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21,502
Bayesian Classification and Regression with High Dimensional Features
stat.ML
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional measurements are available, for example, gene expression data produced by microarr...
computer science
21,503
Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains
stat.ML
Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated an...
computer science
21,504
Pac-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning
stat.ML
This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the se...
computer science
21,505
Classification Constrained Dimensionality Reduction
stat.ML
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as well as the semi-supervised setting. We present an out-of-sample expressions for ...
computer science
21,506
Testing for Homogeneity with Kernel Fisher Discriminant Analysis
stat.ML
We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both ar...
computer science
21,507
On the underestimation of model uncertainty by Bayesian K-nearest neighbors
stat.ML
When using the K-nearest neighbors method, one often ignores uncertainty in the choice of K. To account for such uncertainty, Holmes and Adams (2002) proposed a Bayesian framework for K-nearest neighbors (KNN). Their Bayesian KNN (BKNN) approach uses a pseudo-likelihood function, and standard Markov chain Monte Carlo (...
computer science
21,508
Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis
stat.ML
Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined...
computer science
21,509
Random projection trees for vector quantization
stat.ML
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent dimension of the space in which the data happen to lie.
computer science
21,510
Manifold Learning: The Price of Normalization
stat.ML
We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap, Local Tangent Space Alignment (LTSA), Hessian Eigenmaps (HLLE), and Diffusion maps....
computer science
21,511
Local Procrustes for Manifold Embedding: A Measure of Embedding Quality and Embedding Algorithms
stat.ML
We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al, 2000)). The measure also serves as a natural tool when choosing dimension-reduction ...
computer science
21,512
Supervised functional classification: A theoretical remark and some comparisons
stat.ML
The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we prove the consistency of the k-NN classifier for functional data whose distribu...
computer science
21,513
High-dimensional additive modeling
stat.ML
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, fo...
computer science
21,514
Improved Estimation of High-dimensional Ising Models
stat.ML
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of $\ell_1$-regularized surrogate likelihood that allows us to find a sparse solution...
computer science
21,515
Kernel Regression by Mode Calculation of the Conditional Probability Distribution
stat.ML
The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice difficult, because it requires a global optimization of a complicated function,...
computer science
21,516
Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks
stat.ML
We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type shrinkage estimator, resulting in a procedure that is highly efficient statistically ...
computer science
21,517
Random Forests: some methodological insights
stat.ML
This paper examines from an experimental perspective random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001. It first aims at confirming, known but sparse, advice for using random forests and at proposing some complementary remarks for both ...
computer science
21,518
An information-theoretic derivation of min-cut based clustering
stat.ML
Min-cut clustering, based on minimizing one of two heuristic cost-functions proposed by Shi and Malik, has spawned tremendous research, both analytic and algorithmic, in the graph partitioning and image segmentation communities over the last decade. It is however unclear if these heuristics can be derived from a more g...
computer science
21,519
On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models
stat.ML
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the bro...
computer science
21,520
Reconstruction of Epsilon-Machines in Predictive Frameworks and Decisional States
stat.ML
This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge ex...
computer science
21,521
Lanczos Approximations for the Speedup of Kernel Partial Least Squares Regression
stat.ML
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa...
computer science
21,522
Escaping the curse of dimensionality with a tree-based regressor
stat.ML
We present the first tree-based regressor whose convergence rate depends only on the intrinsic dimension of the data, namely its Assouad dimension. The regressor uses the RPtree partitioning procedure, a simple randomized variant of k-d trees.
computer science
21,523
Finding Exogenous Variables in Data with Many More Variables than Observations
stat.ML
Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including gene expression data need high-dimensional causal modeling in challenging situation...
computer science
21,524
Structured Variable Selection with Sparsity-Inducing Norms
stat.ML
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual $\ell_1$-norm and the group $\ell_1$-norm by allowing the subsets to overlap. T...
computer science
21,525
Supplementary material for Markov equivalence for ancestral graphs
stat.ML
We prove that the criterion for Markov equivalence provided by Zhao et al. (2005) may involve a set of features of a graph that is exponential in the number of vertices.
computer science
21,526
A more robust boosting algorithm
stat.ML
We present a new boosting algorithm, motivated by the large margins theory for boosting. We give experimental evidence that the new algorithm is significantly more robust against label noise than existing boosting algorithm.
computer science
21,527
Classification by Set Cover: The Prototype Vector Machine
stat.ML
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its solution. The PVM selects a relatively small number of representative points which...
