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The connection between Bayesian estimation of a Gaussian random field
and RKHS | stat.ML cs.LG math.ST stat.TH | Reconstruction of a function from noisy data is often formulated as a
regularized optimization problem over an infinite-dimensional reproducing
kernel Hilbert space (RKHS). The solution describes the observed data and has a
small RKHS norm. When the data fit is measured using a quadratic loss, this
estimator has a known statistical interpretation. Given the noisy measurements,
the RKHS estimate represents the posterior mean (minimum variance estimate) of
a Gaussian random field with covariance proportional to the kernel associated
with the RKHS. In this paper, we provide a statistical interpretation when more
general losses are used, such as absolute value, Vapnik or Huber. Specifically,
for any finite set of sampling locations (including where the data were
collected), the MAP estimate for the signal samples is given by the RKHS
estimate evaluated at these locations.
| Aleksandr Y. Aravkin and Bradley M. Bell and James V. Burke and
Gianluigi Pillonetto | null | 1301.5288 | null | null |
Online Learning with Pairwise Loss Functions | stat.ML cs.LG | Efficient online learning with pairwise loss functions is a crucial component
in building large-scale learning system that maximizes the area under the
Receiver Operator Characteristic (ROC) curve. In this paper we investigate the
generalization performance of online learning algorithms with pairwise loss
functions. We show that the existing proof techniques for generalization bounds
of online algorithms with a univariate loss can not be directly applied to
pairwise losses. In this paper, we derive the first result providing
data-dependent bounds for the average risk of the sequence of hypotheses
generated by an arbitrary online learner in terms of an easily computable
statistic, and show how to extract a low risk hypothesis from the sequence. We
demonstrate the generality of our results by applying it to two important
problems in machine learning. First, we analyze two online algorithms for
bipartite ranking; one being a natural extension of the perceptron algorithm
and the other using online convex optimization. Secondly, we provide an
analysis for the risk bound for an online algorithm for supervised metric
learning.
| Yuyang Wang, Roni Khardon, Dmitry Pechyony, Rosie Jones | null | 1301.5332 | null | null |
Why Size Matters: Feature Coding as Nystrom Sampling | cs.LG cs.CV | Recently, the computer vision and machine learning community has been in
favor of feature extraction pipelines that rely on a coding step followed by a
linear classifier, due to their overall simplicity, well understood properties
of linear classifiers, and their computational efficiency. In this paper we
propose a novel view of this pipeline based on kernel methods and Nystrom
sampling. In particular, we focus on the coding of a data point with a local
representation based on a dictionary with fewer elements than the number of
data points, and view it as an approximation to the actual function that would
compute pair-wise similarity to all data points (often too many to compute in
practice), followed by a Nystrom sampling step to select a subset of all data
points.
Furthermore, since bounds are known on the approximation power of Nystrom
sampling as a function of how many samples (i.e. dictionary size) we consider,
we can derive bounds on the approximation of the exact (but expensive to
compute) kernel matrix, and use it as a proxy to predict accuracy as a function
of the dictionary size, which has been observed to increase but also to
saturate as we increase its size. This model may help explaining the positive
effect of the codebook size and justifying the need to stack more layers (often
referred to as deep learning), as flat models empirically saturate as we add
more complexity.
| Oriol Vinyals, Yangqing Jia, Trevor Darrell | null | 1301.5348 | null | null |
Multi-class Generalized Binary Search for Active Inverse Reinforcement
Learning | cs.LG cs.AI stat.ML | This paper addresses the problem of learning a task from demonstration. We
adopt the framework of inverse reinforcement learning, where tasks are
represented in the form of a reward function. Our contribution is a novel
active learning algorithm that enables the learning agent to query the expert
for more informative demonstrations, thus leading to more sample-efficient
learning. For this novel algorithm (Generalized Binary Search for Inverse
Reinforcement Learning, or GBS-IRL), we provide a theoretical bound on sample
complexity and illustrate its applicability on several different tasks. To our
knowledge, GBS-IRL is the first active IRL algorithm with provable sample
complexity bounds. We also discuss our method in light of other existing
methods in the literature and its general applicability in multi-class
classification problems. Finally, motivated by recent work on learning from
demonstration in robots, we also discuss how different forms of human feedback
can be integrated in a transparent manner in our learning framework.
| Francisco Melo and Manuel Lopes | null | 1301.5488 | null | null |
Regularization and nonlinearities for neural language models: when are
they needed? | stat.ML cs.LG | Neural language models (LMs) based on recurrent neural networks (RNN) are
some of the most successful word and character-level LMs. Why do they work so
well, in particular better than linear neural LMs? Possible explanations are
that RNNs have an implicitly better regularization or that RNNs have a higher
capacity for storing patterns due to their nonlinearities or both. Here we
argue for the first explanation in the limit of little training data and the
second explanation for large amounts of text data. We show state-of-the-art
performance on the popular and small Penn dataset when RNN LMs are regularized
with random dropout. Nonetheless, we show even better performance from a
simplified, much less expressive linear RNN model without off-diagonal entries
in the recurrent matrix. We call this model an impulse-response LM (IRLM).
Using random dropout, column normalization and annealed learning rates, IRLMs
develop neurons that keep a memory of up to 50 words in the past and achieve a
perplexity of 102.5 on the Penn dataset. On two large datasets however, the
same regularization methods are unsuccessful for both models and the RNN's
expressivity allows it to overtake the IRLM by 10 and 20 percent perplexity,
respectively. Despite the perplexity gap, IRLMs still outperform RNNs on the
Microsoft Research Sentence Completion (MRSC) task. We develop a slightly
modified IRLM that separates long-context units (LCUs) from short-context units
and show that the LCUs alone achieve a state-of-the-art performance on the MRSC
task of 60.8%. Our analysis indicates that a fruitful direction of research for
neural LMs lies in developing more accessible internal representations, and
suggests an optimization regime of very high momentum terms for effectively
training such models.
| Marius Pachitariu and Maneesh Sahani | null | 1301.5650 | null | null |
Transfer Topic Modeling with Ease and Scalability | cs.CL cs.LG stat.ML | The increasing volume of short texts generated on social media sites, such as
Twitter or Facebook, creates a great demand for effective and efficient topic
modeling approaches. While latent Dirichlet allocation (LDA) can be applied, it
is not optimal due to its weakness in handling short texts with fast-changing
topics and scalability concerns. In this paper, we propose a transfer learning
approach that utilizes abundant labeled documents from other domains (such as
Yahoo! News or Wikipedia) to improve topic modeling, with better model fitting
and result interpretation. Specifically, we develop Transfer Hierarchical LDA
(thLDA) model, which incorporates the label information from other domains via
informative priors. In addition, we develop a parallel implementation of our
model for large-scale applications. We demonstrate the effectiveness of our
thLDA model on both a microblogging dataset and standard text collections
including AP and RCV1 datasets.
| Jeon-Hyung Kang, Jun Ma, Yan Liu | null | 1301.5686 | null | null |
Reinforcement learning from comparisons: Three alternatives is enough,
two is not | math.OC cs.LG math.PR | The paper deals with the problem of finding the best alternatives on the
basis of pairwise comparisons when these comparisons need not be transitive. In
this setting, we study a reinforcement urn model. We prove convergence to the
optimal solution when reinforcement of a winning alternative occurs each time
after considering three random alternatives. The simpler process, which
reinforces the winner of a random pair does not always converges: it may cycle.
| Benoit Laslier and Jean-Francois Laslier | null | 1301.5734 | null | null |
Phase Diagram and Approximate Message Passing for Blind Calibration and
Dictionary Learning | cs.IT cond-mat.stat-mech cs.LG math.IT | We consider dictionary learning and blind calibration for signals and
matrices created from a random ensemble. We study the mean-squared error in the
limit of large signal dimension using the replica method and unveil the
appearance of phase transitions delimiting impossible, possible-but-hard and
possible inference regions. We also introduce an approximate message passing
algorithm that asymptotically matches the theoretical performance, and show
through numerical tests that it performs very well, for the calibration
problem, for tractable system sizes.
| Florent Krzakala, Marc M\'ezard, Lenka Zdeborov\'a | 10.1109/ISIT.2013.6620308 | 1301.5898 | null | null |
Recycling Proof Patterns in Coq: Case Studies | cs.AI cs.LG cs.LO | Development of Interactive Theorem Provers has led to the creation of big
libraries and varied infrastructures for formal proofs. However, despite (or
perhaps due to) their sophistication, the re-use of libraries by non-experts or
across domains is a challenge. In this paper, we provide detailed case studies
and evaluate the machine-learning tool ML4PG built to interactively data-mine
the electronic libraries of proofs, and to provide user guidance on the basis
of proof patterns found in the existing libraries.
| J\'onathan Heras and Ekaterina Komendantskaya | null | 1301.6039 | null | null |
Weighted Last-Step Min-Max Algorithm with Improved Sub-Logarithmic
Regret | cs.LG | In online learning the performance of an algorithm is typically compared to
the performance of a fixed function from some class, with a quantity called
regret. Forster proposed a last-step min-max algorithm which was somewhat
simpler than the algorithm of Vovk, yet with the same regret. In fact the
algorithm he analyzed assumed that the choices of the adversary are bounded,
yielding artificially only the two extreme cases. We fix this problem by
weighing the examples in such a way that the min-max problem will be well
defined, and provide analysis with logarithmic regret that may have better
multiplicative factor than both bounds of Forster and Vovk. We also derive a
new bound that may be sub-logarithmic, as a recent bound of Orabona et.al, but
may have better multiplicative factor. Finally, we analyze the algorithm in a
weak-type of non-stationary setting, and show a bound that is sub-linear if the
non-stationarity is sub-linear as well.
| Edward Moroshko, Koby Crammer | null | 1301.6058 | null | null |
Sample Complexity of Bayesian Optimal Dictionary Learning | cs.LG cond-mat.dis-nn cond-mat.stat-mech cs.IT math.IT | We consider a learning problem of identifying a dictionary matrix D (M times
N dimension) from a sample set of M dimensional vectors Y = N^{-1/2} DX, where
X is a sparse matrix (N times P dimension) in which the density of non-zero
entries is 0<rho< 1. In particular, we focus on the minimum sample size P_c
(sample complexity) necessary for perfectly identifying D of the optimal
learning scheme when D and X are independently generated from certain
distributions. By using the replica method of statistical mechanics, we show
that P_c=O(N) holds as long as alpha = M/N >rho is satisfied in the limit of N
to infinity. Our analysis also implies that the posterior distribution given Y
is condensed only at the correct dictionary D when the compression rate alpha
is greater than a certain critical value alpha_M(rho). This suggests that
belief propagation may allow us to learn D with a low computational complexity
using O(N) samples.
| Ayaka Sakata and Yoshiyuki Kabashima | null | 1301.6199 | null | null |
LA-LDA: A Limited Attention Topic Model for Social Recommendation | cs.SI cs.IR cs.LG | Social media users have finite attention which limits the number of incoming
messages from friends they can process. Moreover, they pay more attention to
opinions and recommendations of some friends more than others. In this paper,
we propose LA-LDA, a latent topic model which incorporates limited,
non-uniformly divided attention in the diffusion process by which opinions and
information spread on the social network. We show that our proposed model is
able to learn more accurate user models from users' social network and item
adoption behavior than models which do not take limited attention into account.
