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Optimal rates of convergence for persistence diagrams in Topological
Data Analysis | math.ST cs.CG cs.LG math.GT stat.TH | Computational topology has recently known an important development toward
data analysis, giving birth to the field of topological data analysis.
Topological persistence, or persistent homology, appears as a fundamental tool
in this field. In this paper, we study topological persistence in general
metric spaces, with a statistical approach. We show that the use of persistent
homology can be naturally considered in general statistical frameworks and
persistence diagrams can be used as statistics with interesting convergence
properties. Some numerical experiments are performed in various contexts to
illustrate our results.
| Fr\'ed\'eric Chazal and Marc Glisse and Catherine Labru\`ere and
Bertrand Michel | null | 1305.6239 | null | null |
Reinforcement Learning for the Soccer Dribbling Task | cs.LG cs.RO stat.ML | We propose a reinforcement learning solution to the \emph{soccer dribbling
task}, a scenario in which a soccer agent has to go from the beginning to the
end of a region keeping possession of the ball, as an adversary attempts to
gain possession. While the adversary uses a stationary policy, the dribbler
learns the best action to take at each decision point. After defining
meaningful variables to represent the state space, and high-level macro-actions
to incorporate domain knowledge, we describe our application of the
reinforcement learning algorithm \emph{Sarsa} with CMAC for function
approximation. Our experiments show that, after the training period, the
dribbler is able to accomplish its task against a strong adversary around 58%
of the time.
| Arthur Carvalho and Renato Oliveira | 10.1109/CIG.2011.6031994 | 1305.6568 | null | null |
Normalized Online Learning | cs.LG stat.ML | We introduce online learning algorithms which are independent of feature
scales, proving regret bounds dependent on the ratio of scales existent in the
data rather than the absolute scale. This has several useful effects: there is
no need to pre-normalize data, the test-time and test-space complexity are
reduced, and the algorithms are more robust.
| Stephane Ross and Paul Mineiro and John Langford | null | 1305.6646 | null | null |
Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process
Mixture | cs.LG stat.ML | This paper presents a novel algorithm, based upon the dependent Dirichlet
process mixture model (DDPMM), for clustering batch-sequential data containing
an unknown number of evolving clusters. The algorithm is derived via a
low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM,
and provides a hard clustering with convergence guarantees similar to those of
the k-means algorithm. Empirical results from a synthetic test with moving
Gaussian clusters and a test with real ADS-B aircraft trajectory data
demonstrate that the algorithm requires orders of magnitude less computational
time than contemporary probabilistic and hard clustering algorithms, while
providing higher accuracy on the examined datasets.
| Trevor Campbell, Miao Liu, Brian Kulis, Jonathan P. How, Lawrence
Carin | null | 1305.6659 | null | null |
Generalized Denoising Auto-Encoders as Generative Models | cs.LG | Recent work has shown how denoising and contractive autoencoders implicitly
capture the structure of the data-generating density, in the case where the
corruption noise is Gaussian, the reconstruction error is the squared error,
and the data is continuous-valued. This has led to various proposals for
sampling from this implicitly learned density function, using Langevin and
Metropolis-Hastings MCMC. However, it remained unclear how to connect the
training procedure of regularized auto-encoders to the implicit estimation of
the underlying data-generating distribution when the data are discrete, or
using other forms of corruption process and reconstruction errors. Another
issue is the mathematical justification which is only valid in the limit of
small corruption noise. We propose here a different attack on the problem,
which deals with all these issues: arbitrary (but noisy enough) corruption,
arbitrary reconstruction loss (seen as a log-likelihood), handling both
discrete and continuous-valued variables, and removing the bias due to
non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).
| Yoshua Bengio, Li Yao, Guillaume Alain, and Pascal Vincent | null | 1305.6663 | null | null |
Predicting the Severity of Breast Masses with Data Mining Methods | cs.LG stat.ML | Mammography is the most effective and available tool for breast cancer
screening. However, the low positive predictive value of breast biopsy
resulting from mammogram interpretation leads to approximately 70% unnecessary
biopsies with benign outcomes. Data mining algorithms could be used to help
physicians in their decisions to perform a breast biopsy on a suspicious lesion
seen in a mammogram image or to perform a short term follow-up examination
instead. In this research paper data mining classification algorithms; Decision
Tree (DT), Artificial Neural Network (ANN), and Support Vector Machine (SVM)
are analyzed on mammographic masses data set. The purpose of this study is to
increase the ability of physicians to determine the severity (benign or
malignant) of a mammographic mass lesion from BI-RADS attributes and the
patient,s age. The whole data set is divided for training the models and test
them by the ratio of 70:30% respectively and the performances of classification
algorithms are compared through three statistical measures; sensitivity,
specificity, and classification accuracy. Accuracy of DT, ANN and SVM are
78.12%, 80.56% and 81.25% of test samples respectively. Our analysis shows that
out of these three classification models SVM predicts severity of breast cancer
with least error rate and highest accuracy.
| Sahar A. Mokhtar and Alaa. M. Elsayad | null | 1305.7057 | null | null |
Test cost and misclassification cost trade-off using reframing | cs.LG | Many solutions to cost-sensitive classification (and regression) rely on some
or all of the following assumptions: we have complete knowledge about the cost
context at training time, we can easily re-train whenever the cost context
changes, and we have technique-specific methods (such as cost-sensitive
decision trees) that can take advantage of that information. In this paper we
address the problem of selecting models and minimising joint cost (integrating
both misclassification cost and test costs) without any of the above
assumptions. We introduce methods and plots (such as the so-called JROC plots)
that can work with any off-the-shelf predictive technique, including ensembles,
such that we reframe the model to use the appropriate subset of attributes (the
feature configuration) during deployment time. In other words, models are
trained with the available attributes (once and for all) and then deployed by
setting missing values on the attributes that are deemed ineffective for
reducing the joint cost. As the number of feature configuration combinations
grows exponentially with the number of features we introduce quadratic methods
that are able to approximate the optimal configuration and model choices, as
shown by the experimental results.
| Celestine Periale Maguedong-Djoumessi, Jos\'e Hern\'andez-Orallo | null | 1305.7111 | null | null |
Alternating Decision trees for early diagnosis of dengue fever | cs.LG q-bio.QM stat.AP | Dengue fever is a flu-like illness spread by the bite of an infected mosquito
which is fast emerging as a major health problem. Timely and cost effective
diagnosis using clinical and laboratory features would reduce the mortality
rates besides providing better grounds for clinical management and disease
surveillance. We wish to develop a robust and effective decision tree based
approach for predicting dengue disease. Our analysis is based on the clinical
characteristics and laboratory measurements of the diseased individuals. We
have developed and trained an alternating decision tree with boosting and
compared its performance with C4.5 algorithm for dengue disease diagnosis. Of
the 65 patient records a diagnosis establishes that 53 individuals have been
confirmed to have dengue fever. An alternating decision tree based algorithm
was able to differentiate the dengue fever using the clinical and laboratory
data with number of correctly classified instances as 89%, F-measure of 0.86
and receiver operator characteristics (ROC) of 0.826 as compared to C4.5 having
correctly classified instances as 78%,h F-measure of 0.738 and ROC of 0.617
respectively. Alternating decision tree based approach with boosting has been
able to predict dengue fever with a higher degree of accuracy than C4.5 based
decision tree using simple clinical and laboratory features. Further analysis
on larger data sets is required to improve the sensitivity and specificity of
the alternating decision trees.
| M. Naresh Kumar | null | 1305.7331 | null | null |
Privileged Information for Data Clustering | cs.LG stat.ML | Many machine learning algorithms assume that all input samples are
independently and identically distributed from some common distribution on
either the input space X, in the case of unsupervised learning, or the input
and output space X x Y in the case of supervised and semi-supervised learning.
In the last number of years the relaxation of this assumption has been explored
and the importance of incorporation of additional information within machine
learning algorithms became more apparent. Traditionally such fusion of
information was the domain of semi-supervised learning. More recently the
inclusion of knowledge from separate hypothetical spaces has been proposed by
Vapnik as part of the supervised setting. In this work we are interested in
exploring Vapnik's idea of master-class learning and the associated learning
using privileged information, however within the unsupervised setting. Adoption
of the advanced supervised learning paradigm for the unsupervised setting
instigates investigation into the difference between privileged and technical
data. By means of our proposed aRi-MAX method stability of the KMeans algorithm
is improved and identification of the best clustering solution is achieved on
an artificial dataset. Subsequently an information theoretic dot product based
algorithm called P-Dot is proposed. This method has the ability to utilize a
wide variety of clustering techniques, individually or in combination, while
fusing privileged and technical data for improved clustering. Application of
the P-Dot method to the task of digit recognition confirms our findings in a
real-world scenario.
| Jan Feyereisl, Uwe Aickelin | null | 1305.7454 | null | null |
On model selection consistency of regularized M-estimators | math.ST cs.LG math.OC stat.ME stat.ML stat.TH | Regularized M-estimators are used in diverse areas of science and engineering
to fit high-dimensional models with some low-dimensional structure. Usually the
low-dimensional structure is encoded by the presence of the (unknown)
parameters in some low-dimensional model subspace. In such settings, it is
desirable for estimates of the model parameters to be \emph{model selection
consistent}: the estimates also fall in the model subspace. We develop a
general framework for establishing consistency and model selection consistency
of regularized M-estimators and show how it applies to some special cases of
interest in statistical learning. Our analysis identifies two key properties of
regularized M-estimators, referred to as geometric decomposability and
irrepresentability, that ensure the estimators are consistent and model
selection consistent.
| Jason D. Lee, Yuekai Sun, Jonathan E. Taylor | null | 1305.7477 | null | null |
Understanding ACT-R - an Outsider's Perspective | cs.LG | The ACT-R theory of cognition developed by John Anderson and colleagues
endeavors to explain how humans recall chunks of information and how they solve
problems. ACT-R also serves as a theoretical basis for "cognitive tutors",
i.e., automatic tutoring systems that help students learn mathematics, computer
programming, and other subjects. The official ACT-R definition is distributed
across a large body of literature spanning many articles and monographs, and
hence it is difficult for an "outsider" to learn the most important aspects of
the theory. This paper aims to provide a tutorial to the core components of the
ACT-R theory.
| Jacob Whitehill | null | 1306.0125 | null | null |
Dynamic Ad Allocation: Bandits with Budgets | cs.LG cs.DS | We consider an application of multi-armed bandits to internet advertising
(specifically, to dynamic ad allocation in the pay-per-click model, with
uncertainty on the click probabilities). We focus on an important practical
issue that advertisers are constrained in how much money they can spend on
their ad campaigns. This issue has not been considered in the prior work on
bandit-based approaches for ad allocation, to the best of our knowledge.
We define a simple, stylized model where an algorithm picks one ad to display
in each round, and each ad has a \emph{budget}: the maximal amount of money
that can be spent on this ad. This model admits a natural variant of UCB1, a
well-known algorithm for multi-armed bandits with stochastic rewards. We derive
strong provable guarantees for this algorithm.
| Aleksandrs Slivkins | null | 1306.0155 | null | null |
Phase Retrieval using Alternating Minimization | stat.ML cs.IT cs.LG math.IT | Phase retrieval problems involve solving linear equations, but with missing
sign (or phase, for complex numbers) information. More than four decades after
it was first proposed, the seminal error reduction algorithm of (Gerchberg and
Saxton 1972) and (Fienup 1982) is still the popular choice for solving many
variants of this problem. The algorithm is based on alternating minimization;
i.e. it alternates between estimating the missing phase information, and the
candidate solution. Despite its wide usage in practice, no global convergence
guarantees for this algorithm are known. In this paper, we show that a
(resampling) variant of this approach converges geometrically to the solution
of one such problem -- finding a vector $\mathbf{x}$ from
$\mathbf{y},\mathbf{A}$, where $\mathbf{y} =
\left|\mathbf{A}^{\top}\mathbf{x}\right|$ and $|\mathbf{z}|$ denotes a vector
of element-wise magnitudes of $\mathbf{z}$ -- under the assumption that
$\mathbf{A}$ is Gaussian.
Empirically, we demonstrate that alternating minimization performs similar to
recently proposed convex techniques for this problem (which are based on
"lifting" to a convex matrix problem) in sample complexity and robustness to
noise. However, it is much more efficient and can scale to large problems.
