LG | We introduce in this paper a new way of optimizing the natural extension of
the quantization error using in k-means clustering to dissimilarity data. The
proposed method is based on hierarchical clustering analysis combined with
multi-level heuristic refinement. The method is computationally efficient and
achieves better quantization errors than the
| Brieuc Conan-Guez (LITA), Fabrice Rossi (SAMM) | null | 1204.6509 | null | null |
A Conjugate Property between Loss Functions and Uncertainty Sets in
Classification Problems | stat.ML cs.LG | In binary classification problems, mainly two approaches have been proposed;
one is loss function approach and the other is uncertainty set approach. The
loss function approach is applied to major learning algorithms such as support
vector machine (SVM) and boosting methods. The loss function represents the
penalty of the decision function on the training samples. In the learning
algorithm, the empirical mean of the loss function is minimized to obtain the
classifier. Against a backdrop of the development of mathematical programming,
nowadays learning algorithms based on loss functions are widely applied to
real-world data analysis. In addition, statistical properties of such learning
algorithms are well-understood based on a lots of theoretical works. On the
other hand, the learning method using the so-called uncertainty set is used in
hard-margin SVM, mini-max probability machine (MPM) and maximum margin MPM. In
the learning algorithm, firstly, the uncertainty set is defined for each binary
label based on the training samples. Then, the best separating hyperplane
between the two uncertainty sets is employed as the decision function. This is
regarded as an extension of the maximum-margin approach. The uncertainty set
approach has been studied as an application of robust optimization in the field
of mathematical programming. The statistical properties of learning algorithms
with uncertainty sets have not been intensively studied. In this paper, we
consider the relation between the above two approaches. We point out that the
uncertainty set is described by using the level set of the conjugate of the
loss function. Based on such relation, we study statistical properties of
learning algorithms using uncertainty sets.
| Takafumi Kanamori, Akiko Takeda, Taiji Suzuki | null | 1204.6583 | null | null |
Residual Belief Propagation for Topic Modeling | cs.LG cs.IR | Fast convergence speed is a desired property for training latent Dirichlet
allocation (LDA), especially in online and parallel topic modeling for massive
data sets. This paper presents a novel residual belief propagation (RBP)
algorithm to accelerate the convergence speed for training LDA. The proposed
RBP uses an informed scheduling scheme for asynchronous message passing, which
passes fast-convergent messages with a higher priority to influence those
slow-convergent messages at each learning iteration. Extensive empirical
studies confirm that RBP significantly reduces the training time until
convergence while achieves a much lower predictive perplexity than other
state-of-the-art training algorithms for LDA, including variational Bayes (VB),
collapsed Gibbs sampling (GS), loopy belief propagation (BP), and residual VB
(RVB).
| Jia Zeng, Xiao-Qin Cao and Zhi-Qiang Liu | null | 1204.6610 | null | null |
A Spectral Algorithm for Latent Dirichlet Allocation | cs.LG stat.ML | The problem of topic modeling can be seen as a generalization of the
clustering problem, in that it posits that observations are generated due to
multiple latent factors (e.g., the words in each document are generated as a
mixture of several active topics, as opposed to just one). This increased
representational power comes at the cost of a more challenging unsupervised
learning problem of estimating the topic probability vectors (the distributions
over words for each topic), when only the words are observed and the
corresponding topics are hidden.
We provide a simple and efficient learning procedure that is guaranteed to
recover the parameters for a wide class of mixture models, including the
popular latent Dirichlet allocation (LDA) model. For LDA, the procedure
correctly recovers both the topic probability vectors and the prior over the
topics, using only trigram statistics (i.e., third order moments, which may be
estimated with documents containing just three words). The method, termed
Excess Correlation Analysis (ECA), is based on a spectral decomposition of low
order moments (third and fourth order) via two singular value decompositions
(SVDs). Moreover, the algorithm is scalable since the SVD operations are
carried out on $k\times k$ matrices, where $k$ is the number of latent factors
(e.g. the number of topics), rather than in the $d$-dimensional observed space
(typically $d \gg k$).
| Animashree Anandkumar, Dean P. Foster, Daniel Hsu, Sham M. Kakade,
Yi-Kai Liu | null | 1204.6703 | null | null |
A Singly-Exponential Time Algorithm for Computing Nonnegative Rank | cs.DS cs.IR cs.LG | Here, we give an algorithm for deciding if the nonnegative rank of a matrix
$M$ of dimension $m \times n$ is at most $r$ which runs in time
$(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time
singly-exponential in $r$. This algorithm (and earlier algorithms) are built on
methods for finding a solution to a system of polynomial inequalities (if one
exists). Notably, the best algorithms for this task run in time exponential in
the number of variables but polynomial in all of the other parameters (the
number of inequalities and the maximum degree).
Hence these algorithms motivate natural algebraic questions whose solution
have immediate {\em algorithmic} implications: How many variables do we need to
represent the decision problem, does $M$ have nonnegative rank at most $r$? A
naive formulation uses $nr + mr$ variables and yields an algorithm that is
exponential in $n$ and $m$ even for constant $r$. (Arora, Ge, Kannan, Moitra,
STOC 2012) recently reduced the number of variables to $2r^2 2^r$, and here we
exponentially reduce the number of variables to $2r^2$ and this yields our main
algorithm. In fact, the algorithm that we obtain is nearly-optimal (under the
Exponential Time Hypothesis) since an algorithm that runs in time $(nm)^{o(r)}$
would yield a subexponential algorithm for 3-SAT .
Our main result is based on establishing a normal form for nonnegative matrix
factorization - which in turn allows us to exploit algebraic dependence among a
large collection of linear transformations with variable entries. Additionally,
we also demonstrate that nonnegative rank cannot be certified by even a very
large submatrix of $M$, and this property also follows from the intuition
gained from viewing nonnegative rank through the lens of systems of polynomial
inequalities.
| Ankur Moitra | null | 1205.0044 | null | null |
$QD$-Learning: A Collaborative Distributed Strategy for Multi-Agent
Reinforcement Learning Through Consensus + Innovations | stat.ML cs.LG cs.MA math.OC math.PR | The paper considers a class of multi-agent Markov decision processes (MDPs),
in which the network agents respond differently (as manifested by the
instantaneous one-stage random costs) to a global controlled state and the
control actions of a remote controller. The paper investigates a distributed
reinforcement learning setup with no prior information on the global state
transition and local agent cost statistics. Specifically, with the agents'
objective consisting of minimizing a network-averaged infinite horizon
discounted cost, the paper proposes a distributed version of $Q$-learning,
$\mathcal{QD}$-learning, in which the network agents collaborate by means of
local processing and mutual information exchange over a sparse (possibly
stochastic) communication network to achieve the network goal. Under the
assumption that each agent is only aware of its local online cost data and the
inter-agent communication network is \emph{weakly} connected, the proposed
distributed scheme is almost surely (a.s.) shown to yield asymptotically the
desired value function and the optimal stationary control policy at each
network agent. The analytical techniques developed in the paper to address the
mixed time-scale stochastic dynamics of the \emph{consensus + innovations}
form, which arise as a result of the proposed interactive distributed scheme,
are of independent interest.
| Soummya Kar, Jose' M.F. Moura and H. Vincent Poor | 10.1109/TSP.2013.2241057 | 1205.0047 | null | null |
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