computer science
21,528
Convex Multiview Fisher Discriminant Analysis
stat.ML
Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.
computer science
21,529
Relative Expected Improvement in Kriging Based Optimization
stat.ML
We propose an extension of the concept of Expected Improvement criterion commonly used in Kriging based optimization. We extend it for more complex Kriging models, e.g. models using derivatives. The target field of application are CFD problems, where objective function are extremely expensive to evaluate, but the theor...
computer science
21,530
Learning Bayesian Networks with the bnlearn R Package
stat.ML
bnlearn is an R package which includes several algorithms for learning the structure of Bayesian networks with either discrete or continuous variables. Both constraint-based and score-based algorithms are implemented, and can use the functionality provided by the snow package to improve their performance via parallel c...
computer science
21,531
Causal Inference on Discrete Data using Additive Noise Models
stat.ML
Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discre...
computer science
21,532
How slow is slow? SFA detects signals that are slower than the driving force
stat.ML
Slow feature analysis (SFA) is a method for extracting slowly varying driving forces from quickly varying nonstationary time series. We show here that it is possible for SFA to detect a component which is even slower than the driving force itself (e.g. the envelope of a modulated sine wave). It is shown that it depends...
computer science
21,533
Sparse Convolved Multiple Output Gaussian Processes
stat.ML
Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function tha...
computer science
21,534
Positive Definite Kernels in Machine Learning
stat.ML
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x...
computer science
21,535
Under-determined reverberant audio source separation using a full-rank spatial covariance model
stat.ML
This article addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain as a zero-mean Gaussian random variable whose covariance encodes the spatial cha...
computer science
21,536
Hyper-sparse optimal aggregation
stat.ML
In this paper, we consider the problem of "hyper-sparse aggregation". Namely, given a dictionary $F = \{f_1, ..., f_M \}$ of functions, we look for an optimal aggregation algorithm that writes $\tilde f = \sum_{j=1}^M \theta_j f_j$ with as many zero coefficients $\theta_j$ as possible. This problem is of particular int...
computer science
21,537
Multi-Way, Multi-View Learning
stat.ML
We extend multi-way, multivariate ANOVA-type analysis to cases where one covariate is the view, with features of each view coming from different, high-dimensional domains. The different views are assumed to be connected by having paired samples; this is a common setup in recent bioinformatics experiments, of which we a...
computer science
21,538
Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes
stat.ML
Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based ...
computer science
21,539
Composite Binary Losses
stat.ML
We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ...
computer science
21,540
A Geometric Proof of Calibration
stat.ML
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and ...
computer science
21,541
Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization
stat.ML
We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K components are uniform distributions along K d-dimensional linear subspaces restric...
computer science
21,542
Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size
stat.ML
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referr...
computer science
21,543
On the Schoenberg Transformations in Data Analysis: Theory and Illustrations
stat.ML
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and v...
computer science
21,544
Visualization of Manifold-Valued Elements by Multidimensional Scaling
stat.ML
The present contribution suggests the use of a multidimensional scaling (MDS) algorithm as a visualization tool for manifold-valued elements. A visualization tool of this kind is useful in signal processing and machine learning whenever learning/adaptation algorithms insist on high-dimensional parameter manifolds.
computer science
21,545
Strong Consistency of Prototype Based Clustering in Probabilistic Space
stat.ML
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullbac...
computer science
21,546
Sparse Linear Identifiable Multivariate Modeling
stat.ML
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for ...
computer science
21,547
Training linear ranking SVMs in linearithmic time using red-black trees
stat.ML
We introduce an efficient method for training the linear ranking support vector machine. The method combines cutting plane optimization with red-black tree based approach to subgradient calculations, and has O(m*s+m*log(m)) time complexity, where m is the number of training examples, and s the average number of non-zer...
computer science
21,548
Improving the Johnson-Lindenstrauss Lemma
stat.ML
The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in $p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k \ge \frac{24\ln \emph{n}}{3\epsilon^2-2\epsilon^3}$, so that the pairwise distances are preserved within a factor of $1\pm\epsilon$. Here, working directly with the ...
computer science
21,549
Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines
stat.ML
We improve recently published results about resources of Restricted Boltzmann Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal Approximators. We show that any distribution p on the set of binary vectors of length n can be arbitrarily well approximated by an RBM with k-1 hidden units, where ...
computer science
21,550
Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
stat.ML
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for lo...