We analyze voting on news items on the social news aggregator Digg and show
that our proposed model is better able to predict held out votes than
alternative models. Our study demonstrates that psycho-socially motivated
models have better ability to describe and predict observed behavior than
models which only consider topics.
| Jeon-Hyung Kang, Kristina Lerman, Lise Getoor | null | 1301.6277 | null | null |
Equitability Analysis of the Maximal Information Coefficient, with
Comparisons | cs.LG q-bio.QM stat.ML | A measure of dependence is said to be equitable if it gives similar scores to
equally noisy relationships of different types. Equitability is important in
data exploration when the goal is to identify a relatively small set of
strongest associations within a dataset as opposed to finding as many non-zero
associations as possible, which often are too many to sift through. Thus an
equitable statistic, such as the maximal information coefficient (MIC), can be
useful for analyzing high-dimensional data sets. Here, we explore both
equitability and the properties of MIC, and discuss several aspects of the
theory and practice of MIC. We begin by presenting an intuition behind the
equitability of MIC through the exploration of the maximization and
normalization steps in its definition. We then examine the speed and optimality
of the approximation algorithm used to compute MIC, and suggest some directions
for improving both. Finally, we demonstrate in a range of noise models and
sample sizes that MIC is more equitable than natural alternatives, such as
mutual information estimation and distance correlation.
| David Reshef (1), Yakir Reshef (1), Michael Mitzenmacher (2), Pardis
Sabeti (2) (1, 2 - contributed equally) | null | 1301.6314 | null | null |
Hierarchical Data Representation Model - Multi-layer NMF | cs.LG | In this paper, we propose a data representation model that demonstrates
hierarchical feature learning using nsNMF. We extend unit algorithm into
several layers. Experiments with document and image data successfully
discovered feature hierarchies. We also prove that proposed method results in
much better classification and reconstruction performance, especially for small
number of features. feature hierarchies.
| Hyun Ah Song, Soo-Young Lee | null | 1301.6316 | null | null |
An improvement to k-nearest neighbor classifier | cs.CV cs.LG stat.ML | K-Nearest neighbor classifier (k-NNC) is simple to use and has little design
time like finding k values in k-nearest neighbor classifier, hence these are
suitable to work with dynamically varying data-sets. There exists some
fundamental improvements over the basic k-NNC, like weighted k-nearest
neighbors classifier (where weights to nearest neighbors are given based on
linear interpolation), using artificially generated training set called
bootstrapped training set, etc. These improvements are orthogonal to space
reduction and classification time reduction techniques, hence can be coupled
with any of them. The paper proposes another improvement to the basic k-NNC
where the weights to nearest neighbors are given based on Gaussian distribution
(instead of linear interpolation as done in weighted k-NNC) which is also
independent of any space reduction and classification time reduction technique.
We formally show that our proposed method is closely related to non-parametric
density estimation using a Gaussian kernel. We experimentally demonstrate using
various standard data-sets that the proposed method is better than the existing
ones in most cases.
| T. Hitendra Sarma, P. Viswanath, D. Sai Koti Reddy and S. Sri Raghava | null | 1301.6324 | null | null |
Discriminative Feature Selection for Uncertain Graph Classification | cs.LG cs.DB stat.ML | Mining discriminative features for graph data has attracted much attention in
recent years due to its important role in constructing graph classifiers,
generating graph indices, etc. Most measurement of interestingness of
discriminative subgraph features are defined on certain graphs, where the
structure of graph objects are certain, and the binary edges within each graph
represent the "presence" of linkages among the nodes. In many real-world
applications, however, the linkage structure of the graphs is inherently
uncertain. Therefore, existing measurements of interestingness based upon
certain graphs are unable to capture the structural uncertainty in these
applications effectively. In this paper, we study the problem of discriminative
subgraph feature selection from uncertain graphs. This problem is challenging
and different from conventional subgraph mining problems because both the
structure of the graph objects and the discrimination score of each subgraph
feature are uncertain. To address these challenges, we propose a novel
discriminative subgraph feature selection method, DUG, which can find
discriminative subgraph features in uncertain graphs based upon different
statistical measures including expectation, median, mode and phi-probability.
We first compute the probability distribution of the discrimination scores for
each subgraph feature based on dynamic programming. Then a branch-and-bound
algorithm is proposed to search for discriminative subgraphs efficiently.
Extensive experiments on various neuroimaging applications (i.e., Alzheimer's
Disease, ADHD and HIV) have been performed to analyze the gain in performance
by taking into account structural uncertainties in identifying discriminative
subgraph features for graph classification.
| Xiangnan Kong, Philip S. Yu, Xue Wang, Ann B. Ragin | null | 1301.6626 | null | null |
Political Disaffection: a case study on the Italian Twitter community | cs.SI cs.LG physics.soc-ph | In our work we analyse the political disaffection or "the subjective feeling
of powerlessness, cynicism, and lack of confidence in the political process,
politicians, and democratic institutions, but with no questioning of the
political regime" by exploiting Twitter data through machine learning
techniques. In order to validate the quality of the time-series generated by
the Twitter data, we highlight the relations of these data with political
disaffection as measured by means of public opinion surveys. Moreover, we show
that important political news of Italian newspapers are often correlated with
the highest peaks of the produced time-series.
| Corrado Monti, Alessandro Rozza, Giovanni Zappella, Matteo Zignani,
Adam Arvidsson, Monica Poletti | null | 1301.6630 | null | null |
Clustering-Based Matrix Factorization | cs.LG | Recommender systems are emerging technologies that nowadays can be found in
many applications such as Amazon, Netflix, and so on. These systems help users
to find relevant information, recommendations, and their preferred items.
Slightly improvement of the accuracy of these recommenders can highly affect
the quality of recommendations. Matrix Factorization is a popular method in
Recommendation Systems showing promising results in accuracy and complexity. In
this paper we propose an extension of matrix factorization which adds general
neighborhood information on the recommendation model. Users and items are
clustered into different categories to see how these categories share
preferences. We then employ these shared interests of categories in a fusion by
Biased Matrix Factorization to achieve more accurate recommendations. This is a
complement for the current neighborhood aware matrix factorization models which
rely on using direct neighborhood information of users and items. The proposed
model is tested on two well-known recommendation system datasets: Movielens100k
and Netflix. Our experiment shows applying the general latent features of
categories into factorized recommender models improves the accuracy of
recommendations. The current neighborhood-aware models need a great number of
neighbors to acheive good accuracies. To the best of our knowledge, the
proposed model is better than or comparable with the current neighborhood-aware
models when they consider fewer number of neighbors.
| Nima Mirbakhsh and Charles X. Ling | null | 1301.6659 | null | null |
Inferring Parameters and Structure of Latent Variable Models by
Variational Bayes | cs.LG stat.ML | Current methods for learning graphical models with latent variables and a
fixed structure estimate optimal values for the model parameters. Whereas this
approach usually produces overfitting and suboptimal generalization
performance, carrying out the Bayesian program of computing the full posterior
distributions over the parameters remains a difficult problem. Moreover,
learning the structure of models with latent variables, for which the Bayesian
approach is crucial, is yet a harder problem. In this paper I present the
Variational Bayes framework, which provides a solution to these problems. This
approach approximates full posterior distributions over model parameters and
structures, as well as latent variables, in an analytical manner without
resorting to sampling methods. Unlike in the Laplace approximation, these
posteriors are generally non-Gaussian and no Hessian needs to be computed. The
resulting algorithm generalizes the standard Expectation Maximization
algorithm, and its convergence is guaranteed. I demonstrate that this algorithm
can be applied to a large class of models in several domains, including
unsupervised clustering and blind source separation.
| Hagai Attias | null | 1301.6676 | null | null |
Relative Loss Bounds for On-line Density Estimation with the Exponential
Family of Distributions | cs.LG stat.ML | We consider on-line density estimation with a parameterized density from the
exponential family. The on-line algorithm receives one example at a time and
maintains a parameter that is essentially an average of the past examples.
After receiving an example the algorithm incurs a loss which is the negative
log-likelihood of the example w.r.t. the past parameter of the algorithm. An
off-line algorithm can choose the best parameter based on all the examples. We
prove bounds on the additional total loss of the on-line algorithm over the
total loss of the off-line algorithm. These relative loss bounds hold for an
arbitrary sequence of examples. The goal is to design algorithms with the best
possible relative loss bounds. We use a certain divergence to derive and
analyze the algorithms. This divergence is a relative entropy between two
exponential distributions.
| Katy S. Azoury, Manfred K. Warmuth | null | 1301.6677 | null | null |
Discovering the Hidden Structure of Complex Dynamic Systems | cs.AI cs.LG | Dynamic Bayesian networks provide a compact and natural representation for
complex dynamic systems. However, in many cases, there is no expert available
from whom a model can be elicited. Learning provides an alternative approach
for constructing models of dynamic systems. In this paper, we address some of
the crucial computational aspects of learning the structure of dynamic systems,
particularly those where some relevant variables are partially observed or even
entirely unknown. Our approach is based on the Structural Expectation
Maximization (SEM) algorithm. The main computational cost of the SEM algorithm
is the gathering of expected sufficient statistics. We propose a novel
approximation scheme that allows these sufficient statistics to be computed
efficiently. We also investigate the fundamental problem of discovering the
existence of hidden variables without exhaustive and expensive search. Our
approach is based on the observation that, in dynamic systems, ignoring a
hidden variable typically results in a violation of the Markov property. Thus,
our algorithm searches for such violations in the data, and introduces hidden
variables to explain them. We provide empirical results showing that the
algorithm is able to learn the dynamics of complex systems in a computationally
tractable way.
| Xavier Boyen, Nir Friedman, Daphne Koller | null | 1301.6683 | null | null |
Comparing Bayesian Network Classifiers | cs.LG cs.AI stat.ML | In this paper, we empirically evaluate algorithms for learning four types of
Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN
augmented Naive-Bayes and general BNs, where the latter two are learned using
two variants of a conditional-independence (CI) based BN-learning algorithm.
Experimental results show the obtained classifiers, learned using the CI based
algorithms, are competitive with (or superior to) the best known classifiers,
based on both Bayesian networks and other formalisms; and that the
computational time for learning and using these classifiers is relatively
small. Moreover, these results also suggest a way to learn yet more effective
classifiers; we demonstrate empirically that this new algorithm does work as
expected. Collectively, these results argue that BN classifiers deserve more
attention in machine learning and data mining communities.
| Jie Cheng, Russell Greiner | null | 1301.6684 | null | null |
Fast Learning from Sparse Data | cs.LG stat.ML | We describe two techniques that significantly improve the running time of
several standard machine-learning algorithms when data is sparse. The first
technique is an algorithm that effeciently extracts one-way and two-way
counts--either real or expected-- from discrete data. Extracting such counts is
a fundamental step in learning algorithms for constructing a variety of models
including decision trees, decision graphs, Bayesian networks, and naive-Bayes
clustering models. The second technique is an algorithm that efficiently
performs the E-step of the EM algorithm (i.e. inference) when applied to a
naive-Bayes clustering model. Using real-world data sets, we demonstrate a
dramatic decrease in running time for algorithms that incorporate these
techniques.
| David Maxwell Chickering, David Heckerman | null | 1301.6685 | null | null |
Learning Polytrees | cs.AI cs.LG | We consider the task of learning the maximum-likelihood polytree from data.
Our first result is a performance guarantee establishing that the optimal
branching (or Chow-Liu tree), which can be computed very easily, constitutes a
good approximation to the best polytree. We then show that it is not possible
to do very much better, since the learning problem is NP-hard even to
approximately solve within some constant factor.
| Sanjoy Dasgupta | null | 1301.6688 | null | null |
Model-Based Bayesian Exploration | cs.AI cs.LG | Reinforcement learning systems are often concerned with balancing exploration
of untested actions against exploitation of actions that are known to be good.
