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10,401
Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)
cs.LG
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convex...
computer science
10,402
Generative Model Selection Using a Scalable and Size-Independent Complex Network Classifier
cs.SI
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...
computer science
10,403
Efficient Classification for Metric Data
cs.LG
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 qu...
computer science
10,404
Flexible sampling of discrete data correlations without the marginal distributions
stat.ML
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 o...
computer science
10,405
Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC
stat.ML
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 Gauss...
computer science
10,406
Robust Support Vector Machines for Speaker Verification Task
cs.LG
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 conven...
computer science
10,407
Completing Any Low-rank Matrix, Provably
stat.ML
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 sam...
computer science
10,408
Dynamic Infinite Mixed-Membership Stochastic Blockmodel
cs.SI
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 s...
computer science
10,409
Physeter catodon localization by sparse coding
cs.LG
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 ...
computer science
10,410
Bregman Alternating Direction Method of Multipliers
math.OC
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 ...
computer science
10,411
Relaxed Sparse Eigenvalue Conditions for Sparse Estimation via Non-convex Regularized Regression
cs.LG
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 regul...
computer science
10,412
Constrained fractional set programs and their application in local clustering and community detection
stat.ML
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 loos...
computer science
10,413
Classifying Single-Trial EEG during Motor Imagery with a Small Training Set
cs.LG
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 b...
computer science
10,414
Outlying Property Detection with Numerical Attributes
cs.LG
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...
computer science
10,415
Hacking Smart Machines with Smarter Ones: How to Extract Meaningful Data from Machine Learning Classifiers
cs.CR
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 mo...
computer science
10,416
Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization
stat.ML
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 introduc...
computer science
10,417
A Statistical Perspective on Algorithmic Leveraging
stat.ME
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales rows/columns of data matrices to reduce the data size before performing computations on...
computer science
10,418
Fourier PCA and Robust Tensor Decomposition
cs.LG
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main appli...
computer science
10,419
Traffic data reconstruction based on Markov random field modeling
stat.ML
We consider the traffic data reconstruction problem. Suppose we have the traffic data of an entire city that are incomplete because some road data are unobserved. The problem is to reconstruct the unobserved parts of the data. In this paper, we propose a new method to reconstruct incomplete traffic data collected from ...
computer science
10,420
Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary $β$-Mixing Processes
cs.LG
Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions showing how practical these bounds can be either to perform model selection (Ambrol...
computer science
10,421
High-dimensional structure estimation in Ising models: Local separation criterion
stat.ML
We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres...
computer science
10,422
Robust Kernel Density Estimation
stat.ML
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical $M$-estimation. We interpret the KDE based on a radial, positive semi-definite ke...
computer science
10,423
On Learning Discrete Graphical Models Using Greedy Methods
cs.LG
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical model...
computer science
10,424
Composite Self-Concordant Minimization
stat.ML
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth...
computer science
10,425
Computational Rationalization: The Inverse Equilibrium Problem
cs.GT
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior is an approximately optimal solution to an unknown decision problem. These tech...
computer science
10,426
Standardizing Interestingness Measures for Association Rules
stat.AP
Interestingness measures provide information that can be used to prune or select association rules. A given value of an interestingness measure is often interpreted relative to the overall range of the values that the interestingness measure can take. However, properties of individual association rules restrict the val...
computer science
10,427
A balanced k-means algorithm for weighted point sets
math.OC
The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been observed in many scientific and business applications. In this paper, we present ...
computer science
10,428
Pylearn2: a machine learning research library
stat.ML
Pylearn2 is a machine learning research library. This does not just mean that it is a collection of machine learning algorithms that share a common API; it means that it has been designed for flexibility and extensibility in order to facilitate research projects that involve new or unusual use cases. In this paper we g...
computer science
10,429
Online and stochastic Douglas-Rachford splitting method for large scale machine learning
cs.NA
Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version)....
computer science
10,430
Minimal Dirichlet energy partitions for graphs
math.OC
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel rearrangement algorithm is proposed, which we show is strictly decreas...
computer science
10,431
Manopt, a Matlab toolbox for optimization on manifolds
cs.MS
Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. S...
computer science
10,432
The Lovasz-Bregman Divergence and connections to rank aggregation, clustering, and web ranking
cs.LG
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show h...