computer science
21,551
Gaussian Mixture Modeling with Gaussian Process Latent Variable Models
stat.ML
Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in...
computer science
21,552
Proximal Methods for Hierarchical Sparse Coding
stat.ML
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has pr...
computer science
21,553
Calibrated Surrogate Losses for Classification with Label-Dependent Costs
stat.ML
We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification risk. Two approaches to surrogate regret bounds are developed. The...
computer science
21,554
Fast Sparse Decomposition by Iterative Detection-Estimation
stat.ML
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many solutions. However, it may be shown that sufficiently sparse solutions may be identi...
computer science
21,555
Task-Driven Dictionary Learning
stat.ML
Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited t...
computer science
21,556
Kernel Bayes' rule
stat.ML
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functio...
computer science
21,557
Concentration inequalities of the cross-validation estimator for Empirical Risk Minimiser
stat.ML
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds in the spirit of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case error of this estimate is not m...
computer science
21,558
The Lasso under Heteroscedasticity
stat.ML
The performance of the Lasso is well understood under the assumptions of the standard linear model with homoscedastic noise. However, in several applications, the standard model does not describe the important features of the data. This paper examines how the Lasso performs on a non-standard model that is motivated by ...
computer science
21,559
An Introduction to Conditional Random Fields
stat.ML
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the ability of graphical models to compactly model multivariate data with the ability of ...
computer science
21,560
Concentration inequalities of the cross-validation estimate for stable predictors
stat.ML
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and \cite{KUNIY02} to characterize cla...
computer science
21,561
Estimating Subagging by cross-validation
stat.ML
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators, both for classification and regressor. General loss functions and class of predictors with both finite and infinite VC-dimension are considered. We slightly generalize the formali...
computer science
21,562
Cross-Domain Object Matching with Model Selection
stat.ML
The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of CDOM, where photos are automatically aligned into a designed frame expressed in the Cartesian coordinate system. CDOM i...
computer science
21,563
Translating biomarkers between multi-way time-series experiments
stat.ML
Translating potential disease biomarkers between multi-species 'omics' experiments is a new direction in biomedical research. The existing methods are limited to simple experimental setups such as basic healthy-diseased comparisons. Most of these methods also require an a priori matching of the variables (e.g., genes o...
computer science
21,564
Fast Convergent Algorithms for Expectation Propagation Approximate Bayesian Inference
stat.ML
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nag...
computer science
21,565
Estimating Networks With Jumps
stat.ML
We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely consid...
computer science
21,566
Ultra-high Dimensional Multiple Output Learning With Simultaneous Orthogonal Matching Pursuit: A Sure Screening Approach
stat.ML
We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variab...
computer science
21,567
A convex model for non-negative matrix factorization and dimensionality reduction on physical space
stat.ML
A collaborative convex framework for factoring a data matrix $X$ into a non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed. We restrict the columns of the dictionary matrix $A$ to coincide with certain columns of the data matrix $X$, thereby guaranteeing a physically meaningful dictionary and ...
computer science
21,568
Large Scale Correlation Screening
stat.ML
This paper treats the problem of screening for variables with high correlations in high dimensional data in which there can be many fewer samples than variables. We focus on threshold-based correlation screening methods for three related applications: screening for variables with large correlations within a single trea...
computer science
21,569
On Nonparametric Guidance for Learning Autoencoder Representations
stat.ML
Unsupervised discovery of latent representations, in addition to being useful for density modeling, visualisation and exploratory data analysis, is also increasingly important for learning features relevant to discriminative tasks. Autoencoders, in particular, have proven to be an effective way to learn latent codes th...
computer science
21,570
Predictive Active Set Selection Methods for Gaussian Processes
stat.ML
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization....
computer science
21,571
Fast Convergence Rate of Multiple Kernel Learning with Elastic-net Regularization
stat.ML
We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non...
computer science
21,572
The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning
stat.ML
We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while our analysis covers all cases $1\leq p\leq\infty$, assuming the different feature ...
computer science
21,573
Multiple Kernel Learning: A Unifying Probabilistic Viewpoint
stat.ML
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the...
computer science
21,574
Additive Kernels for Gaussian Process Modeling
stat.ML
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator, a GP model can beneficially be used for tasks such as prediction, optimization, ...
computer science
21,575
Theoretical Properties of the Overlapping Groups Lasso
stat.ML
We present two sets of theoretical results on the grouped lasso with overlap of Jacob, Obozinski and Vert (2009) in the linear regression setting. This method allows for joint selection of predictors in sparse regression, allowing for complex structured sparsity over the predictors encoded as a set of groups. This flex...