Analytically, for a resampling version of alternating minimization, we show
geometric convergence to the solution, and sample complexity that is off by log
factors from obvious lower bounds. We also establish close to optimal scaling
for the case when the unknown vector is sparse. Our work represents the first
theoretical guarantee for alternating minimization (albeit with resampling) for
any variant of phase retrieval problems in the non-convex setting.
| Praneeth Netrapalli and Prateek Jain and Sujay Sanghavi | null | 1306.0160 | null | null |
RNADE: The real-valued neural autoregressive density-estimator | stat.ML cs.LG | We introduce RNADE, a new model for joint density estimation of real-valued
vectors. Our model calculates the density of a datapoint as the product of
one-dimensional conditionals modeled using mixture density networks with shared
parameters. RNADE learns a distributed representation of the data, while having
a tractable expression for the calculation of densities. A tractable likelihood
allows direct comparison with other methods and training by standard
gradient-based optimizers. We compare the performance of RNADE on several
datasets of heterogeneous and perceptual data, finding it outperforms mixture
models in all but one case.
| Benigno Uria, Iain Murray, Hugo Larochelle | null | 1306.0186 | null | null |
Guided Random Forest in the RRF Package | cs.LG | Random Forest (RF) is a powerful supervised learner and has been popularly
used in many applications such as bioinformatics.
In this work we propose the guided random forest (GRF) for feature selection.
Similar to a feature selection method called guided regularized random forest
(GRRF), GRF is built using the importance scores from an ordinary RF. However,
the trees in GRRF are built sequentially, are highly correlated and do not
allow for parallel computing, while the trees in GRF are built independently
and can be implemented in parallel. Experiments on 10 high-dimensional gene
data sets show that, with a fixed parameter value (without tuning the
parameter), RF applied to features selected by GRF outperforms RF applied to
all features on 9 data sets and 7 of them have significant differences at the
0.05 level. Therefore, both accuracy and interpretability are significantly
improved. GRF selects more features than GRRF, however, leads to better
classification accuracy. Note in this work the guided random forest is guided
by the importance scores from an ordinary random forest, however, it can also
be guided by other methods such as human insights (by specifying $\lambda_i$).
GRF can be used in "RRF" v1.4 (and later versions), a package that also
includes the regularized random forest methods.
| Houtao Deng | null | 1306.0237 | null | null |
Deep Learning using Linear Support Vector Machines | cs.LG stat.ML | Recently, fully-connected and convolutional neural networks have been trained
to achieve state-of-the-art performance on a wide variety of tasks such as
speech recognition, image classification, natural language processing, and
bioinformatics. For classification tasks, most of these "deep learning" models
employ the softmax activation function for prediction and minimize
cross-entropy loss. In this paper, we demonstrate a small but consistent
advantage of replacing the softmax layer with a linear support vector machine.
Learning minimizes a margin-based loss instead of the cross-entropy loss. While
there have been various combinations of neural nets and SVMs in prior art, our
results using L2-SVMs show that by simply replacing softmax with linear SVMs
gives significant gains on popular deep learning datasets MNIST, CIFAR-10, and
the ICML 2013 Representation Learning Workshop's face expression recognition
challenge.
| Yichuan Tang | null | 1306.0239 | null | null |
KERT: Automatic Extraction and Ranking of Topical Keyphrases from
Content-Representative Document Titles | cs.LG cs.IR | We introduce KERT (Keyphrase Extraction and Ranking by Topic), a framework
for topical keyphrase generation and ranking. By shifting from the
unigram-centric traditional methods of unsupervised keyphrase extraction to a
phrase-centric approach, we are able to directly compare and rank phrases of
different lengths. We construct a topical keyphrase ranking function which
implements the four criteria that represent high quality topical keyphrases
(coverage, purity, phraseness, and completeness). The effectiveness of our
approach is demonstrated on two collections of content-representative titles in
the domains of Computer Science and Physics.
| Marina Danilevsky, Chi Wang, Nihit Desai, Jingyi Guo, Jiawei Han | null | 1306.0271 | null | null |
Probabilistic Solutions to Differential Equations and their Application
to Riemannian Statistics | stat.ML cs.LG math.NA | We study a probabilistic numerical method for the solution of both boundary
and initial value problems that returns a joint Gaussian process posterior over
the solution. Such methods have concrete value in the statistics on Riemannian
manifolds, where non-analytic ordinary differential equations are involved in
virtually all computations. The probabilistic formulation permits marginalising
the uncertainty of the numerical solution such that statistics are less
sensitive to inaccuracies. This leads to new Riemannian algorithms for mean
value computations and principal geodesic analysis. Marginalisation also means
results can be less precise than point estimates, enabling a noticeable
speed-up over the state of the art. Our approach is an argument for a wider
point that uncertainty caused by numerical calculations should be tracked
throughout the pipeline of machine learning algorithms.
| Philipp Hennig and S{\o}ren Hauberg | null | 1306.0308 | null | null |
Learning from networked examples in a k-partite graph | cs.LG stat.ML | Many machine learning algorithms are based on the assumption that training
examples are drawn independently. However, this assumption does not hold
anymore when learning from a networked sample where two or more training
examples may share common features. We propose an efficient weighting method
for learning from networked examples and show the sample error bound which is
better than previous work.
| Yuyi Wang, Jan Ramon and Zheng-Chu Guo | null | 1306.0393 | null | null |
Riemannian metrics for neural networks II: recurrent networks and
learning symbolic data sequences | cs.NE cs.LG | Recurrent neural networks are powerful models for sequential data, able to
represent complex dependencies in the sequence that simpler models such as
hidden Markov models cannot handle. Yet they are notoriously hard to train.
Here we introduce a training procedure using a gradient ascent in a Riemannian
metric: this produces an algorithm independent from design choices such as the
encoding of parameters and unit activities. This metric gradient ascent is
designed to have an algorithmic cost close to backpropagation through time for
sparsely connected networks. We use this procedure on gated leaky neural
networks (GLNNs), a variant of recurrent neural networks with an architecture
inspired by finite automata and an evolution equation inspired by
continuous-time networks. GLNNs trained with a Riemannian gradient are
demonstrated to effectively capture a variety of structures in synthetic
problems: basic block nesting as in context-free grammars (an important feature
of natural languages, but difficult to learn), intersections of multiple
independent Markov-type relations, or long-distance relationships such as the
distant-XOR problem. This method does not require adjusting the network
structure or initial parameters: the network used is a sparse random graph and
the initialization is identical for all problems considered.
| Yann Ollivier | null | 1306.0514 | null | null |
On the Performance Bounds of some Policy Search Dynamic Programming
Algorithms | cs.AI cs.LG | We consider the infinite-horizon discounted optimal control problem
formalized by Markov Decision Processes. We focus on Policy Search algorithms,
that compute an approximately optimal policy by following the standard Policy
Iteration (PI) scheme via an -approximate greedy operator (Kakade and Langford,
2002; Lazaric et al., 2010). We describe existing and a few new performance
bounds for Direct Policy Iteration (DPI) (Lagoudakis and Parr, 2003; Fern et
al., 2006; Lazaric et al., 2010) and Conservative Policy Iteration (CPI)
(Kakade and Langford, 2002). By paying a particular attention to the
concentrability constants involved in such guarantees, we notably argue that
the guarantee of CPI is much better than that of DPI, but this comes at the
cost of a relative--exponential in $\frac{1}{\epsilon}$-- increase of time
complexity. We then describe an algorithm, Non-Stationary Direct Policy
Iteration (NSDPI), that can either be seen as 1) a variation of Policy Search
by Dynamic Programming by Bagnell et al. (2003) to the infinite horizon
situation or 2) a simplified version of the Non-Stationary PI with growing
period of Scherrer and Lesner (2012). We provide an analysis of this algorithm,
that shows in particular that it enjoys the best of both worlds: its
performance guarantee is similar to that of CPI, but within a time complexity
similar to that of DPI.
| Bruno Scherrer (INRIA Nancy - Grand Est / LORIA) | null | 1306.0539 | null | null |
Identifying Pairs in Simulated Bio-Medical Time-Series | cs.LG cs.CE | The paper presents a time-series-based classification approach to identify
similarities in pairs of simulated human-generated patterns. An example for a
pattern is a time-series representing a heart rate during a specific
time-range, wherein the time-series is a sequence of data points that represent
the changes in the heart rate values. A bio-medical simulator system was
developed to acquire a collection of 7,871 price patterns of financial
instruments. The financial instruments traded in real-time on three American
stock exchanges, NASDAQ, NYSE, and AMEX, simulate bio-medical measurements. The
system simulates a human in which each price pattern represents one bio-medical
sensor. Data provided during trading hours from the stock exchanges allowed
real-time classification. Classification is based on new machine learning
techniques: self-labeling, which allows the application of supervised learning
methods on unlabeled time-series and similarity ranking, which applied on a
decision tree learning algorithm to classify time-series regardless of type and
quantity.
| Uri Kartoun | null | 1306.0541 | null | null |
Predicting Parameters in Deep Learning | cs.LG cs.NE stat.ML | We demonstrate that there is significant redundancy in the parameterization
of several deep learning models. Given only a few weight values for each
feature it is possible to accurately predict the remaining values. Moreover, we
show that not only can the parameter values be predicted, but many of them need
not be learned at all. We train several different architectures by learning
only a small number of weights and predicting the rest. In the best case we are
able to predict more than 95% of the weights of a network without any drop in
accuracy.
| Misha Denil, Babak Shakibi, Laurent Dinh, Marc'Aurelio Ranzato, Nando
de Freitas | null | 1306.0543 | null | null |
Distributed k-Means and k-Median Clustering on General Topologies | cs.LG cs.DC stat.ML | This paper provides new algorithms for distributed clustering for two popular
center-based objectives, k-median and k-means. These algorithms have provable
guarantees and improve communication complexity over existing approaches.
Following a classic approach in clustering by \cite{har2004coresets}, we reduce
the problem of finding a clustering with low cost to the problem of finding a
coreset of small size. We provide a distributed method for constructing a
global coreset which improves over the previous methods by reducing the
communication complexity, and which works over general communication
topologies. Experimental results on large scale data sets show that this
approach outperforms other coreset-based distributed clustering algorithms.
| Maria Florina Balcan, Steven Ehrlich, Yingyu Liang | null | 1306.0604 | null | null |
Prediction with Missing Data via Bayesian Additive Regression Trees | stat.ML cs.LG | We present a method for incorporating missing data in non-parametric
statistical learning without the need for imputation. We focus on a tree-based
method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness
Incorporated in Attributes," an approach recently proposed incorporating
missingness into decision trees (Twala, 2008). This procedure takes advantage
of the partitioning mechanisms found in tree-based models. Simulations on
generated models and real data indicate that our proposed method can forecast
well on complicated missing-at-random and not-missing-at-random models as well
as models where missingness itself influences the response. Our procedure has
higher predictive performance and is more stable than competitors in many
cases. We also illustrate BART's abilities to incorporate missingness into
uncertainty intervals and to detect the influence of missingness on the model
fit.
| Adam Kapelner and Justin Bleich | null | 1306.0618 | null | null |
Provable Inductive Matrix Completion | cs.LG cs.IT math.IT stat.ML | Consider a movie recommendation system where apart from the ratings
information, side information such as user's age or movie's genre is also
available. Unlike standard matrix completion, in this setting one should be
able to predict inductively on new users/movies. In this paper, we study the
problem of inductive matrix completion in the exact recovery setting. That is,
we assume that the ratings matrix is generated by applying feature vectors to a
low-rank matrix and the goal is to recover back the underlying matrix.
Furthermore, we generalize the problem to that of low-rank matrix estimation
using rank-1 measurements. We study this generic problem and provide conditions
that the set of measurements should satisfy so that the alternating
minimization method (which otherwise is a non-convex method with no convergence
guarantees) is able to recover back the {\em exact} underlying low-rank matrix.