computer science
10,433
New Algorithms for Learning Incoherent and Overcomplete Dictionaries
cs.DS
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, t...
computer science
10,434
Online Ranking: Discrete Choice, Spearman Correlation and Other Feedback
cs.LG
Given a set $V$ of $n$ objects, an online ranking system outputs at each time step a full ranking of the set, observes a feedback of some form and suffers a loss. We study the setting in which the (adversarial) feedback is an element in $V$, and the loss is the position (0th, 1st, 2nd...) of the item in the outputted r...
computer science
10,435
Minimum Probability Flow Learning
cs.LG
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. T...
computer science
10,436
Statistical Decision Making for Authentication and Intrusion Detection
stat.ML
User authentication and intrusion detection differ from standard classification problems in that while we have data generated from legitimate users, impostor or intrusion data is scarce or non-existent. We review existing techniques for dealing with this problem and propose a novel alternative based on a principled sta...
computer science
10,437
Which graphical models are difficult to learn?
stat.ML
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp...
computer science
10,438
Inference of global clusters from locally distributed data
stat.ME
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing ...
computer science
10,439
Convex Analysis and Optimization with Submodular Functions: a Tutorial
cs.LG
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of sub...
computer science
10,440
Robust PCA via Outlier Pursuit
cs.LG
Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting where each point has ...
computer science
10,441
Sparsity regret bounds for individual sequences in online linear regression
stat.ML
We consider the problem of online linear regression on arbitrary deterministic sequences when the ambient dimension d can be much larger than the number of time rounds T. We introduce the notion of sparsity regret bound, which is a deterministic online counterpart of recent risk bounds derived in the stochastic setting...
computer science
10,442
Classification under Data Contamination with Application to Remote Sensing Image Mis-registration
stat.ME
This work is motivated by the problem of image mis-registration in remote sensing and we are interested in determining the resulting loss in the accuracy of pattern classification. A statistical formulation is given where we propose to use data contamination to model and understand the phenomenon of image mis-registrat...
computer science
10,443
Reproducing Kernel Banach Spaces with the l1 Norm
stat.ML
Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous lin...
computer science
10,444
Reproducing Kernel Banach Spaces with the l1 Norm II: Error Analysis for Regularized Least Square Regression
stat.ML
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding t...
computer science
10,445
Efficient First Order Methods for Linear Composite Regularizers
cs.LG
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function \omega with a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods a...
computer science
10,446
Dimension-free tail inequalities for sums of random matrices
math.PR
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens...
computer science
10,447
Convex and Network Flow Optimization for Structured Sparsity
math.OC
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the ca...
computer science
10,448
Cluster Forests
stat.ME
With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local clusterings" and then aggregates via spectral clustering to obtain cluster assignments fo...
computer science
10,449
A sufficient condition on monotonic increase of the number of nonzero entry in the optimizer of L1 norm penalized least-square problem
stat.ML
The $\ell$-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the $\ell$-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path ...
computer science
10,450
On Combining Machine Learning with Decision Making
math.OC
We present a new application and covering number bound for the framework of "Machine Learning with Operational Costs (MLOC)," which is an exploratory form of decision theory. The MLOC framework incorporates knowledge about how a predictive model will be used for a subsequent task, thus combining machine learning with t...
computer science
10,451
Online Learning: Stochastic and Constrained Adversaries
stat.ML
Learning theory has largely focused on two main learning scenarios. The first is the classical statistical setting where instances are drawn i.i.d. from a fixed distribution and the second scenario is the online learning, completely adversarial scenario where adversary at every time step picks the worst instance to pro...
computer science
10,452
Notes on a New Philosophy of Empirical Science
cs.LG
This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can compress a standard benchmark database to a small size, taking into account the len...
computer science
10,453
Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear Programming
math.OC
In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization problems. We extend some existing iterative reweighted $l_1$ (IRL1) a...
computer science
10,454
Sparse LMS via Online Linearized Bregman Iteration
cs.IT
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regulariz...
computer science
10,455
Evaluation of linear classifiers on articles containing pharmacokinetic evidence of drug-drug interactions
stat.ML
Background. Drug-drug interaction (DDI) is a major cause of morbidity and mortality. [...] Biomedical literature mining can aid DDI research by extracting relevant DDI signals from either the published literature or large clinical databases. However, though drug interaction is an ideal area for translational research, ...