The benefit of exploration can be estimated using the classical notion of Value
of Information - the expected improvement in future decision quality arising
from the information acquired by exploration. Estimating this quantity requires
an assessment of the agent's uncertainty about its current value estimates for
states. In this paper we investigate ways of representing and reasoning about
this uncertainty in algorithms where the system attempts to learn a model of
its environment. We explicitly represent uncertainty about the parameters of
the model and build probability distributions over Q-values based on these.
These distributions are used to compute a myopic approximation to the value of
information for each action and hence to select the action that best balances
exploration and exploitation.
| Richard Dearden, Nir Friedman, David Andre | null | 1301.6690 | null | null |
Data Analysis with Bayesian Networks: A Bootstrap Approach | cs.LG cs.AI stat.ML | In recent years there has been significant progress in algorithms and methods
for inducing Bayesian networks from data. However, in complex data analysis
problems, we need to go beyond being satisfied with inducing networks with high
scores. We need to provide confidence measures on features of these networks:
Is the existence of an edge between two nodes warranted? Is the Markov blanket
of a given node robust? Can we say something about the ordering of the
variables? We should be able to address these questions, even when the amount
of data is not enough to induce a high scoring network. In this paper we
propose Efron's Bootstrap as a computationally efficient approach for answering
these questions. In addition, we propose to use these confidence measures to
induce better structures from the data, and to detect the presence of latent
variables.
| Nir Friedman, Moises Goldszmidt, Abraham Wyner | null | 1301.6695 | null | null |
Learning Bayesian Network Structure from Massive Datasets: The "Sparse
Candidate" Algorithm | cs.LG cs.AI stat.ML | Learning Bayesian networks is often cast as an optimization problem, where
the computational task is to find a structure that maximizes a statistically
motivated score. By and large, existing learning tools address this
optimization problem using standard heuristic search techniques. Since the
search space is extremely large, such search procedures can spend most of the
time examining candidates that are extremely unreasonable. This problem becomes
critical when we deal with data sets that are large either in the number of
instances, or the number of attributes. In this paper, we introduce an
algorithm that achieves faster learning by restricting the search space. This
iterative algorithm restricts the parents of each variable to belong to a small
subset of candidates. We then search for a network that satisfies these
constraints. The learned network is then used for selecting better candidates
for the next iteration. We evaluate this algorithm both on synthetic and
real-life data. Our results show that it is significantly faster than
alternative search procedures without loss of quality in the learned
structures.
| Nir Friedman, Iftach Nachman, Dana Pe'er | null | 1301.6696 | null | null |
Parameter Priors for Directed Acyclic Graphical Models and the
Characterization of Several Probability Distributions | cs.LG stat.ML | We show that the only parameter prior for complete Gaussian DAG models that
satisfies global parameter independence, complete model equivalence, and some
weak regularity assumptions, is the normal-Wishart distribution. Our analysis
is based on the following new characterization of the Wishart distribution: let
W be an n x n, n >= 3, positive-definite symmetric matrix of random variables
and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if
W_{11}-W_{12}W_{22}^{-1}W_{12}' is independent of {W_{12}, W_{22}} for every
block partitioning W_{11}, W_{12}, W_{12}', W_{22} of W. Similar
characterizations of the normal and normal-Wishart distributions are provided
as well. We also show how to construct a prior for every DAG model over X from
the prior of a single regression model.
| Dan Geiger, David Heckerman | null | 1301.6697 | null | null |
Probabilistic Latent Semantic Analysis | cs.LG cs.IR stat.ML | Probabilistic Latent Semantic Analysis is a novel statistical technique for
the analysis of two-mode and co-occurrence data, which has applications in
information retrieval and filtering, natural language processing, machine
learning from text, and in related areas. Compared to standard Latent Semantic
Analysis which stems from linear algebra and performs a Singular Value
Decomposition of co-occurrence tables, the proposed method is based on a
mixture decomposition derived from a latent class model. This results in a more
principled approach which has a solid foundation in statistics. In order to
avoid overfitting, we propose a widely applicable generalization of maximum
likelihood model fitting by tempered EM. Our approach yields substantial and
consistent improvements over Latent Semantic Analysis in a number of
experiments.
| Thomas Hofmann | null | 1301.6705 | null | null |
On Supervised Selection of Bayesian Networks | cs.LG stat.ML | Given a set of possible models (e.g., Bayesian network structures) and a data
sample, in the unsupervised model selection problem the task is to choose the
most accurate model with respect to the domain joint probability distribution.
In contrast to this, in supervised model selection it is a priori known that
the chosen model will be used in the future for prediction tasks involving more
``focused' predictive distributions. Although focused predictive distributions
can be produced from the joint probability distribution by marginalization, in
practice the best model in the unsupervised sense does not necessarily perform
well in supervised domains. In particular, the standard marginal likelihood
score is a criterion for the unsupervised task, and, although frequently used
for supervised model selection also, does not perform well in such tasks. In
this paper we study the performance of the marginal likelihood score
empirically in supervised Bayesian network selection tasks by using a large
number of publicly available classification data sets, and compare the results
to those obtained by alternative model selection criteria, including empirical
crossvalidation methods, an approximation of a supervised marginal likelihood
measure, and a supervised version of Dawids prequential(predictive sequential)
principle.The results demonstrate that the marginal likelihood score does NOT
perform well FOR supervised model selection, WHILE the best results are
obtained BY using Dawids prequential r napproach.
| Petri Kontkanen, Petri Myllymaki, Tomi Silander, Henry Tirri | null | 1301.6710 | null | null |
A Bayesian Network Classifier that Combines a Finite Mixture Model and a
Naive Bayes Model | cs.LG cs.AI stat.ML | In this paper we present a new Bayesian network model for classification that
combines the naive-Bayes (NB) classifier and the finite-mixture (FM)
classifier. The resulting classifier aims at relaxing the strong assumptions on
which the two component models are based, in an attempt to improve on their
classification performance, both in terms of accuracy and in terms of
calibration of the estimated probabilities. The proposed classifier is obtained
by superimposing a finite mixture model on the set of feature variables of a
naive Bayes model. We present experimental results that compare the predictive
performance on real datasets of the new classifier with the predictive
performance of the NB classifier and the FM classifier.
| Stefano Monti, Gregory F. Cooper | null | 1301.6723 | null | null |
A Variational Approximation for Bayesian Networks with Discrete and
Continuous Latent Variables | cs.AI cs.LG stat.ML | We show how to use a variational approximation to the logistic function to
perform approximate inference in Bayesian networks containing discrete nodes
with continuous parents. Essentially, we convert the logistic function to a
Gaussian, which facilitates exact inference, and then iteratively adjust the
variational parameters to improve the quality of the approximation. We
demonstrate experimentally that this approximation is faster and potentially
more accurate than sampling. We also introduce a simple new technique for
handling evidence, which allows us to handle arbitrary distributions on
observed nodes, as well as achieving a significant speedup in networks with
discrete variables of large cardinality.
| Kevin Murphy | null | 1301.6724 | null | null |
Loopy Belief Propagation for Approximate Inference: An Empirical Study | cs.AI cs.LG | Recently, researchers have demonstrated that loopy belief propagation - the
use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error-
correcting codes.The most dramatic instance OF this IS the near Shannon - limit
performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO
loopy belief propagation IN a chain - structured Bayesian network. IN this
paper we ask : IS there something special about the error - correcting code
context, OR does loopy propagation WORK AS an approximate inference schemeIN a
more general setting? We compare the marginals computed using loopy propagation
TO the exact ones IN four Bayesian network architectures, including two real -
world networks : ALARM AND QMR.We find that the loopy beliefs often converge
AND WHEN they do, they give a good approximation TO the correct
marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no
obvious relationship TO the correct posteriors. We present SOME initial
investigations INTO the cause OF these oscillations, AND show that SOME simple
methods OF preventing them lead TO the wrong results.
| Kevin Murphy, Yair Weiss, Michael I. Jordan | null | 1301.6725 | null | null |
Learning Bayesian Networks from Incomplete Data with Stochastic Search
Algorithms | cs.AI cs.LG | This paper describes stochastic search approaches, including a new stochastic
algorithm and an adaptive mutation operator, for learning Bayesian networks
from incomplete data. This problem is characterized by a huge solution space
with a highly multimodal landscape. State-of-the-art approaches all involve
using deterministic approaches such as the expectation-maximization algorithm.
These approaches are guaranteed to find local maxima, but do not explore the
landscape for other modes. Our approach evolves structure and the missing data.
We compare our stochastic algorithms and show they all produce accurate
results.
| James W. Myers, Kathryn Blackmond Laskey, Tod S. Levitt | null | 1301.6726 | null | null |
Learning Bayesian Networks with Restricted Causal Interactions | cs.AI cs.LG stat.ML | A major problem for the learning of Bayesian networks (BNs) is the
exponential number of parameters needed for conditional probability tables.
Recent research reduces this complexity by modeling local structure in the
probability tables. We examine the use of log-linear local models. While
log-linear models in this context are not new (Whittaker, 1990; Buntine, 1991;
Neal, 1992; Heckerman and Meek, 1997), for structure learning they are
generally subsumed under a naive Bayes model. We describe an alternative
interpretation, and use a Minimum Message Length (MML) (Wallace, 1987) metric
for structure learning of networks exhibiting causal independence, which we
term first-order networks (FONs). We also investigate local model selection on
a node-by-node basis.
| Julian R. Neil, Chris S. Wallace, Kevin B. Korb | null | 1301.6727 | null | null |
Accelerating EM: An Empirical Study | cs.LG stat.ML | Many applications require that we learn the parameters of a model from data.
EM is a method used to learn the parameters of probabilistic models for which
the data for some of the variables in the models is either missing or hidden.
There are instances in which this method is slow to converge. Therefore,
several accelerations have been proposed to improve the method. None of the
proposed acceleration methods are theoretically dominant and experimental
comparisons are lacking. In this paper, we present the different proposed
accelerations and try to compare them experimentally. From the results of the
experiments, we argue that some acceleration of EM is always possible, but that
which acceleration is superior depends on properties of the problem.
| Luis E. Ortiz, Leslie Pack Kaelbling | null | 1301.6730 | null | null |
Variational Learning in Mixed-State Dynamic Graphical Models | cs.LG stat.ML | Many real-valued stochastic time-series are locally linear (Gassian), but
globally non-linear. For example, the trajectory of a human hand gesture can be
viewed as a linear dynamic system driven by a nonlinear dynamic system that
represents muscle actions. We present a mixed-state dynamic graphical model in
which a hidden Markov model drives a linear dynamic system. This combination
allows us to model both the discrete and continuous causes of trajectories such
as human gestures. The number of computations needed for exact inference is
exponential in the sequence length, so we derive an approximate variational
inference technique that can also be used to learn the parameters of the
discrete and continuous models. We show how the mixed-state model and the
variational technique can be used to classify human hand gestures made with a
computer mouse.
| Vladimir Pavlovic, Brendan J. Frey, Thomas S. Huang | null | 1301.6731 | null | null |
Approximate Learning in Complex Dynamic Bayesian Networks | cs.LG stat.ML | In this paper we extend the work of Smith and Papamichail (1999) and present
fast approximate Bayesian algorithms for learning in complex scenarios where at
any time frame, the relationships between explanatory state space variables can
be described by a Bayesian network that evolve dynamically over time and the
observations taken are not necessarily Gaussian. It uses recent developments in
approximate Bayesian forecasting methods in combination with more familiar
Gaussian propagation algorithms on junction trees. The procedure for learning
state parameters from data is given explicitly for common sampling
distributions and the methodology is illustrated through a real application.