In addition to inductive matrix completion, we show that two other low-rank
estimation problems can be studied in our framework: a) general low-rank matrix
sensing using rank-1 measurements, and b) multi-label regression with missing
labels. For both the problems, we provide novel and interesting bounds on the
number of measurements required by alternating minimization to provably
converges to the {\em exact} low-rank matrix. In particular, our analysis for
the general low rank matrix sensing problem significantly improves the required
storage and computational cost than that required by the RIP-based matrix
sensing methods \cite{RechtFP2007}. Finally, we provide empirical validation of
our approach and demonstrate that alternating minimization is able to recover
the true matrix for the above mentioned problems using a small number of
measurements.
| Prateek Jain and Inderjit S. Dhillon | null | 1306.0626 | null | null |
Online Learning under Delayed Feedback | cs.LG cs.AI stat.ML | Online learning with delayed feedback has received increasing attention
recently due to its several applications in distributed, web-based learning
problems. In this paper we provide a systematic study of the topic, and analyze
the effect of delay on the regret of online learning algorithms. Somewhat
surprisingly, it turns out that delay increases the regret in a multiplicative
way in adversarial problems, and in an additive way in stochastic problems. We
give meta-algorithms that transform, in a black-box fashion, algorithms
developed for the non-delayed case into ones that can handle the presence of
delays in the feedback loop. Modifications of the well-known UCB algorithm are
also developed for the bandit problem with delayed feedback, with the advantage
over the meta-algorithms that they can be implemented with lower complexity.
| Pooria Joulani, Andr\'as Gy\"orgy, Csaba Szepesv\'ari | null | 1306.0686 | null | null |
Fast Gradient-Based Inference with Continuous Latent Variable Models in
Auxiliary Form | cs.LG stat.ML | We propose a technique for increasing the efficiency of gradient-based
inference and learning in Bayesian networks with multiple layers of continuous
latent vari- ables. We show that, in many cases, it is possible to express such
models in an auxiliary form, where continuous latent variables are
conditionally deterministic given their parents and a set of independent
auxiliary variables. Variables of mod- els in this auxiliary form have much
larger Markov blankets, leading to significant speedups in gradient-based
inference, e.g. rapid mixing Hybrid Monte Carlo and efficient gradient-based
optimization. The relative efficiency is confirmed in ex- periments.
| Diederik P Kingma | null | 1306.0733 | null | null |
A Gang of Bandits | cs.LG cs.SI stat.ML | Multi-armed bandit problems are receiving a great deal of attention because
they adequately formalize the exploration-exploitation trade-offs arising in
several industrially relevant applications, such as online advertisement and,
more generally, recommendation systems. In many cases, however, these
applications have a strong social component, whose integration in the bandit
algorithm could lead to a dramatic performance increase. For instance, we may
want to serve content to a group of users by taking advantage of an underlying
network of social relationships among them. In this paper, we introduce novel
algorithmic approaches to the solution of such networked bandit problems. More
specifically, we design and analyze a global strategy which allocates a bandit
algorithm to each network node (user) and allows it to "share" signals
(contexts and payoffs) with the neghboring nodes. We then derive two more
scalable variants of this strategy based on different ways of clustering the
graph nodes. We experimentally compare the algorithm and its variants to
state-of-the-art methods for contextual bandits that do not use the relational
information. Our experiments, carried out on synthetic and real-world datasets,
show a marked increase in prediction performance obtained by exploiting the
network structure.
| Nicol\`o Cesa-Bianchi, Claudio Gentile and Giovanni Zappella | null | 1306.0811 | null | null |
Kernel Mean Estimation and Stein's Effect | stat.ML cs.LG math.ST stat.TH | A mean function in reproducing kernel Hilbert space, or a kernel mean, is an
important part of many applications ranging from kernel principal component
analysis to Hilbert-space embedding of distributions. Given finite samples, an
empirical average is the standard estimate for the true kernel mean. We show
that this estimator can be improved via a well-known phenomenon in statistics
called Stein's phenomenon. After consideration, our theoretical analysis
reveals the existence of a wide class of estimators that are better than the
standard. Focusing on a subset of this class, we propose efficient shrinkage
estimators for the kernel mean. Empirical evaluations on several benchmark
applications clearly demonstrate that the proposed estimators outperform the
standard kernel mean estimator.
| Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Arthur
Gretton, Bernhard Sch\"olkopf | null | 1306.0842 | null | null |
$\propto$SVM for learning with label proportions | cs.LG stat.ML | We study the problem of learning with label proportions in which the training
data is provided in groups and only the proportion of each class in each group
is known. We propose a new method called proportion-SVM, or $\propto$SVM, which
explicitly models the latent unknown instance labels together with the known
group label proportions in a large-margin framework. Unlike the existing works,
our approach avoids making restrictive assumptions about the data. The
$\propto$SVM model leads to a non-convex integer programming problem. In order
to solve it efficiently, we propose two algorithms: one based on simple
alternating optimization and the other based on a convex relaxation. Extensive
experiments on standard datasets show that $\propto$SVM outperforms the
state-of-the-art, especially for larger group sizes.
| Felix X. Yu, Dong Liu, Sanjiv Kumar, Tony Jebara, Shih-Fu Chang | null | 1306.0886 | null | null |
(More) Efficient Reinforcement Learning via Posterior Sampling | stat.ML cs.LG | Most provably-efficient learning algorithms introduce optimism about
poorly-understood states and actions to encourage exploration. We study an
alternative approach for efficient exploration, posterior sampling for
reinforcement learning (PSRL). This algorithm proceeds in repeated episodes of
known duration. At the start of each episode, PSRL updates a prior distribution
over Markov decision processes and takes one sample from this posterior. PSRL
then follows the policy that is optimal for this sample during the episode. The
algorithm is conceptually simple, computationally efficient and allows an agent
to encode prior knowledge in a natural way. We establish an $\tilde{O}(\tau S
\sqrt{AT})$ bound on the expected regret, where $T$ is time, $\tau$ is the
episode length and $S$ and $A$ are the cardinalities of the state and action
spaces. This bound is one of the first for an algorithm not based on optimism,
and close to the state of the art for any reinforcement learning algorithm. We
show through simulation that PSRL significantly outperforms existing algorithms
with similar regret bounds.
| Ian Osband, Daniel Russo, Benjamin Van Roy | null | 1306.0940 | null | null |
Bayesian Differential Privacy through Posterior Sampling | stat.ML cs.LG | Differential privacy formalises privacy-preserving mechanisms that provide
access to a database. We pose the question of whether Bayesian inference itself
can be used directly to provide private access to data, with no modification.
The answer is affirmative: under certain conditions on the prior, sampling from
the posterior distribution can be used to achieve a desired level of privacy
and utility. To do so, we generalise differential privacy to arbitrary dataset
metrics, outcome spaces and distribution families. This allows us to also deal
with non-i.i.d or non-tabular datasets. We prove bounds on the sensitivity of
the posterior to the data, which gives a measure of robustness. We also show
how to use posterior sampling to provide differentially private responses to
queries, within a decision-theoretic framework. Finally, we provide bounds on
the utility and on the distinguishability of datasets. The latter are
complemented by a novel use of Le Cam's method to obtain lower bounds. All our
general results hold for arbitrary database metrics, including those for the
common definition of differential privacy. For specific choices of the metric,
we give a number of examples satisfying our assumptions.
| Christos Dimitrakakis and Blaine Nelson and and Zuhe Zhang and
Aikaterini Mitrokotsa and Benjamin Rubinstein | null | 1306.1066 | null | null |
Discriminative Parameter Estimation for Random Walks Segmentation:
Technical Report | cs.CV cs.LG | The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use
probabilistic segmentation methods. By combining contrast terms with prior
terms, it provides accurate segmentations of medical images in a fully
automated manner. However, one of the main drawbacks of using the RW algorithm
is that its parameters have to be hand-tuned. we propose a novel discriminative
learning framework that estimates the parameters using a training dataset. The
main challenge we face is that the training samples are not fully supervised.
Speci cally, they provide a hard segmentation of the images, instead of a
proba-bilistic segmentation. We overcome this challenge by treating the optimal
probabilistic segmentation that is compatible with the given hard segmentation
as a latent variable. This allows us to employ the latent support vector
machine formulation for parameter estimation. We show that our approach signi
cantly outperforms the baseline methods on a challenging dataset consisting of
real clinical 3D MRI volumes of skeletal muscles.
| Pierre-Yves Baudin (INRIA Saclay - Ile de France), Danny Goodman,
Puneet Kumar (INRIA Saclay - Ile de France, CVN), Noura Azzabou (MIRCEN,
UPMC), Pierre G. Carlier (UPMC), Nikos Paragios (INRIA Saclay - Ile de
France, LIGM, ENPC, MAS), M. Pawan Kumar (INRIA Saclay - Ile de France, CVN) | null | 1306.1083 | null | null |
Deep Generative Stochastic Networks Trainable by Backprop | cs.LG | We introduce a novel training principle for probabilistic models that is an
alternative to maximum likelihood. The proposed Generative Stochastic Networks
(GSN) framework is based on learning the transition operator of a Markov chain
whose stationary distribution estimates the data distribution. The transition
distribution of the Markov chain is conditional on the previous state,
generally involving a small move, so this conditional distribution has fewer
dominant modes, being unimodal in the limit of small moves. Thus, it is easier
to learn because it is easier to approximate its partition function, more like
learning to perform supervised function approximation, with gradients that can
be obtained by backprop. We provide theorems that generalize recent work on the
probabilistic interpretation of denoising autoencoders and obtain along the way
an interesting justification for dependency networks and generalized
pseudolikelihood, along with a definition of an appropriate joint distribution
and sampling mechanism even when the conditionals are not consistent. GSNs can
be used with missing inputs and can be used to sample subsets of variables
given the rest. We validate these theoretical results with experiments on two
image datasets using an architecture that mimics the Deep Boltzmann Machine
Gibbs sampler but allows training to proceed with simple backprop, without the
need for layerwise pretraining.
| Yoshua Bengio, \'Eric Thibodeau-Laufer, Guillaume Alain and Jason
Yosinski | null | 1306.1091 | null | null |
Multiclass Total Variation Clustering | stat.ML cs.LG math.OC | Ideas from the image processing literature have recently motivated a new set
of clustering algorithms that rely on the concept of total variation. While
these algorithms perform well for bi-partitioning tasks, their recursive
extensions yield unimpressive results for multiclass clustering tasks. This
paper presents a general framework for multiclass total variation clustering
that does not rely on recursion. The results greatly outperform previous total
variation algorithms and compare well with state-of-the-art NMF approaches.
| Xavier Bresson, Thomas Laurent, David Uminsky and James H. von Brecht | null | 1306.1185 | null | null |
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau
Functional Minimization | stat.ML cs.LG math.ST physics.data-an stat.TH | We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.
| Cristina Garcia-Cardona, Arjuna Flenner, Allon G. Percus | null | 1306.1298 | null | null |
Verdict Accuracy of Quick Reduct Algorithm using Clustering and
Classification Techniques for Gene Expression Data | cs.LG cs.CE stat.ML | In most gene expression data, the number of training samples is very small
compared to the large number of genes involved in the experiments. However,
among the large amount of genes, only a small fraction is effective for
performing a certain task. Furthermore, a small subset of genes is desirable in
developing gene expression based diagnostic tools for delivering reliable and
understandable results. With the gene selection results, the cost of biological
experiment and decision can be greatly reduced by analyzing only the marker
genes. An important application of gene expression data in functional genomics
is to classify samples according to their gene expression profiles. Feature
selection (FS) is a process which attempts to select more informative features.
