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21,802
The Matrix Generalized Inverse Gaussian Distribution: Properties and Applications
stat.ML
While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways of sampling from the distribution have not been carefully studied. In this paper...
computer science
21,803
Structured Matrix Recovery via the Generalized Dantzig Selector
stat.ML
In recent years, structured matrix recovery problems have gained considerable attention for its real world applications, such as recommender systems and computer vision. Much of the existing work has focused on matrices with low-rank structure, and limited progress has been made matrices with other types of structure. ...
computer science
21,804
Optimal Rates For Regularization Of Statistical Inverse Learning Problems
stat.ML
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimati...
computer science
21,805
1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation
stat.ML
Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-c...
computer science
21,806
Estimating parameters of nonlinear systems using the elitist particle filter based on evolutionary strategies
stat.ML
In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the relevant information of the nonlinear system is captured by an unknown state vecto...
computer science
21,807
Smoothed Hierarchical Dirichlet Process: A Non-Parametric Approach to Constraint Measures
stat.ML
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any models that realistically cater to this phenomenon must exhibit two important p...
computer science
21,808
Random Projection Estimation of Discrete-Choice Models with Large Choice Sets
stat.ML
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation ...
computer science
21,809
Dynamic Pricing with Demand Covariates
stat.ML
We consider a firm that sells products over $T$ periods without knowing the demand function. The firm sequentially sets prices to earn revenue and to learn the underlying demand function simultaneously. A natural heuristic for this problem, commonly used in practice, is greedy iterative least squares (GILS). At each ti...
computer science
21,810
Optimal Transport vs. Fisher-Rao distance between Copulas for Clustering Multivariate Time Series
stat.ML
We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account ...
computer science
21,811
Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via Truncated Rayleigh Flow
stat.ML
Sparse generalized eigenvalue problem plays a pivotal role in a large family of high-dimensional learning tasks, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. However, the theory of sparse generalized eigenvalue problem remains largely unexplored. I...
computer science
21,812
LLE with low-dimensional neighborhood representation
stat.ML
The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W...
computer science
21,813
Persistent Clustering and a Theorem of J. Kleinberg
stat.ML
We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second the idea that one should be able to compare the results of clustering algorithm...
computer science
21,814
Decomposable Principal Component Analysis
stat.ML
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem ...
computer science
21,815
Multi-view predictive partitioning in high dimensions
stat.ML
Many modern data mining applications are concerned with the analysis of datasets in which the observations are described by paired high-dimensional vectorial representations or "views". Some typical examples can be found in web mining and genomics applications. In this article we present an algorithm for data clusterin...
computer science
21,816
Greedy Learning of Markov Network Structure
stat.ML
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that produce the largest reduction in empirical conditional entropy; it is greedy in the se...
computer science
21,817
High Dimensional Semiparametric Gaussian Copula Graphical Models
stat.ML
In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estima...
computer science
21,818
Regularized Tensor Factorizations and Higher-Order Principal Components Analysis
stat.ML
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal component...
computer science
21,819
Robust subspace recovery by Tyler's M-estimator
stat.ML
This paper considers the problem of robust subspace recovery: given a set of $N$ points in $\mathbb{R}^D$, if many lie in a $d$-dimensional subspace, then can we recover the underlying subspace? We show that Tyler's M-estimator can be used to recover the underlying subspace, if the percentage of the inliers is larger t...
computer science
21,820
Warped Mixtures for Nonparametric Cluster Shapes
stat.ML
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce nonparametric cluster shapes. The possibly low-dimensional latent mixture model allow...
computer science
21,821
On the probabilistic continuous complexity conjecture
stat.ML
In this paper we prove the probabilistic continuous complexity conjecture. In continuous complexity theory, this states that the complexity of solving a continuous problem with probability approaching 1 converges (in this limit) to the complexity of solving the same problem in its worst case. We prove the conjecture ho...
computer science
21,822
Developments in the theory of randomized shortest paths with a comparison of graph node distances
stat.ML
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac...
computer science
21,823
An Empirical Comparison of V-fold Penalisation and Cross Validation for Model Selection in Distribution-Free Regression
stat.ML
Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is generally not well documented in the literature. It is the goal of this paper to in...
computer science
21,824
MAD-Bayes: MAP-based Asymptotic Derivations from Bayes
stat.ML
The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective, and the EM algorithm approaches the K-means algorithm. Kulis & Jordan (2012) us...