The efficiency of the dynamic approximation is explored by using the Hellinger
divergence measure and theoretical bounds for the efficacy of such a procedure
are discussed.
| Raffaella Settimi, Jim Q. Smith, A. S. Gargoum | null | 1301.6738 | null | null |
An alternative text representation to TF-IDF and Bag-of-Words | cs.IR cs.LG stat.ML | In text mining, information retrieval, and machine learning, text documents
are commonly represented through variants of sparse Bag of Words (sBoW) vectors
(e.g. TF-IDF). Although simple and intuitive, sBoW style representations suffer
from their inherent over-sparsity and fail to capture word-level synonymy and
polysemy. Especially when labeled data is limited (e.g. in document
classification), or the text documents are short (e.g. emails or abstracts),
many features are rarely observed within the training corpus. This leads to
overfitting and reduced generalization accuracy. In this paper we propose Dense
Cohort of Terms (dCoT), an unsupervised algorithm to learn improved sBoW
document features. dCoT explicitly models absent words by removing and
reconstructing random sub-sets of words in the unlabeled corpus. With this
approach, dCoT learns to reconstruct frequent words from co-occurring
infrequent words and maps the high dimensional sparse sBoW vectors into a
low-dimensional dense representation. We show that the feature removal can be
marginalized out and that the reconstruction can be solved for in closed-form.
We demonstrate empirically, on several benchmark datasets, that dCoT features
significantly improve the classification accuracy across several document
classification tasks.
| Zhixiang (Eddie) Xu, Minmin Chen, Kilian Q. Weinberger, Fei Sha | null | 1301.6770 | null | null |
Guarantees of Total Variation Minimization for Signal Recovery | cs.IT cs.CV cs.LG math.IT | In this paper, we consider using total variation minimization to recover
signals whose gradients have a sparse support, from a small number of
measurements. We establish the proof for the performance guarantee of total
variation (TV) minimization in recovering \emph{one-dimensional} signal with
sparse gradient support. This partially answers the open problem of proving the
fidelity of total variation minimization in such a setting \cite{TVMulti}. In
particular, we have shown that the recoverable gradient sparsity can grow
linearly with the signal dimension when TV minimization is used. Recoverable
sparsity thresholds of TV minimization are explicitly computed for
1-dimensional signal by using the Grassmann angle framework. We also extend our
results to TV minimization for multidimensional signals. Stability of
recovering signal itself using 1-D TV minimization has also been established
through a property called "almost Euclidean property for 1-dimensional TV
norm". We further give a lower bound on the number of random Gaussian
measurements for recovering 1-dimensional signal vectors with $N$ elements and
$K$-sparse gradients. Interestingly, the number of needed measurements is lower
bounded by $\Omega((NK)^{\frac{1}{2}})$, rather than the $O(K\log(N/K))$ bound
frequently appearing in recovering $K$-sparse signal vectors.
| Jian-Feng Cai and Weiyu Xu | null | 1301.6791 | null | null |
Multi-Step Regression Learning for Compositional Distributional
Semantics | cs.CL cs.LG | We present a model for compositional distributional semantics related to the
framework of Coecke et al. (2010), and emulating formal semantics by
representing functions as tensors and arguments as vectors. We introduce a new
learning method for tensors, generalising the approach of Baroni and Zamparelli
(2010). We evaluate it on two benchmark data sets, and find it to outperform
existing leading methods. We argue in our analysis that the nature of this
learning method also renders it suitable for solving more subtle problems
compositional distributional models might face.
| Edward Grefenstette, Georgiana Dinu, Yao-Zhong Zhang, Mehrnoosh
Sadrzadeh and Marco Baroni | null | 1301.6939 | null | null |
On the Consistency of the Bootstrap Approach for Support Vector Machines
and Related Kernel Based Methods | stat.ML cs.LG | It is shown that bootstrap approximations of support vector machines (SVMs)
based on a general convex and smooth loss function and on a general kernel are
consistent. This result is useful to approximate the unknown finite sample
distribution of SVMs by the bootstrap approach.
| Andreas Christmann and Robert Hable | null | 1301.6944 | null | null |
Link prediction for partially observed networks | stat.ML cs.LG cs.SI | Link prediction is one of the fundamental problems in network analysis. In
many applications, notably in genetics, a partially observed network may not
contain any negative examples of absent edges, which creates a difficulty for
many existing supervised learning approaches. We develop a new method which
treats the observed network as a sample of the true network with different
sampling rates for positive and negative examples. We obtain a relative ranking
of potential links by their probabilities, utilizing information on node
covariates as well as on network topology. Empirically, the method performs
well under many settings, including when the observed network is sparse. We
apply the method to a protein-protein interaction network and a school
friendship network.
| Yunpeng Zhao, Elizaveta Levina and Ji Zhu | null | 1301.7047 | null | null |
Empirical Analysis of Predictive Algorithms for Collaborative Filtering | cs.IR cs.LG | Collaborative filtering or recommender systems use a database about user
preferences to predict additional topics or products a new user might like. In
this paper we describe several algorithms designed for this task, including
techniques based on correlation coefficients, vector-based similarity
calculations, and statistical Bayesian methods. We compare the predictive
accuracy of the various methods in a set of representative problem domains. We
use two basic classes of evaluation metrics. The first characterizes accuracy
over a set of individual predictions in terms of average absolute deviation.
The second estimates the utility of a ranked list of suggested items. This
metric uses an estimate of the probability that a user will see a
recommendation in an ordered list. Experiments were run for datasets associated
with 3 application areas, 4 experimental protocols, and the 2 evaluation
metrics for the various algorithms. Results indicate that for a wide range of
conditions, Bayesian networks with decision trees at each node and correlation
methods outperform Bayesian-clustering and vector-similarity methods. Between
correlation and Bayesian networks, the preferred method depends on the nature
of the dataset, nature of the application (ranked versus one-by-one
presentation), and the availability of votes with which to make predictions.
Other considerations include the size of database, speed of predictions, and
learning time.
| John S. Breese, David Heckerman, Carl Kadie | null | 1301.7363 | null | null |
The Bayesian Structural EM Algorithm | cs.LG cs.AI stat.ML | In recent years there has been a flurry of works on learning Bayesian
networks from data. One of the hard problems in this area is how to effectively
learn the structure of a belief network from incomplete data- that is, in the
presence of missing values or hidden variables. In a recent paper, I introduced
an algorithm called Structural EM that combines the standard Expectation
Maximization (EM) algorithm, which optimizes parameters, with structure search
for model selection. That algorithm learns networks based on penalized
likelihood scores, which include the BIC/MDL score and various approximations
to the Bayesian score. In this paper, I extend Structural EM to deal directly
with Bayesian model selection. I prove the convergence of the resulting
algorithm and show how to apply it for learning a large class of probabilistic
models, including Bayesian networks and some variants thereof.
| Nir Friedman | null | 1301.7373 | null | null |
Learning the Structure of Dynamic Probabilistic Networks | cs.AI cs.LG | Dynamic probabilistic networks are a compact representation of complex
stochastic processes. In this paper we examine how to learn the structure of a
DPN from data. We extend structure scoring rules for standard probabilistic
networks to the dynamic case, and show how to search for structure when some of
the variables are hidden. Finally, we examine two applications where such a
technology might be useful: predicting and classifying dynamic behaviors, and
learning causal orderings in biological processes. We provide empirical results
that demonstrate the applicability of our methods in both domains.
| Nir Friedman, Kevin Murphy, Stuart Russell | null | 1301.7374 | null | null |
Learning by Transduction | cs.LG stat.ML | We describe a method for predicting a classification of an object given
classifications of the objects in the training set, assuming that the pairs
object/classification are generated by an i.i.d. process from a continuous
probability distribution. Our method is a modification of Vapnik's
support-vector machine; its main novelty is that it gives not only the
prediction itself but also a practicable measure of the evidence found in
support of that prediction. We also describe a procedure for assigning degrees
of confidence to predictions made by the support vector machine. Some
experimental results are presented, and possible extensions of the algorithms
are discussed.
| Alex Gammerman, Volodya Vovk, Vladimir Vapnik | null | 1301.7375 | null | null |
Graphical Models and Exponential Families | cs.LG stat.ML | We provide a classification of graphical models according to their
representation as subfamilies of exponential families. Undirected graphical
models with no hidden variables are linear exponential families (LEFs),
directed acyclic graphical models and chain graphs with no hidden variables,
including Bayesian networks with several families of local distributions, are
curved exponential families (CEFs) and graphical models with hidden variables
are stratified exponential families (SEFs). An SEF is a finite union of CEFs
satisfying a frontier condition. In addition, we illustrate how one can
automatically generate independence and non-independence constraints on the
distributions over the observable variables implied by a Bayesian network with
hidden variables. The relevance of these results for model selection is
examined.
| Dan Geiger, Christopher Meek | null | 1301.7376 | null | null |
Minimum Encoding Approaches for Predictive Modeling | cs.LG stat.ML | We analyze differences between two information-theoretically motivated
approaches to statistical inference and model selection: the Minimum
Description Length (MDL) principle, and the Minimum Message Length (MML)
principle. Based on this analysis, we present two revised versions of MML: a
pointwise estimator which gives the MML-optimal single parameter model, and a
volumewise estimator which gives the MML-optimal region in the parameter space.
Our empirical results suggest that with small data sets, the MDL approach
yields more accurate predictions than the MML estimators. The empirical results
also demonstrate that the revised MML estimators introduced here perform better
than the original MML estimator suggested by Wallace and Freeman.
| Peter D Grunwald, Petri Kontkanen, Petri Myllymaki, Tomi Silander,
Henry Tirri | null | 1301.7378 | null | null |
Hierarchical Mixtures-of-Experts for Exponential Family Regression
Models with Generalized Linear Mean Functions: A Survey of Approximation and
Consistency Results | cs.LG stat.ML | We investigate a class of hierarchical mixtures-of-experts (HME) models where
exponential family regression models with generalized linear mean functions of
the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function.
Suppose the true response y follows an exponential family regression model with
mean function belonging to a class of smooth functions of the form psi(h(fx))
where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the
HME probability density functions can approximate the true density, at a rate
of O(m^{-2/s}) in L_p norm, and at a rate of O(m^{-4/s}) in Kullback-Leibler
divergence. These rates can be achieved within the family of HME structures
with no more than s-layers, where s is the dimension of the predictor fx. It is
also shown that likelihood-based inference based on HME is consistent in
recovering the truth, in the sense that as the sample size n and the number of
experts m both increase, the mean square error of the predicted mean response
goes to zero. Conditions for such results to hold are stated and discussed.
| Wenxin Jiang, Martin A. Tanner | null | 1301.7390 | null | null |
Large Deviation Methods for Approximate Probabilistic Inference | cs.LG stat.ML | We study two-layer belief networks of binary random variables in which the
conditional probabilities Pr[childlparents] depend monotonically on weighted
sums of the parents. In large networks where exact probabilistic inference is
intractable, we show how to compute upper and lower bounds on many
probabilities of interest. In particular, using methods from large deviation
theory, we derive rigorous bounds on marginal probabilities such as
Pr[children] and prove rates of convergence for the accuracy of our bounds as a
function of network size. Our results apply to networks with generic transfer
function parameterizations of the conditional probability tables, such as
sigmoid and noisy-OR. They also explicitly illustrate the types of averaging
behavior that can simplify the problem of inference in large networks.
| Michael Kearns, Lawrence Saul | null | 1301.7392 | null | null |
Mixture Representations for Inference and Learning in Boltzmann Machines | cs.LG stat.ML | Boltzmann machines are undirected graphical models with two-state stochastic
variables, in which the logarithms of the clique potentials are quadratic
functions of the node states. They have been widely studied in the neural
computing literature, although their practical applicability has been limited
by the difficulty of finding an effective learning algorithm. One
well-established approach, known as mean field theory, represents the
stochastic distribution using a factorized approximation. However, the
corresponding learning algorithm often fails to find a good solution. We
conjecture that this is due to the implicit uni-modality of the mean field
approximation which is therefore unable to capture multi-modality in the true
distribution. In this paper we use variational methods to approximate the
stochastic distribution using multi-modal mixtures of factorized distributions.