It is one of the important steps in knowledge discovery. Conventional
supervised FS methods evaluate various feature subsets using an evaluation
function or metric to select only those features which are related to the
decision classes of the data under consideration. This paper studies a feature
selection method based on rough set theory. Further K-Means, Fuzzy C-Means
(FCM) algorithm have implemented for the reduced feature set without
considering class labels. Then the obtained results are compared with the
original class labels. Back Propagation Network (BPN) has also been used for
classification. Then the performance of K-Means, FCM, and BPN are analyzed
through the confusion matrix. It is found that the BPN is performing well
comparatively.
| T. Chandrasekhar, K. Thangavel, E.N. Sathishkumar | null | 1306.1323 | null | null |
Performance analysis of unsupervised feature selection methods | cs.LG | Feature selection (FS) is a process which attempts to select more informative
features. In some cases, too many redundant or irrelevant features may
overpower main features for classification. Feature selection can remedy this
problem and therefore improve the prediction accuracy and reduce the
computational overhead of classification algorithms. The main aim of feature
selection is to determine a minimal feature subset from a problem domain while
retaining a suitably high accuracy in representing the original features. In
this paper, Principal Component Analysis (PCA), Rough PCA, Unsupervised Quick
Reduct (USQR) algorithm and Empirical Distribution Ranking (EDR) approaches are
applied to discover discriminative features that will be the most adequate ones
for classification. Efficiency of the approaches is evaluated using standard
classification metrics.
| A. Nisthana Parveen, H. Hannah Inbarani, E.N. Sathishkumar | 10.1109/ICCCA.2012.6179181 | 1306.1326 | null | null |
Diffusion map for clustering fMRI spatial maps extracted by independent
component analysis | cs.CE cs.LG stat.ML | Functional magnetic resonance imaging (fMRI) produces data about activity
inside the brain, from which spatial maps can be extracted by independent
component analysis (ICA). In datasets, there are n spatial maps that contain p
voxels. The number of voxels is very high compared to the number of analyzed
spatial maps. Clustering of the spatial maps is usually based on correlation
matrices. This usually works well, although such a similarity matrix inherently
can explain only a certain amount of the total variance contained in the
high-dimensional data where n is relatively small but p is large. For
high-dimensional space, it is reasonable to perform dimensionality reduction
before clustering. In this research, we used the recently developed diffusion
map for dimensionality reduction in conjunction with spectral clustering. This
research revealed that the diffusion map based clustering worked as well as the
more traditional methods, and produced more compact clusters when needed.
| Tuomo Sipola, Fengyu Cong, Tapani Ristaniemi, Vinoo Alluri, Petri
Toiviainen, Elvira Brattico, Asoke K. Nandi | 10.1109/MLSP.2013.6661923 | 1306.1350 | null | null |
Tight Lower Bound on the Probability of a Binomial Exceeding its
Expectation | cs.LG stat.ML | We give the proof of a tight lower bound on the probability that a binomial
random variable exceeds its expected value. The inequality plays an important
role in a variety of contexts, including the analysis of relative deviation
bounds in learning theory and generalization bounds for unbounded loss
functions.
| Spencer Greenberg, Mehryar Mohri | null | 1306.1433 | null | null |
Highly Scalable, Parallel and Distributed AdaBoost Algorithm using Light
Weight Threads and Web Services on a Network of Multi-Core Machines | cs.DC cs.LG | AdaBoost is an important algorithm in machine learning and is being widely
used in object detection. AdaBoost works by iteratively selecting the best
amongst weak classifiers, and then combines several weak classifiers to obtain
a strong classifier. Even though AdaBoost has proven to be very effective, its
learning execution time can be quite large depending upon the application e.g.,
in face detection, the learning time can be several days. Due to its increasing
use in computer vision applications, the learning time needs to be drastically
reduced so that an adaptive near real time object detection system can be
incorporated. In this paper, we develop a hybrid parallel and distributed
AdaBoost algorithm that exploits the multiple cores in a CPU via light weight
threads, and also uses multiple machines via a web service software
architecture to achieve high scalability. We present a novel hierarchical web
services based distributed architecture and achieve nearly linear speedup up to
the number of processors available to us. In comparison with the previously
published work, which used a single level master-slave parallel and distributed
implementation [1] and only achieved a speedup of 2.66 on four nodes, we
achieve a speedup of 95.1 on 31 workstations each having a quad-core processor,
resulting in a learning time of only 4.8 seconds per feature.
| Munther Abualkibash, Ahmed ElSayed, Ausif Mahmood | null | 1306.1467 | null | null |
Gaussian Process-Based Decentralized Data Fusion and Active Sensing for
Mobility-on-Demand System | cs.RO cs.DC cs.LG cs.MA | Mobility-on-demand (MoD) systems have recently emerged as a promising
paradigm of one-way vehicle sharing for sustainable personal urban mobility in
densely populated cities. In this paper, we enhance the capability of a MoD
system by deploying robotic shared vehicles that can autonomously cruise the
streets to be hailed by users. A key challenge to managing the MoD system
effectively is that of real-time, fine-grained mobility demand sensing and
prediction. This paper presents a novel decentralized data fusion and active
sensing algorithm for real-time, fine-grained mobility demand sensing and
prediction with a fleet of autonomous robotic vehicles in a MoD system. Our
Gaussian process (GP)-based decentralized data fusion algorithm can achieve a
fine balance between predictive power and time efficiency. We theoretically
guarantee its predictive performance to be equivalent to that of a
sophisticated centralized sparse approximation for the GP model: The
computation of such a sparse approximate GP model can thus be distributed among
the MoD vehicles, hence achieving efficient and scalable demand prediction.
Though our decentralized active sensing strategy is devised to gather the most
informative demand data for demand prediction, it can achieve a dual effect of
fleet rebalancing to service the mobility demands. Empirical evaluation on
real-world mobility demand data shows that our proposed algorithm can achieve a
better balance between predictive accuracy and time efficiency than
state-of-the-art algorithms.
| Jie Chen, Kian Hsiang Low, Colin Keng-Yan Tan | null | 1306.1491 | null | null |
Policy Search: Any Local Optimum Enjoys a Global Performance Guarantee | cs.LG cs.AI cs.RO math.OC | Local Policy Search is a popular reinforcement learning approach for handling
large state spaces. Formally, it searches locally in a paramet erized policy
space in order to maximize the associated value function averaged over some
predefined distribution. It is probably commonly b elieved that the best one
can hope in general from such an approach is to get a local optimum of this
criterion. In this article, we show th e following surprising result:
\emph{any} (approximate) \emph{local optimum} enjoys a \emph{global performance
guarantee}. We compare this g uarantee with the one that is satisfied by Direct
Policy Iteration, an approximate dynamic programming algorithm that does some
form of Poli cy Search: if the approximation error of Local Policy Search may
generally be bigger (because local search requires to consider a space of s
tochastic policies), we argue that the concentrability coefficient that appears
in the performance bound is much nicer. Finally, we discuss several practical
and theoretical consequences of our analysis.
| Bruno Scherrer (INRIA Nancy - Grand Est / LORIA), Matthieu Geist | null | 1306.1520 | null | null |
Fast greedy algorithm for subspace clustering from corrupted and
incomplete data | cs.LG cs.DS math.NA stat.ML | We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm
providing an efficient method for clustering data belonging to a few
low-dimensional linear or affine subspaces. The main difference of our
algorithm from predecessors is its ability to work with noisy data having a
high rate of erasures (missed entries with the known coordinates) and errors
(corrupted entries with unknown coordinates). We discuss here how to implement
the fast version of the greedy algorithm with the maximum efficiency whose
greedy strategy is incorporated into iterations of the basic algorithm.
We provide numerical evidences that, in the subspace clustering capability,
the fast greedy algorithm outperforms not only the existing state-of-the art
SSC algorithm taken by the authors as a basic algorithm but also the recent
GSSC algorithm. At the same time, its computational cost is only slightly
higher than the cost of SSC.
The numerical evidence of the algorithm significant advantage is presented
for a few synthetic models as well as for the Extended Yale B dataset of facial
images. In particular, the face recognition misclassification rate turned out
to be 6-20 times lower than for the SSC algorithm. We provide also the
numerical evidence that the FGSSC algorithm is able to perform clustering of
corrupted data efficiently even when the sum of subspace dimensions
significantly exceeds the dimension of the ambient space.
| Alexander Petukhov and Inna Kozlov | null | 1306.1716 | null | null |
Loss-Proportional Subsampling for Subsequent ERM | cs.LG stat.ML | We propose a sampling scheme suitable for reducing a data set prior to
selecting a hypothesis with minimum empirical risk. The sampling only considers
a subset of the ultimate (unknown) hypothesis set, but can nonetheless
guarantee that the final excess risk will compare favorably with utilizing the
entire original data set. We demonstrate the practical benefits of our approach
on a large dataset which we subsample and subsequently fit with boosted trees.
| Paul Mineiro, Nikos Karampatziakis | null | 1306.1840 | null | null |
Emotional Expression Classification using Time-Series Kernels | cs.CV cs.LG stat.ML | Estimation of facial expressions, as spatio-temporal processes, can take
advantage of kernel methods if one considers facial landmark positions and
their motion in 3D space. We applied support vector classification with kernels
derived from dynamic time-warping similarity measures. We achieved over 99%
accuracy - measured by area under ROC curve - using only the 'motion pattern'
of the PCA compressed representation of the marker point vector, the so-called
shape parameters. Beyond the classification of full motion patterns, several
expressions were recognized with over 90% accuracy in as few as 5-6 frames from
their onset, about 200 milliseconds.
| Andras Lorincz, Laszlo Jeni, Zoltan Szabo, Jeffrey Cohn, Takeo Kanade | 10.1109/CVPRW.2013.131 | 1306.1913 | null | null |
Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean
Separation | stat.ML cs.LG math.ST stat.TH | While several papers have investigated computationally and statistically
efficient methods for learning Gaussian mixtures, precise minimax bounds for
their statistical performance as well as fundamental limits in high-dimensional
settings are not well-understood. In this paper, we provide precise information
theoretic bounds on the clustering accuracy and sample complexity of learning a
mixture of two isotropic Gaussians in high dimensions under small mean
separation. If there is a sparse subset of relevant dimensions that determine
the mean separation, then the sample complexity only depends on the number of
relevant dimensions and mean separation, and can be achieved by a simple
computationally efficient procedure. Our results provide the first step of a
theoretical basis for recent methods that combine feature selection and
clustering.
| Martin Azizyan, Aarti Singh, Larry Wasserman | null | 1306.2035 | null | null |
Logistic Tensor Factorization for Multi-Relational Data | stat.ML cs.LG | Tensor factorizations have become increasingly popular approaches for various
learning tasks on structured data. In this work, we extend the RESCAL tensor
factorization, which has shown state-of-the-art results for multi-relational
learning, to account for the binary nature of adjacency tensors. We study the
improvements that can be gained via this approach on various benchmark datasets
and show that the logistic extension can improve the prediction results
significantly.
| Maximilian Nickel, Volker Tresp | null | 1306.2084 | null | null |
Predicting Risk-of-Readmission for Congestive Heart Failure Patients: A
Multi-Layer Approach | cs.LG stat.AP | Mitigating risk-of-readmission of Congestive Heart Failure (CHF) patients
within 30 days of discharge is important because such readmissions are not only
expensive but also critical indicator of provider care and quality of
treatment. Accurately predicting the risk-of-readmission may allow hospitals to
identify high-risk patients and eventually improve quality of care by
identifying factors that contribute to such readmissions in many scenarios. In
this paper, we investigate the problem of predicting risk-of-readmission as a
supervised learning problem, using a multi-layer classification approach.
Earlier contributions inadequately attempted to assess a risk value for 30 day
readmission by building a direct predictive model as opposed to our approach.
We first split the problem into various stages, (a) at risk in general (b) risk
within 60 days (c) risk within 30 days, and then build suitable classifiers for
each stage, thereby increasing the ability to accurately predict the risk using
multiple layers of decision. The advantage of our approach is that we can use
different classification models for the subtasks that are more suited for the
respective problems. Moreover, each of the subtasks can be solved using
different features and training data leading to a highly confident diagnosis or
risk compared to a one-shot single layer approach. An experimental evaluation
on actual hospital patient record data from Multicare Health Systems shows that
our model is significantly better at predicting risk-of-readmission of CHF
patients within 30 days after discharge compared to prior attempts.
| Kiyana Zolfaghar, Nele Verbiest, Jayshree Agarwal, Naren Meadem,
Si-Chi Chin, Senjuti Basu Roy, Ankur Teredesai, David Hazel, Paul Amoroso,
Lester Reed | null | 1306.2094 | null | null |
A Novel Approach for Single Gene Selection Using Clustering and
Dimensionality Reduction | cs.CE cs.LG | We extend the standard rough set-based approach to deal with huge amounts of
numeric attributes versus small amount of available objects. Here, a novel
approach of clustering along with dimensionality reduction; Hybrid Fuzzy C
Means-Quick Reduct (FCMQR) algorithm is proposed for single gene selection.