computer science
21,576
The Discrete Infinite Logistic Normal Distribution
stat.ML
We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN...
computer science
21,577
Sufficient Component Analysis for Supervised Dimension Reduction
stat.ML
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing ...
computer science
21,578
Sharp Convergence Rate and Support Consistency of Multiple Kernel Learning with Sparse and Dense Regularization
stat.ML
We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing un...
computer science
21,579
Fast Learning Rate of lp-MKL and its Minimax Optimality
stat.ML
In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the d...
computer science
21,580
Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noise
stat.ML
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model...
computer science
21,581
Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit
stat.ML
In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold" refers to the topology properties of the structure. The approximating manifold is ...
computer science
21,582
Multi-scale Mining of fMRI data with Hierarchical Structured Sparsity
stat.ML
Inverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Inverse inference ta...
computer science
21,583
A Risk Comparison of Ordinary Least Squares vs Ridge Regression
stat.ML
We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that ...
computer science
21,584
Closed-form EM for Sparse Coding and its Application to Source Separation
stat.ML
We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic P...
computer science
21,585
Independent screening for single-index hazard rate models with ultra-high dimensional features
stat.ML
In data sets with many more features than observations, independent screening based on all univariate regression models leads to a computationally convenient variable selection method. Recent efforts have shown that in the case of generalized linear models, independent screening may suffice to capture all relevant feat...
computer science
21,586
Minimax Policies for Combinatorial Prediction Games
stat.ML
We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the ...
computer science
21,587
PAC learnability under non-atomic measures: a problem by Vidyasagar
stat.ML
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli property with respect to non-atomic measures is no longer a necessary condition, and cons...
computer science
21,588
Restricted Collapsed Draw: Accurate Sampling for Hierarchical Chinese Restaurant Process Hidden Markov Models
stat.ML
We propose a restricted collapsed draw (RCD) sampler, a general Markov chain Monte Carlo sampler of simultaneous draws from a hierarchical Chinese restaurant process (HCRP) with restriction. Models that require simultaneous draws from a hierarchical Dirichlet process with restriction, such as infinite Hidden markov mod...
computer science
21,589
Multi-stage Convex Relaxation for Feature Selection
stat.ML
A number of recent work studied the effectiveness of feature selection using Lasso. It is known that under the restricted isometry properties (RIP), Lasso does not generally lead to the exact recovery of the set of nonzero coefficients, due to the looseness of convex relaxation. This paper considers the feature selecti...
computer science
21,590
Causal Network Inference via Group Sparse Regularization
stat.ML
This paper addresses the problem of inferring sparse causal networks modeled by multivariate auto-regressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score." In particular, we sh...
computer science
21,591
Source Separation and Clustering of Phase-Locked Subspaces: Derivations and Proofs
stat.ML
Due to space limitations, our submission "Source Separation and Clustering of Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on Neural Networks in 2011, presented some results without proof. Those proofs are provided in this paper.
computer science
21,592
Pitman-Yor Diffusion Trees
stat.ML
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove som...
computer science
21,593
ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis
stat.ML
Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA r...
computer science
21,594
Online algorithms for Nonnegative Matrix Factorization with the Itakura-Saito divergence
stat.ML
Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is the dimension of the input power spectrograms, and K the number of basis spectra),...
computer science
21,595
Sparse Inverse Covariance Estimation via an Adaptive Gradient-Based Method
stat.ML
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is numerically very challenging. We address this challenge by developing a new adaptive...
computer science
21,596
On the Evaluation Criterions for the Active Learning Processes
stat.ML
In many data mining applications collection of sufficiently large datasets is the most time consuming and expensive. On the other hand, industrial methods of data collection create huge databases, and make difficult direct applications of the advanced machine learning algorithms. To address the above problems, we consi...
computer science
21,597
Algebraic Geometric Comparison of Probability Distributions
stat.ML
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective f...
computer science
21,598
A consistent adjacency spectral embedding for stochastic blockmodel graphs
stat.ML
We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustere...
computer science
21,599
Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
stat.ML
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper propo...
computer science
21,600
A General Theory of Concave Regularization for High Dimensional Sparse Estimation Problems
stat.ML
Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local solutions obtained via specialized numerical procedures. Still, the fundamental...
computer science
21,601
Bayesian Group Factor Analysis
stat.ML
We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternati...
computer science