We present results for both inference and learning to demonstrate the
effectiveness of this approach.
| Neil D. Lawrence, Christopher M. Bishop, Michael I. Jordan | null | 1301.7393 | null | null |
An Experimental Comparison of Several Clustering and Initialization
Methods | cs.LG stat.ML | We examine methods for clustering in high dimensions. In the first part of
the paper, we perform an experimental comparison between three batch clustering
algorithms: the Expectation-Maximization (EM) algorithm, a winner take all
version of the EM algorithm reminiscent of the K-means algorithm, and
model-based hierarchical agglomerative clustering. We learn naive-Bayes models
with a hidden root node, using high-dimensional discrete-variable data sets
(both real and synthetic). We find that the EM algorithm significantly
outperforms the other methods, and proceed to investigate the effect of various
initialization schemes on the final solution produced by the EM algorithm. The
initializations that we consider are (1) parameters sampled from an
uninformative prior, (2) random perturbations of the marginal distribution of
the data, and (3) the output of hierarchical agglomerative clustering. Although
the methods are substantially different, they lead to learned models that are
strikingly similar in quality.
| Marina Meila, David Heckerman | null | 1301.7401 | null | null |
A Multivariate Discretization Method for Learning Bayesian Networks from
Mixed Data | cs.AI cs.LG | In this paper we address the problem of discretization in the context of
learning Bayesian networks (BNs) from data containing both continuous and
discrete variables. We describe a new technique for <EM>multivariate</EM>
discretization, whereby each continuous variable is discretized while taking
into account its interaction with the other variables. The technique is based
on the use of a Bayesian scoring metric that scores the discretization policy
for a continuous variable given a BN structure and the observed data. Since the
metric is relative to the BN structure currently being evaluated, the
discretization of a variable needs to be dynamically adjusted as the BN
structure changes.
| Stefano Monti, Gregory F. Cooper | null | 1301.7403 | null | null |
On the Geometry of Bayesian Graphical Models with Hidden Variables | cs.LG stat.ML | In this paper we investigate the geometry of the likelihood of the unknown
parameters in a simple class of Bayesian directed graphs with hidden variables.
This enables us, before any numerical algorithms are employed, to obtain
certain insights in the nature of the unidentifiability inherent in such
models, the way posterior densities will be sensitive to prior densities and
the typical geometrical form these posterior densities might take. Many of
these insights carry over into more complicated Bayesian networks with
systematic missing data.
| Raffaella Settimi, Jim Q. Smith | null | 1301.7411 | null | null |
Learning Mixtures of DAG Models | cs.LG cs.AI stat.ML | We describe computationally efficient methods for learning mixtures in which
each component is a directed acyclic graphical model (mixtures of DAGs or
MDAGs). We argue that simple search-and-score algorithms are infeasible for a
variety of problems, and introduce a feasible approach in which parameter and
structure search is interleaved and expected data is treated as real data. Our
approach can be viewed as a combination of (1) the Cheeseman--Stutz asymptotic
approximation for model posterior probability and (2) the
Expectation--Maximization algorithm. We evaluate our procedure for selecting
among MDAGs on synthetic and real examples.
| Bo Thiesson, Christopher Meek, David Maxwell Chickering, David
Heckerman | null | 1301.7415 | null | null |
Information driven self-organization of complex robotic behaviors | cs.RO cs.IT cs.LG math.IT | Information theory is a powerful tool to express principles to drive
autonomous systems because it is domain invariant and allows for an intuitive
interpretation. This paper studies the use of the predictive information (PI),
also called excess entropy or effective measure complexity, of the sensorimotor
process as a driving force to generate behavior. We study nonlinear and
nonstationary systems and introduce the time-local predicting information
(TiPI) which allows us to derive exact results together with explicit update
rules for the parameters of the controller in the dynamical systems framework.
In this way the information principle, formulated at the level of behavior, is
translated to the dynamics of the synapses. We underpin our results with a
number of case studies with high-dimensional robotic systems. We show the
spontaneous cooperativity in a complex physical system with decentralized
control. Moreover, a jointly controlled humanoid robot develops a high
behavioral variety depending on its physics and the environment it is
dynamically embedded into. The behavior can be decomposed into a succession of
low-dimensional modes that increasingly explore the behavior space. This is a
promising way to avoid the curse of dimensionality which hinders learning
systems to scale well.
| Georg Martius, Ralf Der, Nihat Ay | 10.1371/journal.pone.0063400 | 1301.7473 | null | null |
Rank regularization and Bayesian inference for tensor completion and
extrapolation | cs.IT cs.LG math.IT stat.ML | A novel regularizer of the PARAFAC decomposition factors capturing the
tensor's rank is proposed in this paper, as the key enabler for completion of
three-way data arrays with missing entries. Set in a Bayesian framework, the
tensor completion method incorporates prior information to enhance its
smoothing and prediction capabilities. This probabilistic approach can
naturally accommodate general models for the data distribution, lending itself
to various fitting criteria that yield optimum estimates in the
maximum-a-posteriori sense. In particular, two algorithms are devised for
Gaussian- and Poisson-distributed data, that minimize the rank-regularized
least-squares error and Kullback-Leibler divergence, respectively. The proposed
technique is able to recover the "ground-truth'' tensor rank when tested on
synthetic data, and to complete brain imaging and yeast gene expression
datasets with 50% and 15% of missing entries respectively, resulting in
recovery errors at -10dB and -15dB.
| Juan Andres Bazerque, Gonzalo Mateos, and Georgios B. Giannakis | 10.1109/TSP.2013.2278516 | 1301.7619 | null | null |
Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks | cs.LG cs.SI stat.ML | This paper considers networks where relationships between nodes are
represented by directed dissimilarities. The goal is to study methods for the
determination of hierarchical clusters, i.e., a family of nested partitions
indexed by a connectivity parameter, induced by the given dissimilarity
structures. Our construction of hierarchical clustering methods is based on
defining admissible methods to be those methods that abide by the axioms of
value - nodes in a network with two nodes are clustered together at the maximum
of the two dissimilarities between them - and transformation - when
dissimilarities are reduced, the network may become more clustered but not
less. Several admissible methods are constructed and two particular methods,
termed reciprocal and nonreciprocal clustering, are shown to provide upper and
lower bounds in the space of admissible methods. Alternative clustering
methodologies and axioms are further considered. Allowing the outcome of
hierarchical clustering to be asymmetric, so that it matches the asymmetry of
the original data, leads to the inception of quasi-clustering methods. The
existence of a unique quasi-clustering method is shown. Allowing clustering in
a two-node network to proceed at the minimum of the two dissimilarities
generates an alternative axiomatic construction. There is a unique clustering
method in this case too. The paper also develops algorithms for the computation
of hierarchical clusters using matrix powers on a min-max dioid algebra and
studies the stability of the methods proposed. We proved that most of the
methods introduced in this paper are such that similar networks yield similar
hierarchical clustering results. Algorithms are exemplified through their
application to networks describing internal migration within states of the
United States (U.S.) and the interrelation between sectors of the U.S. economy.
| Gunnar Carlsson, Facundo M\'emoli, Alejandro Ribeiro and Santiago
Segarra | null | 1301.7724 | null | null |
Distribution-Free Distribution Regression | stat.ML cs.LG math.ST stat.TH | `Distribution regression' refers to the situation where a response Y depends
on a covariate P where P is a probability distribution. The model is Y=f(P) +
mu where f is an unknown regression function and mu is a random error.
Typically, we do not observe P directly, but rather, we observe a sample from
P. In this paper we develop theory and methods for distribution-free versions
of distribution regression. This means that we do not make distributional
assumptions about the error term mu and covariate P. We prove that when the
effective dimension is small enough (as measured by the doubling dimension),
then the excess prediction risk converges to zero with a polynomial rate.
| Barnabas Poczos, Alessandro Rinaldo, Aarti Singh, Larry Wasserman | null | 1302.0082 | null | null |
Sparse Multiple Kernel Learning with Geometric Convergence Rate | cs.LG stat.ML | In this paper, we study the problem of sparse multiple kernel learning (MKL),
where the goal is to efficiently learn a combination of a fixed small number of
kernels from a large pool that could lead to a kernel classifier with a small
prediction error. We develop an efficient algorithm based on the greedy
coordinate descent algorithm, that is able to achieve a geometric convergence
rate under appropriate conditions. The convergence rate is achieved by
measuring the size of functional gradients by an empirical $\ell_2$ norm that
depends on the empirical data distribution. This is in contrast to previous
algorithms that use a functional norm to measure the size of gradients, which
is independent from the data samples. We also establish a generalization error
bound of the learned sparse kernel classifier using the technique of local
Rademacher complexity.
| Rong Jin, Tianbao Yang, Mehrdad Mahdavi | null | 1302.0315 | null | null |
Fast Damage Recovery in Robotics with the T-Resilience Algorithm | cs.RO cs.AI cs.LG | Damage recovery is critical for autonomous robots that need to operate for a
long time without assistance. Most current methods are complex and costly
because they require anticipating each potential damage in order to have a
contingency plan ready. As an alternative, we introduce the T-resilience
algorithm, a new algorithm that allows robots to quickly and autonomously
discover compensatory behaviors in unanticipated situations. This algorithm
equips the robot with a self-model and discovers new behaviors by learning to
avoid those that perform differently in the self-model and in reality. Our
algorithm thus does not identify the damaged parts but it implicitly searches
for efficient behaviors that do not use them. We evaluate the T-Resilience
algorithm on a hexapod robot that needs to adapt to leg removal, broken legs
and motor failures; we compare it to stochastic local search, policy gradient
and the self-modeling algorithm proposed by Bongard et al. The behavior of the
robot is assessed on-board thanks to a RGB-D sensor and a SLAM algorithm. Using
only 25 tests on the robot and an overall running time of 20 minutes,
T-Resilience consistently leads to substantially better results than the other
approaches.
| Sylvain Koos, Antoine Cully, Jean-Baptiste Mouret | 10.1177/0278364913499192 | 1302.0386 | null | null |
Generalization Guarantees for a Binary Classification Framework for
Two-Stage Multiple Kernel Learning | cs.LG stat.ML | We present generalization bounds for the TS-MKL framework for two stage
multiple kernel learning. We also present bounds for sparse kernel learning
formulations within the TS-MKL framework.
| Purushottam Kar | null | 1302.0406 | null | null |
Parallel D2-Clustering: Large-Scale Clustering of Discrete Distributions | cs.LG cs.CV | The discrete distribution clustering algorithm, namely D2-clustering, has
demonstrated its usefulness in image classification and annotation where each
object is represented by a bag of weighed vectors. The high computational
complexity of the algorithm, however, limits its applications to large-scale
problems. We present a parallel D2-clustering algorithm with substantially
improved scalability. A hierarchical structure for parallel computing is
devised to achieve a balance between the individual-node computation and the
integration process of the algorithm. Additionally, it is shown that even with
a single CPU, the hierarchical structure results in significant speed-up.