Gene selection is a process to select genes which are more informative. It is
one of the important steps in knowledge discovery. The problem is that all
genes are not important in gene expression data. Some of the genes may be
redundant, and others may be irrelevant and noisy. In this study, the entire
dataset is divided in proper grouping of similar genes by applying Fuzzy C
Means (FCM) algorithm. A high class discriminated genes has been selected based
on their degree of dependence by applying Quick Reduct algorithm based on Rough
Set Theory to all the resultant clusters. Average Correlation Value (ACV) is
calculated for the high class discriminated genes. The clusters which have the
ACV value a s 1 is determined as significant clusters, whose classification
accuracy will be equal or high when comparing to the accuracy of the entire
dataset. The proposed algorithm is evaluated using WEKA classifiers and
compared. Finally, experimental results related to the leukemia cancer data
confirm that our approach is quite promising, though it surely requires further
research.
| E.N.Sathishkumar, K.Thangavel, T.Chandrasekhar | null | 1306.2118 | null | null |
Asymptotically Optimal Sequential Estimation of the Mean Based on
Inclusion Principle | math.ST cs.LG math.PR stat.TH | A large class of problems in sciences and engineering can be formulated as
the general problem of constructing random intervals with pre-specified
coverage probabilities for the mean. Wee propose a general approach for
statistical inference of mean values based on accumulated observational data.
We show that the construction of such random intervals can be accomplished by
comparing the endpoints of random intervals with confidence sequences for the
mean. Asymptotic results are obtained for such sequential methods.
| Xinjia Chen | null | 1306.2290 | null | null |
Markov random fields factorization with context-specific independences | cs.AI cs.LG | Markov random fields provide a compact representation of joint probability
distributions by representing its independence properties in an undirected
graph. The well-known Hammersley-Clifford theorem uses these conditional
independences to factorize a Gibbs distribution into a set of factors. However,
an important issue of using a graph to represent independences is that it
cannot encode some types of independence relations, such as the
context-specific independences (CSIs). They are a particular case of
conditional independences that is true only for a certain assignment of its
conditioning set; in contrast to conditional independences that must hold for
all its assignments. This work presents a method for factorizing a Markov
random field according to CSIs present in a distribution, and formally
guarantees that this factorization is correct. This is presented in our main
contribution, the context-specific Hammersley-Clifford theorem, a
generalization to CSIs of the Hammersley-Clifford theorem that applies for
conditional independences.
| Alejandro Edera, Facundo Bromberg, and Federico Schl\"uter | null | 1306.2295 | null | null |
Generative Model Selection Using a Scalable and Size-Independent Complex
Network Classifier | cs.SI cs.LG physics.soc-ph stat.ML | Real networks exhibit nontrivial topological features such as heavy-tailed
degree distribution, high clustering, and small-worldness. Researchers have
developed several generative models for synthesizing artificial networks that
are structurally similar to real networks. An important research problem is to
identify the generative model that best fits to a target network. In this
paper, we investigate this problem and our goal is to select the model that is
able to generate graphs similar to a given network instance. By the means of
generating synthetic networks with seven outstanding generative models, we have
utilized machine learning methods to develop a decision tree for model
selection. Our proposed method, which is named "Generative Model Selection for
Complex Networks" (GMSCN), outperforms existing methods with respect to
accuracy, scalability and size-independence.
| Sadegh Motallebi, Sadegh Aliakbary, Jafar Habibi | 10.1063/1.4840235 | 1306.2298 | null | null |
Auditing: Active Learning with Outcome-Dependent Query Costs | cs.LG | We propose a learning setting in which unlabeled data is free, and the cost
of a label depends on its value, which is not known in advance. We study binary
classification in an extreme case, where the algorithm only pays for negative
labels. Our motivation are applications such as fraud detection, in which
investigating an honest transaction should be avoided if possible. We term the
setting auditing, and consider the auditing complexity of an algorithm: the
number of negative labels the algorithm requires in order to learn a hypothesis
with low relative error. We design auditing algorithms for simple hypothesis
classes (thresholds and rectangles), and show that with these algorithms, the
auditing complexity can be significantly lower than the active label
complexity. We also discuss a general competitive approach for auditing and
possible modifications to the framework.
| Sivan Sabato and Anand D. Sarwate and Nathan Srebro | null | 1306.2347 | null | null |
DISCOMAX: A Proximity-Preserving Distance Correlation Maximization
Algorithm | cs.LG stat.ML | In a regression setting we propose algorithms that reduce the dimensionality
of the features while simultaneously maximizing a statistical measure of
dependence known as distance correlation between the low-dimensional features
and a response variable. This helps in solving the prediction problem with a
low-dimensional set of features. Our setting is different from subset-selection
algorithms where the problem is to choose the best subset of features for
regression. Instead, we attempt to generate a new set of low-dimensional
features as in a feature-learning setting. We attempt to keep our proposed
approach as model-free and our algorithm does not assume the application of any
specific regression model in conjunction with the low-dimensional features that
it learns. The algorithm is iterative and is fomulated as a combination of the
majorization-minimization and concave-convex optimization procedures. We also
present spectral radius based convergence results for the proposed iterations.
| Praneeth Vepakomma and Ahmed Elgammal | null | 1306.2533 | null | null |
Efficient Classification for Metric Data | cs.LG cs.DS stat.ML | Recent advances in large-margin classification of data residing in general
metric spaces (rather than Hilbert spaces) enable classification under various
natural metrics, such as string edit and earthmover distance. A general
framework developed for this purpose by von Luxburg and Bousquet [JMLR, 2004]
left open the questions of computational efficiency and of providing direct
bounds on generalization error.
We design a new algorithm for classification in general metric spaces, whose
runtime and accuracy depend on the doubling dimension of the data points, and
can thus achieve superior classification performance in many common scenarios.
The algorithmic core of our approach is an approximate (rather than exact)
solution to the classical problems of Lipschitz extension and of Nearest
Neighbor Search. The algorithm's generalization performance is guaranteed via
the fat-shattering dimension of Lipschitz classifiers, and we present
experimental evidence of its superiority to some common kernel methods. As a
by-product, we offer a new perspective on the nearest neighbor classifier,
which yields significantly sharper risk asymptotics than the classic analysis
of Cover and Hart [IEEE Trans. Info. Theory, 1967].
| Lee-Ad Gottlieb and Aryeh Kontorovich and Robert Krauthgamer | null | 1306.2547 | null | null |
The association problem in wireless networks: a Policy Gradient
Reinforcement Learning approach | cs.NI cs.IT cs.LG math.IT | The purpose of this paper is to develop a self-optimized association
algorithm based on PGRL (Policy Gradient Reinforcement Learning), which is both
scalable, stable and robust. The term robust means that performance degradation
in the learning phase should be forbidden or limited to predefined thresholds.
The algorithm is model-free (as opposed to Value Iteration) and robust (as
opposed to Q-Learning). The association problem is modeled as a Markov Decision
Process (MDP). The policy space is parameterized. The parameterized family of
policies is then used as expert knowledge for the PGRL. The PGRL converges
towards a local optimum and the average cost decreases monotonically during the
learning process. The properties of the solution make it a good candidate for
practical implementation. Furthermore, the robustness property allows to use
the PGRL algorithm in an "always-on" learning mode.
| Richard Combes and Ilham El Bouloumi and Stephane Senecal and Zwi
Altman | null | 1306.2554 | null | null |
Concentration bounds for temporal difference learning with linear
function approximation: The case of batch data and uniform sampling | cs.LG stat.ML | We propose a stochastic approximation (SA) based method with randomization of
samples for policy evaluation using the least squares temporal difference
(LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal
difference learning with linear function approximation, albeit with samples
picked uniformly from a given dataset. Our method results in an $O(d)$
improvement in complexity in comparison to LSTD, where $d$ is the dimension of
the data. We provide non-asymptotic bounds for our proposed method, both in
high probability and in expectation, under the assumption that the matrix
underlying the LSTD solution is positive definite. The latter assumption can be
easily satisfied for the pathwise LSTD variant proposed in [23]. Moreover, we
also establish that using our method in place of LSTD does not impact the rate
of convergence of the approximate value function to the true value function.
These rate results coupled with the low computational complexity of our method
make it attractive for implementation in big data settings, where $d$ is large.
A similar low-complexity alternative for least squares regression is well-known
as the stochastic gradient descent (SGD) algorithm. We provide finite-time
bounds for SGD. We demonstrate the practicality of our method as an efficient
alternative for pathwise LSTD empirically by combining it with the least
squares policy iteration (LSPI) algorithm in a traffic signal control
application. We also conduct another set of experiments that combines the SA
based low-complexity variant for least squares regression with the LinUCB
algorithm for contextual bandits, using the large scale news recommendation
dataset from Yahoo.
| L.A. Prashanth, Nathaniel Korda and R\'emi Munos | null | 1306.2557 | null | null |
Large Margin Low Rank Tensor Analysis | cs.LG cs.NA | Other than vector representations, the direct objects of human cognition are
generally high-order tensors, such as 2D images and 3D textures. From this
fact, two interesting questions naturally arise: How does the human brain
represent these tensor perceptions in a "manifold" way, and how can they be
recognized on the "manifold"? In this paper, we present a supervised model to
learn the intrinsic structure of the tensors embedded in a high dimensional
Euclidean space. With the fixed point continuation procedures, our model
automatically and jointly discovers the optimal dimensionality and the
representations of the low dimensional embeddings. This makes it an effective
simulation of the cognitive process of human brain. Furthermore, the
generalization of our model based on similarity between the learned low
dimensional embeddings can be viewed as counterpart of recognition of human
brain. Experiments on applications for object recognition and face recognition
demonstrate the superiority of our proposed model over state-of-the-art
approaches.
| Guoqiang Zhong and Mohamed Cheriet | null | 1306.2663 | null | null |
Precisely Verifying the Null Space Conditions in Compressed Sensing: A
Sandwiching Algorithm | cs.IT cs.LG cs.SY math.IT math.OC stat.ML | In this paper, we propose new efficient algorithms to verify the null space
condition in compressed sensing (CS). Given an $(n-m) \times n$ ($m>0$) CS
matrix $A$ and a positive $k$, we are interested in computing $\displaystyle
\alpha_k = \max_{\{z: Az=0,z\neq 0\}}\max_{\{K: |K|\leq k\}}$ ${\|z_K
\|_{1}}{\|z\|_{1}}$, where $K$ represents subsets of $\{1,2,...,n\}$, and $|K|$
is the cardinality of $K$. In particular, we are interested in finding the
maximum $k$ such that $\alpha_k < {1}{2}$. However, computing $\alpha_k$ is
known to be extremely challenging. In this paper, we first propose a series of
new polynomial-time algorithms to compute upper bounds on $\alpha_k$. Based on
these new polynomial-time algorithms, we further design a new sandwiching
algorithm, to compute the \emph{exact} $\alpha_k$ with greatly reduced
complexity. When needed, this new sandwiching algorithm also achieves a smooth
tradeoff between computational complexity and result accuracy. Empirical
results show the performance improvements of our algorithm over existing known
methods; and our algorithm outputs precise values of $\alpha_k$, with much
lower complexity than exhaustive search.
| Myung Cho and Weiyu Xu | null | 1306.2665 | null | null |
R3MC: A Riemannian three-factor algorithm for low-rank matrix completion | math.OC cs.LG | We exploit the versatile framework of Riemannian optimization on quotient
manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank
matrix completion. The underlying search space of fixed-rank matrices is
endowed with a novel Riemannian metric that is tailored to the least-squares
cost. Numerical comparisons suggest that R3MC robustly outperforms
state-of-the-art algorithms across different problem instances, especially
those that combine scarcely sampled and ill-conditioned data.
| B. Mishra and R. Sepulchre | null | 1306.2672 | null | null |
Flexible sampling of discrete data correlations without the marginal
distributions | stat.ML cs.LG stat.CO | Learning the joint dependence of discrete variables is a fundamental problem
in machine learning, with many applications including prediction, clustering
and dimensionality reduction. More recently, the framework of copula modeling
has gained popularity due to its modular parametrization of joint
distributions. Among other properties, copulas provide a recipe for combining
flexible models for univariate marginal distributions with parametric families
suitable for potentially high dimensional dependence structures. More
radically, the extended rank likelihood approach of Hoff (2007) bypasses
learning marginal models completely when such information is ancillary to the
learning task at hand as in, e.g., standard dimensionality reduction problems
or copula parameter estimation. The main idea is to represent data by their
observable rank statistics, ignoring any other information from the marginals.