computer science
10,456
A fast compression-based similarity measure with applications to content-based image retrieval
stat.ML
Compression-based similarity measures are effectively employed in applications on diverse data types with a basically parameter-free approach. Nevertheless, there are problems in applying these techniques to medium-to-large datasets which have been seldom addressed. This paper proposes a similarity measure based on com...
computer science
10,457
Distributed High Dimensional Information Theoretical Image Registration via Random Projections
cs.IT
Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in high dimensions. On the other hand, consistent estimation from pairwise distances...
computer science
10,458
A Scalable CUR Matrix Decomposition Algorithm: Lower Time Complexity and Tighter Bound
cs.LG
The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the adv...
computer science
10,459
Privacy Aware Learning
stat.ML
We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of statistical estimation procedures. As a consequence, we exhibit a precise tradeoff be...
computer science
10,460
A Fast Distributed Proximal-Gradient Method
cs.DC
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has...
computer science
10,461
Inferring clonal evolution of tumors from single nucleotide somatic mutations
cs.LG
High-throughput sequencing allows the detection and quantification of frequencies of somatic single nucleotide variants (SNV) in heterogeneous tumor cell populations. In some cases, the evolutionary history and population frequency of the subclonal lineages of tumor cells present in the sample can be reconstructed from...
computer science
10,462
Markov Determinantal Point Processes
cs.LG
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to...
computer science
10,463
Mechanism Design for Cost Optimal PAC Learning in the Presence of Strategic Noisy Annotators
cs.LG
We consider the problem of Probably Approximate Correct (PAC) learning of a binary classifier from noisy labeled examples acquired from multiple annotators (each characterized by a respective classification noise rate). First, we consider the complete information scenario, where the learner knows the noise rates of all...
computer science
10,464
Spectral Estimation of Conditional Random Graph Models for Large-Scale Network Data
cs.SI
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coe...
computer science
10,465
Response Aware Model-Based Collaborative Filtering
cs.LG
Previous work on recommender systems mainly focus on fitting the ratings provided by users. However, the response patterns, i.e., some items are rated while others not, are generally ignored. We argue that failing to observe such response patterns can lead to biased parameter estimation and sub-optimal model performanc...
computer science
10,466
A Model-Based Approach to Rounding in Spectral Clustering
cs.LG
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the leading eigenvectors. The last step is sometimes referred to as rounding, where one ne...
computer science
10,467
Efficiently Searching for Frustrated Cycles in MAP Inference
cs.DS
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to intr...
computer science
10,468
Latent Structured Ranking
cs.LG
Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding...
computer science
10,469
Latent Dirichlet Allocation Uncovers Spectral Characteristics of Drought Stressed Plants
cs.LG
Understanding the adaptation process of plants to drought stress is essential in improving management practices, breeding strategies as well as engineering viable crops for a sustainable agriculture in the coming decades. Hyper-spectral imaging provides a particularly promising approach to gain such understanding since...
computer science
10,470
Factorized Multi-Modal Topic Model
cs.LG
Multi-modal data collections, such as corpora of paired images and text snippets, require analysis methods beyond single-view component and topic models. For continuous observations the current dominant approach is based on extensions of canonical correlation analysis, factorizing the variation into components shared b...
computer science
10,471
Pairwise MRF Calibration by Perturbation of the Bethe Reference Point
cs.LG
We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagati...
computer science
10,472
Large-Scale Sparse Principal Component Analysis with Application to Text Data
stat.ML
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact tha...
computer science
10,473
Selective Transfer Learning for Cross Domain Recommendation
cs.LG
Collaborative filtering (CF) aims to predict users' ratings on items according to historical user-item preference data. In many real-world applications, preference data are usually sparse, which would make models overfit and fail to give accurate predictions. Recently, several research works show that by transferring k...
computer science
10,474
Tensor decompositions for learning latent variable models
cs.LG
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically...
computer science
10,475
Linear Convergence of Variance-Reduced Stochastic Gradient without Strong Convexity
cs.NA
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t...
computer science
10,476
Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
cs.LG
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for these l...