Experiments on real-world large-scale image data, Youtube video data, and
protein sequence data demonstrate the efficiency and wide applicability of the
parallel D2-clustering algorithm. The loss in clustering accuracy is minor in
comparison with the original sequential algorithm.
| Yu Zhang, James Z. Wang and Jia Li | null | 1302.0435 | null | null |
A game-theoretic framework for classifier ensembles using weighted
majority voting with local accuracy estimates | cs.LG | In this paper, a novel approach for the optimal combination of binary
classifiers is proposed. The classifier combination problem is approached from
a Game Theory perspective. The proposed framework of adapted weighted majority
rules (WMR) is tested against common rank-based, Bayesian and simple majority
models, as well as two soft-output averaging rules. Experiments with ensembles
of Support Vector Machines (SVM), Ordinary Binary Tree Classifiers (OBTC) and
weighted k-nearest-neighbor (w/k-NN) models on benchmark datasets indicate that
this new adaptive WMR model, employing local accuracy estimators and the
analytically computed optimal weights outperform all the other simple
combination rules.
| Harris V. Georgiou, Michael E. Mavroforakis | null | 1302.0540 | null | null |
Multi-Robot Informative Path Planning for Active Sensing of
Environmental Phenomena: A Tale of Two Algorithms | cs.LG cs.AI cs.MA cs.RO | A key problem of robotic environmental sensing and monitoring is that of
active sensing: How can a team of robots plan the most informative observation
paths to minimize the uncertainty in modeling and predicting an environmental
phenomenon? This paper presents two principled approaches to efficient
information-theoretic path planning based on entropy and mutual information
criteria for in situ active sensing of an important broad class of
widely-occurring environmental phenomena called anisotropic fields. Our
proposed algorithms are novel in addressing a trade-off between active sensing
performance and time efficiency. An important practical consequence is that our
algorithms can exploit the spatial correlation structure of Gaussian
process-based anisotropic fields to improve time efficiency while preserving
near-optimal active sensing performance. We analyze the time complexity of our
algorithms and prove analytically that they scale better than state-of-the-art
algorithms with increasing planning horizon length. We provide theoretical
guarantees on the active sensing performance of our algorithms for a class of
exploration tasks called transect sampling, which, in particular, can be
improved with longer planning time and/or lower spatial correlation along the
transect. Empirical evaluation on real-world anisotropic field data shows that
our algorithms can perform better or at least as well as the state-of-the-art
algorithms while often incurring a few orders of magnitude less computational
time, even when the field conditions are less favorable.
| Nannan Cao, Kian Hsiang Low, John M. Dolan | null | 1302.0723 | null | null |
Exact Sparse Recovery with L0 Projections | stat.ML cs.IT cs.LG math.IT math.ST stat.TH | Many applications concern sparse signals, for example, detecting anomalies
from the differences between consecutive images taken by surveillance cameras.
This paper focuses on the problem of recovering a K-sparse signal x in N
dimensions. In the mainstream framework of compressed sensing (CS), the vector
x is recovered from M non-adaptive linear measurements y = xS, where S (of size
N x M) is typically a Gaussian (or Gaussian-like) design matrix, through some
optimization procedure such as linear programming (LP).
In our proposed method, the design matrix S is generated from an
$\alpha$-stable distribution with $\alpha\approx 0$. Our decoding algorithm
mainly requires one linear scan of the coordinates, followed by a few
iterations on a small number of coordinates which are "undetermined" in the
previous iteration. Comparisons with two strong baselines, linear programming
(LP) and orthogonal matching pursuit (OMP), demonstrate that our algorithm can
be significantly faster in decoding speed and more accurate in recovery
quality, for the task of exact spare recovery. Our procedure is robust against
measurement noise. Even when there are no sufficient measurements, our
algorithm can still reliably recover a significant portion of the nonzero
coordinates.
To provide the intuition for understanding our method, we also analyze the
procedure by assuming an idealistic setting. Interestingly, when K=2, the
"idealized" algorithm achieves exact recovery with merely 3 measurements,
regardless of N. For general K, the required sample size of the "idealized"
algorithm is about 5K.
| Ping Li and Cun-Hui Zhang | null | 1302.0895 | null | null |
Improved Accuracy of PSO and DE using Normalization: an Application to
Stock Price Prediction | cs.NE cs.LG | Data Mining is being actively applied to stock market since 1980s. It has
been used to predict stock prices, stock indexes, for portfolio management,
trend detection and for developing recommender systems. The various algorithms
which have been used for the same include ANN, SVM, ARIMA, GARCH etc. Different
hybrid models have been developed by combining these algorithms with other
algorithms like roughest, fuzzy logic, GA, PSO, DE, ACO etc. to improve the
efficiency. This paper proposes DE-SVM model (Differential EvolutionSupport
vector Machine) for stock price prediction. DE has been used to select best
free parameters combination for SVM to improve results. The paper also compares
the results of prediction with the outputs of SVM alone and PSO-SVM model
(Particle Swarm Optimization). The effect of normalization of data on the
accuracy of prediction has also been studied.
| Savinderjit Kaur (Department of Information Technology, UIET, PU,
Chandigarh, India), Veenu Mangat (Department of Information Technology, UIET,
PU, Chandigarh, India) | null | 1302.0962 | null | null |
RandomBoost: Simplified Multi-class Boosting through Randomization | cs.LG | We propose a novel boosting approach to multi-class classification problems,
in which multiple classes are distinguished by a set of random projection
matrices in essence. The approach uses random projections to alleviate the
proliferation of binary classifiers typically required to perform multi-class
classification. The result is a multi-class classifier with a single
vector-valued parameter, irrespective of the number of classes involved. Two
variants of this approach are proposed. The first method randomly projects the
original data into new spaces, while the second method randomly projects the
outputs of learned weak classifiers. These methods are not only conceptually
simple but also effective and easy to implement. A series of experiments on
synthetic, machine learning and visual recognition data sets demonstrate that
our proposed methods compare favorably to existing multi-class boosting
algorithms in terms of both the convergence rate and classification accuracy.
| Sakrapee Paisitkriangkrai, Chunhua Shen, Qinfeng Shi, Anton van den
Hengel | null | 1302.0963 | null | null |
A Comparison of Relaxations of Multiset Cannonical Correlation Analysis
and Applications | cs.LG | Canonical correlation analysis is a statistical technique that is used to
find relations between two sets of variables. An important extension in pattern
analysis is to consider more than two sets of variables. This problem can be
expressed as a quadratically constrained quadratic program (QCQP), commonly
referred to Multi-set Canonical Correlation Analysis (MCCA). This is a
non-convex problem and so greedy algorithms converge to local optima without
any guarantees on global optimality. In this paper, we show that despite being
highly structured, finding the optimal solution is NP-Hard. This motivates our
relaxation of the QCQP to a semidefinite program (SDP). The SDP is convex, can
be solved reasonably efficiently and comes with both absolute and
output-sensitive approximation quality. In addition to theoretical guarantees,
we do an extensive comparison of the QCQP method and the SDP relaxation on a
variety of synthetic and real world data. Finally, we present two useful
extensions: we incorporate kernel methods and computing multiple sets of
canonical vectors.
| Jan Rupnik, Primoz Skraba, John Shawe-Taylor, Sabrina Guettes | null | 1302.0974 | null | null |
The price of bandit information in multiclass online classification | cs.LG | We consider two scenarios of multiclass online learning of a hypothesis class
$H\subseteq Y^X$. In the {\em full information} scenario, the learner is
exposed to instances together with their labels. In the {\em bandit} scenario,
the true label is not exposed, but rather an indication whether the learner's
prediction is correct or not. We show that the ratio between the error rates in
the two scenarios is at most $8\cdot|Y|\cdot \log(|Y|)$ in the realizable case,
and $\tilde{O}(\sqrt{|Y|})$ in the agnostic case. The results are tight up to a
logarithmic factor and essentially answer an open question from (Daniely et.
al. - Multiclass learnability and the erm principle).
We apply these results to the class of $\gamma$-margin multiclass linear
classifiers in $\reals^d$. We show that the bandit error rate of this class is
$\tilde{\Theta}(\frac{|Y|}{\gamma^2})$ in the realizable case and
$\tilde{\Theta}(\frac{1}{\gamma}\sqrt{|Y|T})$ in the agnostic case. This
resolves an open question from (Kakade et. al. - Efficient bandit algorithms
for online multiclass prediction).
| Amit Daniely and Tom Helbertal | null | 1302.1043 | null | null |
When are the most informative components for inference also the
principal components? | math.ST cs.DS cs.IT cs.LG math.IT math.PR stat.TH | Which components of the singular value decomposition of a signal-plus-noise
data matrix are most informative for the inferential task of detecting or
estimating an embedded low-rank signal matrix? Principal component analysis
ascribes greater importance to the components that capture the greatest
variation, i.e., the singular vectors associated with the largest singular
values. This choice is often justified by invoking the Eckart-Young theorem
even though that work addresses the problem of how to best represent a
signal-plus-noise matrix using a low-rank approximation and not how to
best_infer_ the underlying low-rank signal component.
Here we take a first-principles approach in which we start with a
signal-plus-noise data matrix and show how the spectrum of the noise-only
component governs whether the principal or the middle components of the
singular value decomposition of the data matrix will be the informative
components for inference. Simply put, if the noise spectrum is supported on a
connected interval, in a sense we make precise, then the use of the principal
components is justified. When the noise spectrum is supported on multiple
intervals, then the middle components might be more informative than the
principal components.
The end result is a proper justification of the use of principal components
in the setting where the noise matrix is i.i.d. Gaussian and the identification
of scenarios, generically involving heterogeneous noise models such as mixtures
of Gaussians, where the middle components might be more informative than the
principal components so that they may be exploited to extract additional
processing gain. Our results show how the blind use of principal components can
lead to suboptimal or even faulty inference because of phase transitions that
separate a regime where the principal components are informative from a regime
where they are uninformative.
| Raj Rao Nadakuditi | null | 1302.1232 | null | null |
A Polynomial Time Algorithm for Lossy Population Recovery | cs.DS cs.LG | We give a polynomial time algorithm for the lossy population recovery
problem. In this problem, the goal is to approximately learn an unknown
distribution on binary strings of length $n$ from lossy samples: for some
parameter $\mu$ each coordinate of the sample is preserved with probability
$\mu$ and otherwise is replaced by a `?'. The running time and number of
samples needed for our algorithm is polynomial in $n$ and $1/\varepsilon$ for
each fixed $\mu>0$. This improves on algorithm of Wigderson and Yehudayoff that
runs in quasi-polynomial time for any $\mu > 0$ and the polynomial time
algorithm of Dvir et al which was shown to work for $\mu \gtrapprox 0.30$ by
Batman et al. In fact, our algorithm also works in the more general framework
of Batman et al. in which there is no a priori bound on the size of the support
of the distribution. The algorithm we analyze is implicit in previous work; our
main contribution is to analyze the algorithm by showing (via linear
programming duality and connections to complex analysis) that a certain matrix
associated with the problem has a robust local inverse even though its
condition number is exponentially small. A corollary of our result is the first
polynomial time algorithm for learning DNFs in the restriction access model of
Dvir et al.
| Ankur Moitra, Michael Saks | null | 1302.1515 | null | null |
Update Rules for Parameter Estimation in Bayesian Networks | cs.LG stat.ML | This paper re-examines the problem of parameter estimation in Bayesian
networks with missing values and hidden variables from the perspective of
recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified
framework for parameter estimation that encompasses both on-line learning,
where the model is continuously adapted to new data cases as they arrive, and
the more traditional batch learning, where a pre-accumulated set of samples is
used in a one-time model selection process. In the batch case, our framework
encompasses both the gradient projection algorithm and the EM algorithm for
Bayesian networks. The framework also leads to new on-line and batch parameter
update schemes, including a parameterized version of EM. We provide both
empirical and theoretical results indicating that parameterized EM allows
faster convergence to the maximum likelihood parameters than does standard EM.