Inference is typically done in a Bayesian framework with Gaussian copulas, and
it is complicated by the fact this implies sampling within a space where the
number of constraints increases quadratically with the number of data points.
The result is slow mixing when using off-the-shelf Gibbs sampling. We present
an efficient algorithm based on recent advances on constrained Hamiltonian
Markov chain Monte Carlo that is simple to implement and does not require
paying for a quadratic cost in sample size.
| Alfredo Kalaitzis and Ricardo Silva | null | 1306.2685 | null | null |
Copula Mixed-Membership Stochastic Blockmodel for Intra-Subgroup
Correlations | cs.LG stat.ML | The \emph{Mixed-Membership Stochastic Blockmodel (MMSB)} is a popular
framework for modeling social network relationships. It can fully exploit each
individual node's participation (or membership) in a social structure. Despite
its powerful representations, this model makes an assumption that the
distributions of relational membership indicators between two nodes are
independent. Under many social network settings, however, it is possible that
certain known subgroups of people may have high or low correlations in terms of
their membership categories towards each other, and such prior information
should be incorporated into the model. To this end, we introduce a \emph{Copula
Mixed-Membership Stochastic Blockmodel (cMMSB)} where an individual Copula
function is employed to jointly model the membership pairs of those nodes
within the subgroup of interest. The model enables the use of various Copula
functions to suit the scenario, while maintaining the membership's marginal
distribution, as needed, for modeling membership indicators with other nodes
outside of the subgroup of interest. We describe the proposed model and its
inference algorithm in detail for both the finite and infinite cases. In the
experiment section, we compare our algorithms with other popular models in
terms of link prediction, using both synthetic and real world data.
| Xuhui Fan, Longbing Cao, Richard Yi Da Xu | null | 1306.2733 | null | null |
Horizontal and Vertical Ensemble with Deep Representation for
Classification | cs.LG stat.ML | Representation learning, especially which by using deep learning, has been
widely applied in classification. However, how to use limited size of labeled
data to achieve good classification performance with deep neural network, and
how can the learned features further improve classification remain indefinite.
In this paper, we propose Horizontal Voting Vertical Voting and Horizontal
Stacked Ensemble methods to improve the classification performance of deep
neural networks. In the ICML 2013 Black Box Challenge, via using these methods
independently, Bing Xu achieved 3rd in public leaderboard, and 7th in private
leaderboard; Jingjing Xie achieved 4th in public leaderboard, and 5th in
private leaderboard.
| Jingjing Xie, Bing Xu, Zhang Chuang | null | 1306.2759 | null | null |
Understanding Dropout: Training Multi-Layer Perceptrons with Auxiliary
Independent Stochastic Neurons | cs.NE cs.LG stat.ML | In this paper, a simple, general method of adding auxiliary stochastic
neurons to a multi-layer perceptron is proposed. It is shown that the proposed
method is a generalization of recently successful methods of dropout (Hinton et
al., 2012), explicit noise injection (Vincent et al., 2010; Bishop, 1995) and
semantic hashing (Salakhutdinov & Hinton, 2009). Under the proposed framework,
an extension of dropout which allows using separate dropping probabilities for
different hidden neurons, or layers, is found to be available. The use of
different dropping probabilities for hidden layers separately is empirically
investigated.
| Kyunghyun Cho | null | 1306.2801 | null | null |
Bayesian Inference and Learning in Gaussian Process State-Space Models
with Particle MCMC | stat.ML cs.LG cs.SY | State-space models are successfully used in many areas of science,
engineering and economics to model time series and dynamical systems. We
present a fully Bayesian approach to inference \emph{and learning} (i.e. state
estimation and system identification) in nonlinear nonparametric state-space
models. We place a Gaussian process prior over the state transition dynamics,
resulting in a flexible model able to capture complex dynamical phenomena. To
enable efficient inference, we marginalize over the transition dynamics
function and infer directly the joint smoothing distribution using specially
tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the
smoothing distribution is computed, the state transition predictive
distribution can be formulated analytically. Our approach preserves the full
nonparametric expressivity of the model and can make use of sparse Gaussian
processes to greatly reduce computational complexity.
| Roger Frigola, Fredrik Lindsten, Thomas B. Sch\"on, Carl E. Rasmussen | null | 1306.2861 | null | null |
Robust Support Vector Machines for Speaker Verification Task | cs.LG cs.SD stat.ML | An important step in speaker verification is extracting features that best
characterize the speaker voice. This paper investigates a front-end processing
that aims at improving the performance of speaker verification based on the
SVMs classifier, in text independent mode. This approach combines features
based on conventional Mel-cepstral Coefficients (MFCCs) and Line Spectral
Frequencies (LSFs) to constitute robust multivariate feature vectors. To reduce
the high dimensionality required for training these feature vectors, we use a
dimension reduction method called principal component analysis (PCA). In order
to evaluate the robustness of these systems, different noisy environments have
been used. The obtained results using TIMIT database showed that, using the
paradigm that combines these spectral cues leads to a significant improvement
in verification accuracy, especially with PCA reduction for low signal-to-noise
ratio noisy environment.
| Kawthar Yasmine Zergat, Abderrahmane Amrouche | null | 1306.2906 | null | null |
Reinforcement learning with restrictions on the action set | cs.GT cs.LG math.PR | Consider a 2-player normal-form game repeated over time. We introduce an
adaptive learning procedure, where the players only observe their own realized
payoff at each stage. We assume that agents do not know their own payoff
function, and have no information on the other player. Furthermore, we assume
that they have restrictions on their own action set such that, at each stage,
their choice is limited to a subset of their action set. We prove that the
empirical distributions of play converge to the set of Nash equilibria for
zero-sum and potential games, and games where one player has two actions.
| Mario Bravo (ISCI), Mathieu Faure (AMSE) | null | 1306.2918 | null | null |
Completing Any Low-rank Matrix, Provably | stat.ML cs.IT cs.LG math.IT | Matrix completion, i.e., the exact and provable recovery of a low-rank matrix
from a small subset of its elements, is currently only known to be possible if
the matrix satisfies a restrictive structural constraint---known as {\em
incoherence}---on its row and column spaces. In these cases, the subset of
elements is sampled uniformly at random.
In this paper, we show that {\em any} rank-$ r $ $ n$-by-$ n $ matrix can be
exactly recovered from as few as $O(nr \log^2 n)$ randomly chosen elements,
provided this random choice is made according to a {\em specific biased
distribution}: the probability of any element being sampled should be
proportional to the sum of the leverage scores of the corresponding row, and
column. Perhaps equally important, we show that this specific form of sampling
is nearly necessary, in a natural precise sense; this implies that other
perhaps more intuitive sampling schemes fail.
We further establish three ways to use the above result for the setting when
leverage scores are not known \textit{a priori}: (a) a sampling strategy for
the case when only one of the row or column spaces are incoherent, (b) a
two-phase sampling procedure for general matrices that first samples to
estimate leverage scores followed by sampling for exact recovery, and (c) an
analysis showing the advantages of weighted nuclear/trace-norm minimization
over the vanilla un-weighted formulation for the case of non-uniform sampling.
| Yudong Chen, Srinadh Bhojanapalli, Sujay Sanghavi, Rachel Ward | null | 1306.2979 | null | null |
Dynamic Infinite Mixed-Membership Stochastic Blockmodel | cs.SI cs.LG stat.ML | Directional and pairwise measurements are often used to model
inter-relationships in a social network setting. The Mixed-Membership
Stochastic Blockmodel (MMSB) was a seminal work in this area, and many of its
capabilities were extended since then. In this paper, we propose the
\emph{Dynamic Infinite Mixed-Membership stochastic blockModel (DIM3)}, a
generalised framework that extends the existing work to a potentially infinite
number of communities and mixture memberships for each of the network's nodes.
This model is in a dynamic setting, where additional model parameters are
introduced to reflect the degree of persistence between one's memberships at
consecutive times. Accordingly, two effective posterior sampling strategies and
their results are presented using both synthetic and real data.
| Xuhui Fan, Longbing Cao, Richard Yi Da Xu | null | 1306.2999 | null | null |
A Convergence Theorem for the Graph Shift-type Algorithms | stat.ML cs.LG | Graph Shift (GS) algorithms are recently focused as a promising approach for
discovering dense subgraphs in noisy data. However, there are no theoretical
foundations for proving the convergence of the GS Algorithm. In this paper, we
propose a generic theoretical framework consisting of three key GS components:
simplex of generated sequence set, monotonic and continuous objective function
and closed mapping. We prove that GS algorithms with such components can be
transformed to fit the Zangwill's convergence theorem, and the sequence set
generated by the GS procedures always terminates at a local maximum, or at
worst, contains a subsequence which converges to a local maximum of the
similarity measure function. The framework is verified by expanding it to other
GS-type algorithms and experimental results.
| Xuhui Fan, Longbing Cao | null | 1306.3002 | null | null |
Non-parametric Power-law Data Clustering | cs.LG cs.CV stat.ML | It has always been a great challenge for clustering algorithms to
automatically determine the cluster numbers according to the distribution of
datasets. Several approaches have been proposed to address this issue,
including the recent promising work which incorporate Bayesian Nonparametrics
into the $k$-means clustering procedure. This approach shows simplicity in
implementation and solidity in theory, while it also provides a feasible way to
inference in large scale datasets. However, several problems remains unsolved
in this pioneering work, including the power-law data applicability, mechanism
to merge centers to avoid the over-fitting problem, clustering order problem,
e.t.c.. To address these issues, the Pitman-Yor Process based k-means (namely
\emph{pyp-means}) is proposed in this paper. Taking advantage of the Pitman-Yor
Process, \emph{pyp-means} treats clusters differently by dynamically and
adaptively changing the threshold to guarantee the generation of power-law
clustering results. Also, one center agglomeration procedure is integrated into
the implementation to be able to merge small but close clusters and then
adaptively determine the cluster number. With more discussion on the clustering
order, the convergence proof, complexity analysis and extension to spectral
clustering, our approach is compared with traditional clustering algorithm and
variational inference methods. The advantages and properties of pyp-means are
validated by experiments on both synthetic datasets and real world datasets.
| Xuhui Fan, Yiling Zeng, Longbing Cao | null | 1306.3003 | null | null |
Physeter catodon localization by sparse coding | cs.LG cs.CE stat.ML | This paper presents a spermwhale' localization architecture using jointly a
bag-of-features (BoF) approach and machine learning framework. BoF methods are
known, especially in computer vision, to produce from a collection of local
features a global representation invariant to principal signal transformations.
Our idea is to regress supervisely from these local features two rough
estimates of the distance and azimuth thanks to some datasets where both
acoustic events and ground-truth position are now available. Furthermore, these
estimates can feed a particle filter system in order to obtain a precise
spermwhale' position even in mono-hydrophone configuration. Anti-collision
system and whale watching are considered applications of this work.
| S\'ebastien Paris and Yann Doh and Herv\'e Glotin and Xanadu Halkias
and Joseph Razik | null | 1306.3058 | null | null |
Guaranteed Classification via Regularized Similarity Learning | cs.LG | Learning an appropriate (dis)similarity function from the available data is a
central problem in machine learning, since the success of many machine learning
algorithms critically depends on the choice of a similarity function to compare
examples. Despite many approaches for similarity metric learning have been
proposed, there is little theoretical study on the links between similarity
met- ric learning and the classification performance of the result classifier.