computer science
10,477
Probabilistic ODE Solvers with Runge-Kutta Means
stat.ML
Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability d...
computer science
10,478
Learning with Cross-Kernels and Ideal PCA
cs.LG
We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of the matrix scales with the number of data points, and (b) cross-kernels, as oppos...
computer science
10,479
Learning Latent Variable Gaussian Graphical Models
stat.ML
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. I...
computer science
10,480
A low variance consistent test of relative dependency
stat.ML
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more dependent on a first target variable or a second. Dependence is measured via the Hilbe...
computer science
10,481
The Laplacian K-modes algorithm for clustering
cs.LG
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text...
computer science
10,482
RAPID: Rapidly Accelerated Proximal Gradient Algorithms for Convex Minimization
stat.ML
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each proximal gradient step in APG so that a biconvex function $f(\theta\mathbf{x})$ is m...
computer science
10,483
Primitives for Dynamic Big Model Parallelism
stat.ML
When training large machine learning models with many variables or parameters, a single machine is often inadequate since the model may be too large to fit in memory, while training can take a long time even with stochastic updates. A natural recourse is to turn to distributed cluster computing, in order to harness add...
computer science
10,484
Variational Gaussian Process State-Space Models
cs.LG
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dy...
computer science
10,485
Inferring causal structure: a quantum advantage
cs.LG
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unle...
computer science
10,486
Enhancing Pure-Pixel Identification Performance via Preconditioning
stat.ML
In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization algorithms. Our analysis focuses on the successive projection algorithm (SPA), ...
computer science
10,487
On semidefinite relaxations for the block model
cs.LG
The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. W...
computer science
10,488
On the Maximum Entropy Property of the First-Order Stable Spline Kernel and its Implications
math.ST
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the ...
computer science
10,489
Convex Optimization Learning of Faithful Euclidean Distance Representations in Nonlinear Dimensionality Reduction
stat.ML
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance Unfolding (MVU) and Minimum Volume Embedding (MVE) use Semi-Definite Programming (SDP...
computer science
10,490
Combining predictions from linear models when training and test inputs differ
stat.ME
Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the assumption that the test inputs are identical to the training inputs, which is seldom re...
computer science
10,491
A scaled gradient projection method for Bayesian learning in dynamical systems
math.NA
A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this can be addressed in a Bayesian framework, where model complexity is regulated by ...
computer science
10,492
Mass-Univariate Hypothesis Testing on MEEG Data using Cross-Validation
stat.ML
Recent advances in statistical theory, together with advances in the computational power of computers, provide alternative methods to do mass-univariate hypothesis testing in which a large number of univariate tests, can be properly used to compare MEEG data at a large number of time-frequency points and scalp location...
computer science
10,493
Reconstructing subclonal composition and evolution from whole genome sequencing of tumors
cs.LG
Tumors often contain multiple subpopulations of cancerous cells defined by distinct somatic mutations. We describe a new method, PhyloWGS, that can be applied to WGS data from one or more tumor samples to reconstruct complete genotypes of these subpopulations based on variant allele frequencies (VAFs) of point mutation...
computer science
10,494
Learning Laplacian Matrix in Smooth Graph Signal Representations
cs.LG
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending...
computer science
10,495
Simple connectome inference from partial correlation statistics in calcium imaging
stat.ML
In this work, we propose a simple yet effective solution to the problem of connectome inference in calcium imaging data. The proposed algorithm consists of two steps. First, processing the raw signals to detect neural peak activities. Second, inferring the degree of association between neurons from partial correlation ...
computer science
10,496
Differentially Private Online Learning
cs.LG
In this paper, we consider the problem of preserving privacy in the online learning setting. We study the problem in the online convex programming (OCP) framework---a popular online learning setting with several interesting theoretical and practical implications---while using differential privacy as the formal privacy ...
computer science
10,497
Active Ranking using Pairwise Comparisons
cs.LG
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the o...
computer science
10,498
VC dimension of ellipsoids
math.CO
We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian...
computer science
10,499
Manifold estimation and singular deconvolution under Hausdorff loss
math.ST
We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.
computer science
10,500
Complexity Analysis of the Lasso Regularization Path
stat.ML
The regularization path of the Lasso can be shown to be piecewise linear, making it possible to "follow" and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to a...
computer science