| Eric Bauer, Daphne Koller, Yoram Singer | null | 1302.1519 | null | null |
A Bayesian Approach to Learning Bayesian Networks with Local Structure | cs.LG cs.AI stat.ML | Recently several researchers have investigated techniques for using data to
learn Bayesian networks containing compact representations for the conditional
probability distributions (CPDs) stored at each node. The majority of this work
has concentrated on using decision-tree representations for the CPDs. In
addition, researchers typically apply non-Bayesian (or asymptotically Bayesian)
scoring functions such as MDL to evaluate the goodness-of-fit of networks to
the data. In this paper we investigate a Bayesian approach to learning Bayesian
networks that contain the more general decision-graph representations of the
CPDs. First, we describe how to evaluate the posterior probability that is, the
Bayesian score of such a network, given a database of observed cases. Second,
we describe various search spaces that can be used, in conjunction with a
scoring function and a search procedure, to identify one or more high-scoring
networks. Finally, we present an experimental evaluation of the search spaces,
using a greedy algorithm and a Bayesian scoring function.
| David Maxwell Chickering, David Heckerman, Christopher Meek | null | 1302.1528 | null | null |
Exploring Parallelism in Learning Belief Networks | cs.AI cs.LG | It has been shown that a class of probabilistic domain models cannot be
learned correctly by several existing algorithms which employ a single-link
look ahead search. When a multi-link look ahead search is used, the
computational complexity of the learning algorithm increases. We study how to
use parallelism to tackle the increased complexity in learning such models and
to speed up learning in large domains. An algorithm is proposed to decompose
the learning task for parallel processing. A further task decomposition is used
to balance load among processors and to increase the speed-up and efficiency.
For learning from very large datasets, we present a regrouping of the available
processors such that slow data access through file can be replaced by fast
memory access. Our implementation in a parallel computer demonstrates the
effectiveness of the algorithm.
| TongSheng Chu, Yang Xiang | null | 1302.1529 | null | null |
Sequential Update of Bayesian Network Structure | cs.AI cs.LG | There is an obvious need for improving the performance and accuracy of a
Bayesian network as new data is observed. Because of errors in model
construction and changes in the dynamics of the domains, we cannot afford to
ignore the information in new data. While sequential update of parameters for a
fixed structure can be accomplished using standard techniques, sequential
update of network structure is still an open problem. In this paper, we
investigate sequential update of Bayesian networks were both parameters and
structure are expected to change. We introduce a new approach that allows for
the flexible manipulation of the tradeoff between the quality of the learned
networks and the amount of information that is maintained about past
observations. We formally describe our approach including the necessary
modifications to the scoring functions for learning Bayesian networks, evaluate
its effectiveness through an empirical study, and extend it to the case of
missing data.
| Nir Friedman, Moises Goldszmidt | null | 1302.1538 | null | null |
Learning Bayesian Nets that Perform Well | cs.AI cs.LG | A Bayesian net (BN) is more than a succinct way to encode a probabilistic
distribution; it also corresponds to a function used to answer queries. A BN
can therefore be evaluated by the accuracy of the answers it returns. Many
algorithms for learning BNs, however, attempt to optimize another criterion
(usually likelihood, possibly augmented with a regularizing term), which is
independent of the distribution of queries that are posed. This paper takes the
"performance criteria" seriously, and considers the challenge of computing the
BN whose performance - read "accuracy over the distribution of queries" - is
optimal. We show that many aspects of this learning task are more difficult
than the corresponding subtasks in the standard model.
| Russell Greiner, Adam J. Grove, Dale Schuurmans | null | 1302.1542 | null | null |
Models and Selection Criteria for Regression and Classification | cs.LG stat.ML | When performing regression or classification, we are interested in the
conditional probability distribution for an outcome or class variable Y given a
set of explanatoryor input variables X. We consider Bayesian models for this
task. In particular, we examine a special class of models, which we call
Bayesian regression/classification (BRC) models, that can be factored into
independent conditional (y|x) and input (x) models. These models are
convenient, because the conditional model (the portion of the full model that
we care about) can be analyzed by itself. We examine the practice of
transforming arbitrary Bayesian models to BRC models, and argue that this
practice is often inappropriate because it ignores prior knowledge that may be
important for learning. In addition, we examine Bayesian methods for learning
models from data. We discuss two criteria for Bayesian model selection that are
appropriate for repression/classification: one described by Spiegelhalter et
al. (1993), and another by Buntine (1993). We contrast these two criteria using
the prequential framework of Dawid (1984), and give sufficient conditions under
which the criteria agree.
| David Heckerman, Christopher Meek | null | 1302.1545 | null | null |
Learning Belief Networks in Domains with Recursively Embedded Pseudo
Independent Submodels | cs.AI cs.LG | A pseudo independent (PI) model is a probabilistic domain model (PDM) where
proper subsets of a set of collectively dependent variables display marginal
independence. PI models cannot be learned correctly by many algorithms that
rely on a single link search. Earlier work on learning PI models has suggested
a straightforward multi-link search algorithm. However, when a domain contains
recursively embedded PI submodels, it may escape the detection of such an
algorithm. In this paper, we propose an improved algorithm that ensures the
learning of all embedded PI submodels whose sizes are upper bounded by a
predetermined parameter. We show that this improved learning capability only
increases the complexity slightly beyond that of the previous algorithm. The
performance of the new algorithm is demonstrated through experiment.
| Jun Hu, Yang Xiang | null | 1302.1549 | null | null |
An Information-Theoretic Analysis of Hard and Soft Assignment Methods
for Clustering | cs.LG stat.ML | Assignment methods are at the heart of many algorithms for unsupervised
learning and clustering - in particular, the well-known K-means and
Expectation-Maximization (EM) algorithms. In this work, we study several
different methods of assignment, including the "hard" assignments used by
K-means and the ?soft' assignments used by EM. While it is known that K-means
minimizes the distortion on the data and EM maximizes the likelihood, little is
known about the systematic differences of behavior between the two algorithms.
Here we shed light on these differences via an information-theoretic analysis.
The cornerstone of our results is a simple decomposition of the expected
distortion, showing that K-means (and its extension for inferring general
parametric densities from unlabeled sample data) must implicitly manage a
trade-off between how similar the data assigned to each cluster are, and how
the data are balanced among the clusters. How well the data are balanced is
measured by the entropy of the partition defined by the hard assignments. In
addition to letting us predict and verify systematic differences between
K-means and EM on specific examples, the decomposition allows us to give a
rather general argument showing that K ?means will consistently find densities
with less "overlap" than EM. We also study a third natural assignment method
that we call posterior assignment, that is close in spirit to the soft
assignments of EM, but leads to a surprisingly different algorithm.
| Michael Kearns, Yishay Mansour, Andrew Y. Ng | null | 1302.1552 | null | null |
Structure and Parameter Learning for Causal Independence and Causal
Interaction Models | cs.AI cs.LG | This paper discusses causal independence models and a generalization of these
models called causal interaction models. Causal interaction models are models
that have independent mechanisms where a mechanism can have several causes. In
addition to introducing several particular types of causal interaction models,
we show how we can apply the Bayesian approach to learning causal interaction
models obtaining approximate posterior distributions for the models and obtain
MAP and ML estimates for the parameters. We illustrate the approach with a
simulation study of learning model posteriors.
| Christopher Meek, David Heckerman | null | 1302.1561 | null | null |
Learning Bayesian Networks from Incomplete Databases | cs.AI cs.LG | Bayesian approaches to learn the graphical structure of Bayesian Belief
Networks (BBNs) from databases share the assumption that the database is
complete, that is, no entry is reported as unknown. Attempts to relax this
assumption involve the use of expensive iterative methods to discriminate among
different structures. This paper introduces a deterministic method to learn the
graphical structure of a BBN from a possibly incomplete database. Experimental
evaluations show a significant robustness of this method and a remarkable
independence of its execution time from the number of missing data.
| Marco Ramoni, Paola Sebastiani | null | 1302.1565 | null | null |
Bounded regret in stochastic multi-armed bandits | math.ST cs.LG stat.ML stat.TH | We study the stochastic multi-armed bandit problem when one knows the value
$\mu^{(\star)}$ of an optimal arm, as a well as a positive lower bound on the
smallest positive gap $\Delta$. We propose a new randomized policy that attains
a regret {\em uniformly bounded over time} in this setting. We also prove
several lower bounds, which show in particular that bounded regret is not
possible if one only knows $\Delta$, and bounded regret of order $1/\Delta$ is
not possible if one only knows $\mu^{(\star)}$
| S\'ebastien Bubeck, Vianney Perchet and Philippe Rigollet | null | 1302.1611 | null | null |
Feature Selection for Microarray Gene Expression Data using Simulated
Annealing guided by the Multivariate Joint Entropy | q-bio.QM cs.CE cs.LG stat.ML | In this work a new way to calculate the multivariate joint entropy is
presented. This measure is the basis for a fast information-theoretic based
evaluation of gene relevance in a Microarray Gene Expression data context. Its
low complexity is based on the reuse of previous computations to calculate
current feature relevance. The mu-TAFS algorithm --named as such to
differentiate it from previous TAFS algorithms-- implements a simulated
annealing technique specially designed for feature subset selection. The
algorithm is applied to the maximization of gene subset relevance in several
public-domain microarray data sets. The experimental results show a notoriously
high classification performance and low size subsets formed by biologically
meaningful genes.
| Fernando Gonz\'alez, Llu\'is A. Belanche | null | 1302.1733 | null | null |
An ANN-based Method for Detecting Vocal Fold Pathology | cs.LG cs.CV cs.SD | There are different algorithms for vocal fold pathology diagnosis. These
algorithms usually have three stages which are Feature Extraction, Feature
Reduction and Classification. While the third stage implies a choice of a
variety of machine learning methods, the first and second stages play a
critical role in performance and accuracy of the classification system. In this
paper we present initial study of feature extraction and feature reduction in
the task of vocal fold pathology diagnosis. A new type of feature vector, based
on wavelet packet decomposition and Mel-Frequency-Cepstral-Coefficients
(MFCCs), is proposed. Also Principal Component Analysis (PCA) is used for
feature reduction. An Artificial Neural Network is used as a classifier for
evaluating the performance of our proposed method.
| Vahid Majidnezhad and Igor Kheidorov | 10.5120/10089-4722 | 1302.1772 | null | null |
Passive Learning with Target Risk | cs.LG | In this paper we consider learning in passive setting but with a slight
modification. We assume that the target expected loss, also referred to as
target risk, is provided in advance for learner as prior knowledge. Unlike most
studies in the learning theory that only incorporate the prior knowledge into
the generalization bounds, we are able to explicitly utilize the target risk in
the learning process. Our analysis reveals a surprising result on the sample
complexity of learning: by exploiting the target risk in the learning
algorithm, we show that when the loss function is both strongly convex and
smooth, the sample complexity reduces to $\O(\log (\frac{1}{\epsilon}))$, an
exponential improvement compared to the sample complexity
$\O(\frac{1}{\epsilon})$ for learning with strongly convex loss functions.