In this paper, we propose a regularized similarity learning formulation
associated with general matrix-norms, and establish their generalization
bounds. We show that the generalization error of the resulting linear separator
can be bounded by the derived generalization bound of similarity learning. This
shows that a good gen- eralization of the learnt similarity function guarantees
a good classification of the resulting linear classifier. Our results extend
and improve those obtained by Bellet at al. [3]. Due to the techniques
dependent on the notion of uniform stability [6], the bound obtained there
holds true only for the Frobenius matrix- norm regularization. Our techniques
using the Rademacher complexity [5] and its related Khinchin-type inequality
enable us to establish bounds for regularized similarity learning formulations
associated with general matrix-norms including sparse L 1 -norm and mixed
(2,1)-norm.
| Zheng-Chu Guo and Yiming Ying | null | 1306.3108 | null | null |
Learning Using Privileged Information: SVM+ and Weighted SVM | stat.ML cs.LG | Prior knowledge can be used to improve predictive performance of learning
algorithms or reduce the amount of data required for training. The same goal is
pursued within the learning using privileged information paradigm which was
recently introduced by Vapnik et al. and is aimed at utilizing additional
information available only at training time -- a framework implemented by SVM+.
We relate the privileged information to importance weighting and show that the
prior knowledge expressible with privileged features can also be encoded by
weights associated with every training example. We show that a weighted SVM can
always replicate an SVM+ solution, while the converse is not true and we
construct a counterexample highlighting the limitations of SVM+. Finally, we
touch on the problem of choosing weights for weighted SVMs when privileged
features are not available.
| Maksim Lapin, Matthias Hein, Bernt Schiele | 10.1016/j.neunet.2014.02.002 | 1306.3161 | null | null |
Learning to encode motion using spatio-temporal synchrony | cs.CV cs.LG stat.ML | We consider the task of learning to extract motion from videos. To this end,
we show that the detection of spatial transformations can be viewed as the
detection of synchrony between the image sequence and a sequence of features
undergoing the motion we wish to detect. We show that learning about synchrony
is possible using very fast, local learning rules, by introducing
multiplicative "gating" interactions between hidden units across frames. This
makes it possible to achieve competitive performance in a wide variety of
motion estimation tasks, using a small fraction of the time required to learn
features, and to outperform hand-crafted spatio-temporal features by a large
margin. We also show how learning about synchrony can be viewed as performing
greedy parameter estimation in the well-known motion energy model.
| Kishore Reddy Konda, Roland Memisevic, Vincent Michalski | null | 1306.3162 | null | null |
Confidence Intervals and Hypothesis Testing for High-Dimensional
Regression | stat.ME cs.IT cs.LG math.IT | Fitting high-dimensional statistical models often requires the use of
non-linear parameter estimation procedures. As a consequence, it is generally
impossible to obtain an exact characterization of the probability distribution
of the parameter estimates. This in turn implies that it is extremely
challenging to quantify the \emph{uncertainty} associated with a certain
parameter estimate. Concretely, no commonly accepted procedure exists for
computing classical measures of uncertainty and statistical significance as
confidence intervals or $p$-values for these models.
We consider here high-dimensional linear regression problem, and propose an
efficient algorithm for constructing confidence intervals and $p$-values. The
resulting confidence intervals have nearly optimal size. When testing for the
null hypothesis that a certain parameter is vanishing, our method has nearly
optimal power.
Our approach is based on constructing a `de-biased' version of regularized
M-estimators. The new construction improves over recent work in the field in
that it does not assume a special structure on the design matrix. We test our
method on synthetic data and a high-throughput genomic data set about
riboflavin production rate.
| Adel Javanmard and Andrea Montanari | null | 1306.3171 | null | null |
Bregman Alternating Direction Method of Multipliers | math.OC cs.LG stat.ML | The mirror descent algorithm (MDA) generalizes gradient descent by using a
Bregman divergence to replace squared Euclidean distance. In this paper, we
similarly generalize the alternating direction method of multipliers (ADMM) to
Bregman ADMM (BADMM), which allows the choice of different Bregman divergences
to exploit the structure of problems. BADMM provides a unified framework for
ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM.
We establish the global convergence and the $O(1/T)$ iteration complexity for
BADMM. In some cases, BADMM can be faster than ADMM by a factor of
$O(n/\log(n))$. In solving the linear program of mass transportation problem,
BADMM leads to massive parallelism and can easily run on GPU. BADMM is several
times faster than highly optimized commercial software Gurobi.
| Huahua Wang and Arindam Banerjee | null | 1306.3203 | null | null |
Sparse Inverse Covariance Matrix Estimation Using Quadratic
Approximation | cs.LG stat.ML | The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown
to have strong statistical guarantees in recovering a sparse inverse covariance
matrix, or alternatively the underlying graph structure of a Gaussian Markov
Random Field, from very limited samples. We propose a novel algorithm for
solving the resulting optimization problem which is a regularized
log-determinant program. In contrast to recent state-of-the-art methods that
largely use first order gradient information, our algorithm is based on
Newton's method and employs a quadratic approximation, but with some
modifications that leverage the structure of the sparse Gaussian MLE problem.
We show that our method is superlinearly convergent, and present experimental
results using synthetic and real-world application data that demonstrate the
considerable improvements in performance of our method when compared to other
state-of-the-art methods.
| Cho-Jui Hsieh, Matyas A. Sustik, Inderjit S. Dhillon and Pradeep
Ravikumar | null | 1306.3212 | null | null |
Relaxed Sparse Eigenvalue Conditions for Sparse Estimation via
Non-convex Regularized Regression | cs.LG cs.NA stat.ML | Non-convex regularizers usually improve the performance of sparse estimation
in practice. To prove this fact, we study the conditions of sparse estimations
for the sharp concave regularizers which are a general family of non-convex
regularizers including many existing regularizers. For the global solutions of
the regularized regression, our sparse eigenvalue based conditions are weaker
than that of L1-regularization for parameter estimation and sparseness
estimation. For the approximate global and approximate stationary (AGAS)
solutions, almost the same conditions are also enough. We show that the desired
AGAS solutions can be obtained by coordinate descent (CD) based methods.
Finally, we perform some experiments to show the performance of CD methods on
giving AGAS solutions and the degree of weakness of the estimation conditions
required by the sharp concave regularizers.
| Zheng Pan, Changshui Zhang | null | 1306.3343 | null | null |
Constrained fractional set programs and their application in local
clustering and community detection | stat.ML cs.LG math.OC | The (constrained) minimization of a ratio of set functions is a problem
frequently occurring in clustering and community detection. As these
optimization problems are typically NP-hard, one uses convex or spectral
relaxations in practice. While these relaxations can be solved globally
optimally, they are often too loose and thus lead to results far away from the
optimum. In this paper we show that every constrained minimization problem of a
ratio of non-negative set functions allows a tight relaxation into an
unconstrained continuous optimization problem. This result leads to a flexible
framework for solving constrained problems in network analysis. While a
globally optimal solution for the resulting non-convex problem cannot be
guaranteed, we outperform the loose convex or spectral relaxations by a large
margin on constrained local clustering problems.
| Thomas B\"uhler, Syama Sundar Rangapuram, Simon Setzer, Matthias Hein | null | 1306.3409 | null | null |
Classifying Single-Trial EEG during Motor Imagery with a Small Training
Set | cs.LG cs.HC stat.ML | Before the operation of a motor imagery based brain-computer interface (BCI)
adopting machine learning techniques, a cumbersome training procedure is
unavoidable. The development of a practical BCI posed the challenge of
classifying single-trial EEG with a small training set. In this letter, we
addressed this problem by employing a series of signal processing and machine
learning approaches to alleviate overfitting and obtained test accuracy similar
to training accuracy on the datasets from BCI Competition III and our own
experiments.
| Yijun Wang | null | 1306.3474 | null | null |
Hyperparameter Optimization and Boosting for Classifying Facial
Expressions: How good can a "Null" Model be? | cs.CV cs.LG stat.ML | One of the goals of the ICML workshop on representation and learning is to
establish benchmark scores for a new data set of labeled facial expressions.
This paper presents the performance of a "Null" model consisting of
convolutions with random weights, PCA, pooling, normalization, and a linear
readout. Our approach focused on hyperparameter optimization rather than novel
model components. On the Facial Expression Recognition Challenge held by the
Kaggle website, our hyperparameter optimization approach achieved a score of
60% accuracy on the test data. This paper also introduces a new ensemble
construction variant that combines hyperparameter optimization with the
construction of ensembles. This algorithm constructed an ensemble of four
models that scored 65.5% accuracy. These scores rank 12th and 5th respectively
among the 56 challenge participants. It is worth noting that our approach was
developed prior to the release of the data set, and applied without
modification; our strong competition performance suggests that the TPE
hyperparameter optimization algorithm and domain expertise encoded in our Null
model can generalize to new image classification data sets.
| James Bergstra and David D. Cox | null | 1306.3476 | null | null |
Approximation Algorithms for Bayesian Multi-Armed Bandit Problems | cs.DS cs.LG | In this paper, we consider several finite-horizon Bayesian multi-armed bandit
problems with side constraints which are computationally intractable (NP-Hard)
and for which no optimal (or near optimal) algorithms are known to exist with
sub-exponential running time. All of these problems violate the standard
exchange property, which assumes that the reward from the play of an arm is not
contingent upon when the arm is played. Not only are index policies suboptimal
in these contexts, there has been little analysis of such policies in these
problem settings. We show that if we consider near-optimal policies, in the
sense of approximation algorithms, then there exists (near) index policies.
Conceptually, if we can find policies that satisfy an approximate version of
the exchange property, namely, that the reward from the play of an arm depends
on when the arm is played to within a constant factor, then we have an avenue
towards solving these problems. However such an approximate version of the
idling bandit property does not hold on a per-play basis and are shown to hold
in a global sense. Clearly, such a property is not necessarily true of
arbitrary single arm policies and finding such single arm policies is
nontrivial. We show that by restricting the state spaces of arms we can find
single arm policies and that these single arm policies can be combined into
global (near) index policies where the approximate version of the exchange
property is true in expectation. The number of different bandit problems that
can be addressed by this technique already demonstrate its wide applicability.
| Sudipto Guha and Kamesh Munagala | null | 1306.3525 | null | null |
Outlying Property Detection with Numerical Attributes | cs.LG cs.DB stat.ML | The outlying property detection problem is the problem of discovering the
properties distinguishing a given object, known in advance to be an outlier in
a database, from the other database objects. In this paper, we analyze the
problem within a context where numerical attributes are taken into account,
which represents a relevant case left open in the literature. We introduce a
measure to quantify the degree the outlierness of an object, which is
associated with the relative likelihood of the value, compared to the to the
relative likelihood of other objects in the database. As a major contribution,
we present an efficient algorithm to compute the outlierness relative to
significant subsets of the data. The latter subsets are characterized in a
"rule-based" fashion, and hence the basis for the underlying explanation of the
outlierness.
| Fabrizio Angiulli and Fabio Fassetti and Luigi Palopoli and Giuseppe
Manco | null | 1306.3558 | null | null |
Online Alternating Direction Method (longer version) | cs.LG math.OC | Online optimization has emerged as powerful tool in large scale optimization.
In this pa- per, we introduce efficient online optimization algorithms based on
the alternating direction method (ADM), which can solve online convex
optimization under linear constraints where the objective could be non-smooth.
We introduce new proof techniques for ADM in the batch setting, which yields a
O(1/T) convergence rate for ADM and forms the basis for regret anal- ysis in
the online setting. We consider two scenarios in the online setting, based on
whether an additional Bregman divergence is needed or not. In both settings, we
establish regret bounds for both the objective function as well as constraints
violation for general and strongly convex functions. We also consider inexact
ADM updates where certain terms are linearized to yield efficient updates and
show the stochastic convergence rates. In addition, we briefly discuss that
online ADM can be used as projection- free online learning algorithm in some
scenarios. Preliminary results are presented to illustrate the performance of
the proposed algorithms.
| Huahua Wang and Arindam Banerjee | null | 1306.3721 | null | null |
Spectral Experts for Estimating Mixtures of Linear Regressions | cs.LG stat.ML | Discriminative latent-variable models are typically learned using EM or
gradient-based optimization, which suffer from local optima. In this paper, we
develop a new computationally efficient and provably consistent estimator for a
mixture of linear regressions, a simple instance of a discriminative
latent-variable model. Our approach relies on a low-rank linear regression to
recover a symmetric tensor, which can be factorized into the parameters using a
tensor power method. We prove rates of convergence for our estimator and
provide an empirical evaluation illustrating its strengths relative to local
optimization (EM).
| Arun Tejasvi Chaganty and Percy Liang | null | 1306.3729 | null | null |
Cluster coloring of the Self-Organizing Map: An information
visualization perspective | cs.LG cs.HC | This paper takes an information visualization perspective to visual
representations in the general SOM paradigm. This involves viewing SOM-based
visualizations through the eyes of Bertin's and Tufte's theories on data
graphics. The regular grid shape of the Self-Organizing Map (SOM), while being
a virtue for linking visualizations to it, restricts representation of cluster
structures. From the viewpoint of information visualization, this paper
provides a general, yet simple, solution to projection-based coloring of the
SOM that reveals structures. First, the proposed color space is easy to
construct and customize to the purpose of use, while aiming at being
perceptually correct and informative through two separable dimensions. Second,
the coloring method is not dependent on any specific method of projection, but
is rather modular to fit any objective function suitable for the task at hand.
The cluster coloring is illustrated on two datasets: the iris data, and welfare
and poverty indicators.
| Peter Sarlin and Samuel R\"onnqvist | null | 1306.3860 | null | null |
On-line PCA with Optimal Regrets | cs.LG | We carefully investigate the on-line version of PCA, where in each trial a
learning algorithm plays a k-dimensional subspace, and suffers the compression
loss on the next instance when projected into the chosen subspace. In this
setting, we analyze two popular on-line algorithms, Gradient Descent (GD) and
Exponentiated Gradient (EG). We show that both algorithms are essentially
optimal in the worst-case. This comes as a surprise, since EG is known to
perform sub-optimally when the instances are sparse. This different behavior of
EG for PCA is mainly related to the non-negativity of the loss in this case,
which makes the PCA setting qualitatively different from other settings studied
in the literature. Furthermore, we show that when considering regret bounds as
function of a loss budget, EG remains optimal and strictly outperforms GD.
Next, we study the extension of the PCA setting, in which the Nature is allowed
to play with dense instances, which are positive matrices with bounded largest
eigenvalue. Again we can show that EG is optimal and strictly better than GD in
this setting.
| Jiazhong Nie and Wojciech Kotlowski and Manfred K. Warmuth | null | 1306.3895 | null | null |
Stability of Multi-Task Kernel Regression Algorithms | cs.LG stat.ML | We study the stability properties of nonlinear multi-task regression in
reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a.
multi-task kernels, are appropriate for learning prob- lems with nonscalar
outputs like multi-task learning and structured out- put prediction. We show
that multi-task kernel regression algorithms are uniformly stable in the
general case of infinite-dimensional output spaces. We then derive under mild
assumption on the kernel generaliza- tion bounds of such algorithms, and we
show their consistency even with non Hilbert-Schmidt operator-valued kernels .
We demonstrate how to apply the results to various multi-task kernel regression
methods such as vector-valued SVR and functional ridge regression.
| Julien Audiffren (LIF), Hachem Kadri (LIF) | null | 1306.3905 | null | null |
On Finding the Largest Mean Among Many | stat.ML cs.LG | Sampling from distributions to find the one with the largest mean arises in a
broad range of applications, and it can be mathematically modeled as a
multi-armed bandit problem in which each distribution is associated with an
arm. This paper studies the sample complexity of identifying the best arm
(largest mean) in a multi-armed bandit problem. Motivated by large-scale
applications, we are especially interested in identifying situations where the
total number of samples that are necessary and sufficient to find the best arm
scale linearly with the number of arms. We present a single-parameter
multi-armed bandit model that spans the range from linear to superlinear sample
complexity. We also give a new algorithm for best arm identification, called
PRISM, with linear sample complexity for a wide range of mean distributions.
The algorithm, like most exploration procedures for multi-armed bandits, is
adaptive in the sense that the next arms to sample are selected based on
previous samples. We compare the sample complexity of adaptive procedures with
simpler non-adaptive procedures using new lower bounds. For many problem
instances, the increased sample complexity required by non-adaptive procedures
is a polynomial factor of the number of arms.
| Kevin Jamieson, Matthew Malloy, Robert Nowak, Sebastien Bubeck | null | 1306.3917 | null | null |
Parallel Coordinate Descent Newton Method for Efficient
$\ell_1$-Regularized Minimization | cs.LG cs.NA | The recent years have witnessed advances in parallel algorithms for large
scale optimization problems. Notwithstanding demonstrated success, existing
algorithms that parallelize over features are usually limited by divergence
issues under high parallelism or require data preprocessing to alleviate these
problems. In this work, we propose a Parallel Coordinate Descent Newton
algorithm using multidimensional approximate Newton steps (PCDN), where the
off-diagonal elements of the Hessian are set to zero to enable parallelization.
It randomly partitions the feature set into $b$ bundles/subsets with size of
$P$, and sequentially processes each bundle by first computing the descent
directions for each feature in parallel and then conducting $P$-dimensional
line search to obtain the step size. We show that: (1) PCDN is guaranteed to
converge globally despite increasing parallelism; (2) PCDN converges to the
specified accuracy $\epsilon$ within the limited iteration number of
$T_\epsilon$, and $T_\epsilon$ decreases with increasing parallelism (bundle
size $P$). Using the implementation technique of maintaining intermediate
quantities, we minimize the data transfer and synchronization cost of the
$P$-dimensional line search. For concreteness, the proposed PCDN algorithm is
applied to $\ell_1$-regularized logistic regression and $\ell_2$-loss SVM.
Experimental evaluations on six benchmark datasets show that the proposed PCDN
algorithm exploits parallelism well and outperforms the state-of-the-art
methods in speed without losing accuracy.
| An Bian, Xiong Li, Yuncai Liu, Ming-Hsuan Yang | null | 1306.4080 | null | null |
Bioclimating Modelling: A Machine Learning Perspective | cs.LG stat.ML | Many machine learning (ML) approaches are widely used to generate bioclimatic
models for prediction of geographic range of organism as a function of climate.
Applications such as prediction of range shift in organism, range of invasive
species influenced by climate change are important parameters in understanding
the impact of climate change. However, success of machine learning-based
approaches depends on a number of factors. While it can be safely said that no
particular ML technique can be effective in all applications and success of a
technique is predominantly dependent on the application or the type of the
problem, it is useful to understand their behaviour to ensure informed choice
of techniques. This paper presents a comprehensive review of machine
learning-based bioclimatic model generation and analyses the factors
influencing success of such models. Considering the wide use of statistical
techniques, in our discussion we also include conventional statistical
techniques used in bioclimatic modelling.
| Maumita Bhattacharya | null | 1306.4152 | null | null |
Joint estimation of sparse multivariate regression and conditional
graphical models | stat.ML cs.LG | Multivariate regression model is a natural generalization of the classical
univari- ate regression model for fitting multiple responses. In this paper, we
propose a high- dimensional multivariate conditional regression model for
constructing sparse estimates of the multivariate regression coefficient matrix
that accounts for the dependency struc- ture among the multiple responses. The
proposed method decomposes the multivariate regression problem into a series of
penalized conditional log-likelihood of each response conditioned on the
covariates and other responses. It allows simultaneous estimation of the sparse
regression coefficient matrix and the sparse inverse covariance matrix. The
asymptotic selection consistency and normality are established for the
diverging dimension of the covariates and number of responses. The
effectiveness of the pro- posed method is also demonstrated in a variety of
simulated examples as well as an application to the Glioblastoma multiforme
cancer data.
| Junhui Wang | null | 1306.4410 | null | null |
Hacking Smart Machines with Smarter Ones: How to Extract Meaningful Data
from Machine Learning Classifiers | cs.CR cs.LG stat.ML | Machine Learning (ML) algorithms are used to train computers to perform a
variety of complex tasks and improve with experience. Computers learn how to
recognize patterns, make unintended decisions, or react to a dynamic
environment. Certain trained machines may be more effective than others because
they are based on more suitable ML algorithms or because they were trained
through superior training sets. Although ML algorithms are known and publicly
released, training sets may not be reasonably ascertainable and, indeed, may be
guarded as trade secrets. While much research has been performed about the
privacy of the elements of training sets, in this paper we focus our attention
on ML classifiers and on the statistical information that can be unconsciously
or maliciously revealed from them. We show that it is possible to infer
unexpected but useful information from ML classifiers. In particular, we build
a novel meta-classifier and train it to hack other classifiers, obtaining
meaningful information about their training sets. This kind of information
leakage can be exploited, for example, by a vendor to build more effective
classifiers or to simply acquire trade secrets from a competitor's apparatus,
potentially violating its intellectual property rights.
| Giuseppe Ateniese, Giovanni Felici, Luigi V. Mancini, Angelo
Spognardi, Antonio Villani, Domenico Vitali | null | 1306.4447 | null | null |
Table of Content detection using Machine Learning | cs.LG cs.DL cs.IR | Table of content (TOC) detection has drawn attention now a day because it
plays an important role in digitization of multipage document. Generally book
document is multipage document. So it becomes necessary to detect Table of
Content page for easy navigation of multipage document and also to make
information retrieval faster for desirable data from the multipage document.
All the Table of content pages follow the different layout, different way of
presenting the contents of the document like chapter, section, subsection etc.
This paper introduces a new method to detect Table of content using machine
learning technique with different features. With the main aim to detect Table
of Content pages is to structure the document according to their contents.
| Rachana Parikh and Avani R. Vasant | null | 1306.4631 | null | null |
A Fuzzy Based Approach to Text Mining and Document Clustering | cs.LG cs.IR | Fuzzy logic deals with degrees of truth. In this paper, we have shown how to
apply fuzzy logic in text mining in order to perform document clustering. We
took an example of document clustering where the documents had to be clustered
into two categories. The method involved cleaning up the text and stemming of
words. Then, we chose m number of features which differ significantly in their
word frequencies (WF), normalized by document length, between documents
belonging to these two clusters. The documents to be clustered were represented
as a collection of m normalized WF values. Fuzzy c-means (FCM) algorithm was
used to cluster these documents into two clusters. After the FCM execution
finished, the documents in the two clusters were analysed for the values of
their respective m features. It was known that documents belonging to a
document type, say X, tend to have higher WF values for some particular
features. If the documents belonging to a cluster had higher WF values for
those same features, then that cluster was said to represent X. By fuzzy logic,
we not only get the cluster name, but also the degree to which a document
belongs to a cluster.
| Sumit Goswami and Mayank Singh Shishodia | null | 1306.4633 | null | null |
Stochastic Majorization-Minimization Algorithms for Large-Scale
Optimization | stat.ML cs.LG math.OC | Majorization-minimization algorithms consist of iteratively minimizing a
majorizing surrogate of an objective function. Because of its simplicity and
its wide applicability, this principle has been very popular in statistics and
in signal processing. In this paper, we intend to make this principle scalable.
We introduce a stochastic majorization-minimization scheme which is able to
deal with large-scale or possibly infinite data sets. When applied to convex
optimization problems under suitable assumptions, we show that it achieves an
expected convergence rate of $O(1/\sqrt{n})$ after $n$ iterations, and of
$O(1/n)$ for strongly convex functions. Equally important, our scheme almost
surely converges to stationary points for a large class of non-convex problems.
We develop several efficient algorithms based on our framework. First, we
propose a new stochastic proximal gradient method, which experimentally matches
state-of-the-art solvers for large-scale $\ell_1$-logistic regression. Second,
we develop an online DC programming algorithm for non-convex sparse estimation.
Finally, we demonstrate the effectiveness of our approach for solving
large-scale structured matrix factorization problems.
| Julien Mairal (INRIA Grenoble Rh\^one-Alpes / LJK Laboratoire Jean
Kuntzmann) | null | 1306.4650 | null | null |
Multiarmed Bandits With Limited Expert Advice | cs.LG | We solve the COLT 2013 open problem of \citet{SCB} on minimizing regret in
the setting of advice-efficient multiarmed bandits with expert advice. We give
an algorithm for the setting of K arms and N experts out of which we are
allowed to query and use only M experts' advices in each round, which has a
regret bound of \tilde{O}\bigP{\sqrt{\frac{\min\{K, M\} N}{M} T}} after T
rounds. We also prove that any algorithm for this problem must have expected
regret at least \tilde{\Omega}\bigP{\sqrt{\frac{\min\{K, M\} N}{M}T}}, thus
showing that our upper bound is nearly tight.
| Satyen Kale | null | 1306.4653 | null | null |
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