Furthermore, our proof is constructive and is based on a computationally
efficient stochastic optimization algorithm for such settings which demonstrate
that the proposed algorithm is practically useful.
| Mehrdad Mahdavi and Rong Jin | null | 1302.2157 | null | null |
Minimax Optimal Algorithms for Unconstrained Linear Optimization | cs.LG | We design and analyze minimax-optimal algorithms for online linear
optimization games where the player's choice is unconstrained. The player
strives to minimize regret, the difference between his loss and the loss of a
post-hoc benchmark strategy. The standard benchmark is the loss of the best
strategy chosen from a bounded comparator set. When the the comparison set and
the adversary's gradients satisfy L_infinity bounds, we give the value of the
game in closed form and prove it approaches sqrt(2T/pi) as T -> infinity.
Interesting algorithms result when we consider soft constraints on the
comparator, rather than restricting it to a bounded set. As a warmup, we
analyze the game with a quadratic penalty. The value of this game is exactly
T/2, and this value is achieved by perhaps the simplest online algorithm of
all: unprojected gradient descent with a constant learning rate.
We then derive a minimax-optimal algorithm for a much softer penalty
function. This algorithm achieves good bounds under the standard notion of
regret for any comparator point, without needing to specify the comparator set
in advance. The value of this game converges to sqrt{e} as T ->infinity; we
give a closed-form for the exact value as a function of T. The resulting
algorithm is natural in unconstrained investment or betting scenarios, since it
guarantees at worst constant loss, while allowing for exponential reward
against an "easy" adversary.
| H. Brendan McMahan | null | 1302.2176 | null | null |
Learning Universally Quantified Invariants of Linear Data Structures | cs.PL cs.FL cs.LG | We propose a new automaton model, called quantified data automata over words,
that can model quantified invariants over linear data structures, and build
poly-time active learning algorithms for them, where the learner is allowed to
query the teacher with membership and equivalence queries. In order to express
invariants in decidable logics, we invent a decidable subclass of QDAs, called
elastic QDAs, and prove that every QDA has a unique
minimally-over-approximating elastic QDA. We then give an application of these
theoretically sound and efficient active learning algorithms in a passive
learning framework and show that we can efficiently learn quantified linear
data structure invariants from samples obtained from dynamic runs for a large
class of programs.
| Pranav Garg, Christof Loding, P. Madhusudan, Daniel Neider | null | 1302.2273 | null | null |
A Time Series Forest for Classification and Feature Extraction | cs.LG | We propose a tree ensemble method, referred to as time series forest (TSF),
for time series classification. TSF employs a combination of the entropy gain
and a distance measure, referred to as the Entrance (entropy and distance)
gain, for evaluating the splits. Experimental studies show that the Entrance
gain criterion improves the accuracy of TSF. TSF randomly samples features at
each tree node and has a computational complexity linear in the length of a
time series and can be built using parallel computing techniques such as
multi-core computing used here. The temporal importance curve is also proposed
to capture the important temporal characteristics useful for classification.
Experimental studies show that TSF using simple features such as mean,
deviation and slope outperforms strong competitors such as one-nearest-neighbor
classifiers with dynamic time warping, is computationally efficient, and can
provide insights into the temporal characteristics.
| Houtao Deng, George Runger, Eugene Tuv, Martyanov Vladimir | null | 1302.2277 | null | null |
Extracting useful rules through improved decision tree induction using
information entropy | cs.LG | Classification is widely used technique in the data mining domain, where
scalability and efficiency are the immediate problems in classification
algorithms for large databases. We suggest improvements to the existing C4.5
decision tree algorithm. In this paper attribute oriented induction (AOI) and
relevance analysis are incorporated with concept hierarchys knowledge and
HeightBalancePriority algorithm for construction of decision tree along with
Multi level mining. The assignment of priorities to attributes is done by
evaluating information entropy, at different levels of abstraction for building
decision tree using HeightBalancePriority algorithm. Modified DMQL queries are
used to understand and explore the shortcomings of the decision trees generated
by C4.5 classifier for education dataset and the results are compared with the
proposed approach.
| Mohd Mahmood Ali, Mohd S Qaseem, Lakshmi Rajamani, A Govardhan | 10.5121/ijist.2013.3103 | 1302.2436 | null | null |
Online Regret Bounds for Undiscounted Continuous Reinforcement Learning | cs.LG | We derive sublinear regret bounds for undiscounted reinforcement learning in
continuous state space. The proposed algorithm combines state aggregation with
the use of upper confidence bounds for implementing optimism in the face of
uncertainty. Beside the existence of an optimal policy which satisfies the
Poisson equation, the only assumptions made are Holder continuity of rewards
and transition probabilities.
| Ronald Ortner and Daniil Ryabko | null | 1302.2550 | null | null |
Selecting the State-Representation in Reinforcement Learning | cs.LG | The problem of selecting the right state-representation in a reinforcement
learning problem is considered. Several models (functions mapping past
observations to a finite set) of the observations are given, and it is known
that for at least one of these models the resulting state dynamics are indeed
Markovian. Without knowing neither which of the models is the correct one, nor
what are the probabilistic characteristics of the resulting MDP, it is required
to obtain as much reward as the optimal policy for the correct model (or for
the best of the correct models, if there are several). We propose an algorithm
that achieves that, with a regret of order T^{2/3} where T is the horizon time.
| Odalric-Ambrym Maillard, R\'emi Munos, Daniil Ryabko | null | 1302.2552 | null | null |
Optimal Regret Bounds for Selecting the State Representation in
Reinforcement Learning | cs.LG | We consider an agent interacting with an environment in a single stream of
actions, observations, and rewards, with no reset. This process is not assumed
to be a Markov Decision Process (MDP). Rather, the agent has several
representations (mapping histories of past interactions to a discrete state
space) of the environment with unknown dynamics, only some of which result in
an MDP. The goal is to minimize the average regret criterion against an agent
who knows an MDP representation giving the highest optimal reward, and acts
optimally in it. Recent regret bounds for this setting are of order
$O(T^{2/3})$ with an additive term constant yet exponential in some
characteristics of the optimal MDP. We propose an algorithm whose regret after
$T$ time steps is $O(\sqrt{T})$, with all constants reasonably small. This is
optimal in $T$ since $O(\sqrt{T})$ is the optimal regret in the setting of
learning in a (single discrete) MDP.
| Odalric-Ambrym Maillard, Phuong Nguyen, Ronald Ortner, Daniil Ryabko | null | 1302.2553 | null | null |
The trace norm constrained matrix-variate Gaussian process for multitask
bipartite ranking | cs.LG stat.ML | We propose a novel hierarchical model for multitask bipartite ranking. The
proposed approach combines a matrix-variate Gaussian process with a generative
model for task-wise bipartite ranking. In addition, we employ a novel trace
constrained variational inference approach to impose low rank structure on the
posterior matrix-variate Gaussian process. The resulting posterior covariance
function is derived in closed form, and the posterior mean function is the
solution to a matrix-variate regression with a novel spectral elastic net
regularizer. Further, we show that variational inference for the trace
constrained matrix-variate Gaussian process combined with maximum likelihood
parameter estimation for the bipartite ranking model is jointly convex. Our
motivating application is the prioritization of candidate disease genes. The
goal of this task is to aid the identification of unobserved associations
between human genes and diseases using a small set of observed associations as
well as kernels induced by gene-gene interaction networks and disease
ontologies. Our experimental results illustrate the performance of the proposed
model on real world datasets. Moreover, we find that the resulting low rank
solution improves the computational scalability of training and testing as
compared to baseline models.
| Oluwasanmi Koyejo and Cheng Lee and Joydeep Ghosh | null | 1302.2576 | null | null |
Geometrical complexity of data approximators | stat.ML cs.LG | There are many methods developed to approximate a cloud of vectors embedded
in high-dimensional space by simpler objects: starting from principal points
and linear manifolds to self-organizing maps, neural gas, elastic maps, various
types of principal curves and principal trees, and so on. For each type of
approximators the measure of the approximator complexity was developed too.
These measures are necessary to find the balance between accuracy and
complexity and to define the optimal approximations of a given type. We propose
a measure of complexity (geometrical complexity) which is applicable to
approximators of several types and which allows comparing data approximations
of different types.
| E. M. Mirkes, A. Zinovyev, A. N. Gorban | 10.1007/978-3-642-38679-4_50 | 1302.2645 | null | null |
Latent Self-Exciting Point Process Model for Spatial-Temporal Networks | cs.SI cs.LG stat.ML | We propose a latent self-exciting point process model that describes
geographically distributed interactions between pairs of entities. In contrast
to most existing approaches that assume fully observable interactions, here we
consider a scenario where certain interaction events lack information about
participants. Instead, this information needs to be inferred from the available
observations. We develop an efficient approximate algorithm based on
variational expectation-maximization to infer unknown participants in an event
given the location and the time of the event. We validate the model on
synthetic as well as real-world data, and obtain very promising results on the
identity-inference task. We also use our model to predict the timing and
participants of future events, and demonstrate that it compares favorably with
baseline approaches.
| Yoon-Sik Cho, Aram Galstyan, P. Jeffrey Brantingham, George Tita | 10.3934/dcdsb.2014.19.1335 | 1302.2671 | null | null |
Competing With Strategies | stat.ML cs.GT cs.LG | We study the problem of online learning with a notion of regret defined with
respect to a set of strategies. We develop tools for analyzing the minimax
rates and for deriving regret-minimization algorithms in this scenario. While
the standard methods for minimizing the usual notion of regret fail, through
our analysis we demonstrate existence of regret-minimization methods that
compete with such sets of strategies as: autoregressive algorithms, strategies
based on statistical models, regularized least squares, and follow the
regularized leader strategies. In several cases we also derive efficient
learning algorithms.
| Wei Han, Alexander Rakhlin, Karthik Sridharan | null | 1302.2672 | null | null |
A Tensor Approach to Learning Mixed Membership Community Models | cs.LG cs.SI stat.ML | Community detection is the task of detecting hidden communities from observed
interactions. Guaranteed community detection has so far been mostly limited to
models with non-overlapping communities such as the stochastic block model. In
this paper, we remove this restriction, and provide guaranteed community
detection for a family of probabilistic network models with overlapping
communities, termed as the mixed membership Dirichlet model, first introduced
by Airoldi et al. This model allows for nodes to have fractional memberships in
multiple communities and assumes that the community memberships are drawn from
a Dirichlet distribution. Moreover, it contains the stochastic block model as a
special case. We propose a unified approach to learning these models via a
tensor spectral decomposition method. Our estimator is based on low-order
moment tensor of the observed network, consisting of 3-star counts. Our
learning method is fast and is based on simple linear algebraic operations,
e.g. singular value decomposition and tensor power iterations. We provide
guaranteed recovery of community memberships and model parameters and present a
careful finite sample analysis of our learning method. As an important special
case, our results match the best known scaling requirements for the
(homogeneous) stochastic block model.
| Anima Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade | null | 1302.2684 | null | null |
Adaptive Metric Dimensionality Reduction | cs.LG cs.DS stat.ML | We study adaptive data-dependent dimensionality reduction in the context of
supervised learning in general metric spaces. Our main statistical contribution
is a generalization bound for Lipschitz functions in metric spaces that are
doubling, or nearly doubling. On the algorithmic front, we describe an analogue
of PCA for metric spaces: namely an efficient procedure that approximates the
data's intrinsic dimension, which is often much lower than the ambient
dimension. Our approach thus leverages the dual benefits of low dimensionality:
(1) more efficient algorithms, e.g., for proximity search, and (2) more
optimistic generalization bounds.
| Lee-Ad Gottlieb, Aryeh Kontorovich, Robert Krauthgamer | null | 1302.2752 | null | null |
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