computer science
21,825
A complexity analysis of statistical learning algorithms
stat.ML
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes ...
computer science
21,826
Feature vector regularization in machine learning
stat.ML
Problems in machine learning (ML) can involve noisy input data, and ML classification methods have reached limiting accuracies when based on standard ML data sets consisting of feature vectors and their classes. Greater accuracy will require incorporation of prior structural information on data into learning. We study ...
computer science
21,827
Blind Analysis of EGM Signals: Sparsity-Aware Formulation
stat.ML
This technical note considers the problems of blind sparse learning and inference of electrogram (EGM) signals under atrial fibrillation (AF) conditions. First of all we introduce a mathematical model for the observed signals that takes into account the multiple foci typically appearing inside the heart during AF. Then...
computer science
21,828
Regression shrinkage and grouping of highly correlated predictors with HORSES
stat.ML
Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. We propose a new method called Hexagonal Operator for Regression with Shrinkage and Equality Selection, HORSES for short, that simultaneously selects positively correlated variables and...
computer science
21,829
Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models
stat.ML
It has been shown that AIC-type criteria are asymptotically efficient selectors of the tuning parameter in non-concave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically ...
computer science
21,830
Towards Identification of Relevant Variables in the observed Aerosol Optical Depth Bias between MODIS and AERONET observations
stat.ML
Measurements made by satellite remote sensing, Moderate Resolution Imaging Spectroradiometer (MODIS), and globally distributed Aerosol Robotic Network (AERONET) are compared. Comparison of the two datasets measurements for aerosol optical depth values show that there are biases between the two data products. In this pa...
computer science
21,831
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
stat.ML
We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the fun...
computer science
21,832
Consistency of Online Random Forests
stat.ML
As a testament to their success, the theory of random forests has long been outpaced by their application in practice. In this paper, we take a step towards narrowing this gap by providing a consistency result for online random forests.
computer science
21,833
Spectral Clustering with Unbalanced Data
stat.ML
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor performance on well-known graphs such as $k$-NN, full-RBF, $\epsilon$-graphs. This is...
computer science
21,834
A bag-of-paths framework for network data analysis
stat.ML
This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representati...
computer science
21,835
A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem
stat.ML
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we ...
computer science
21,836
Dictionary LASSO: Guaranteed Sparse Recovery under Linear Transformation
stat.ML
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in \mathbb{R}^{n}$ is the noise vector whose entries follow i.i.d. centered sub-Gaussian dist...
computer science
21,837
Learning Mixtures of Bernoulli Templates by Two-Round EM with Performance Guarantee
stat.ML
Dasgupta and Shulman showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is sufficiently high. In this paper, we generalize their theory to learning mixture...
computer science
21,838
Inferring Team Strengths Using a Discrete Markov Random Field
stat.ML
We propose an original model for inferring team strengths using a Markov Random Field, which can be used to generate historical estimates of the offensive and defensive strengths of a team over time. This model was designed to be applied to sports such as soccer or hockey, in which contest outcomes take value in a limi...
computer science
21,839
Sparse Approximate Inference for Spatio-Temporal Point Process Models
stat.ML
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we expl...
computer science
21,840
Factored expectation propagation for input-output FHMM models in systems biology
stat.ML
We consider the problem of joint modelling of metabolic signals and gene expression in systems biology applications. We propose an approach based on input-output factorial hidden Markov models and propose a structured variational inference approach to infer the structure and states of the model. We start from the class...
computer science
21,841
Out-of-sample Extension for Latent Position Graphs
stat.ML
We consider the problem of vertex classification for graphs constructed from the latent position model. It was shown previously that the approach of embedding the graphs into some Euclidean space followed by classification in that space can yields a universally consistent vertex classifier. However, a major technical d...
computer science
21,842
Adaptive estimation of the copula correlation matrix for semiparametric elliptical copulas
stat.ML
We study the adaptive estimation of copula correlation matrix $\Sigma$ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for $\Sigma$ is the plug-in estimator $\hat{\Sigma}$ with Kendall's t...
computer science
21,843
Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution
stat.ML
Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good prop...
computer science
21,844
Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
stat.ML
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. Building on...
computer science
21,845
Joint Modeling and Registration of Cell Populations in Cohorts of High-Dimensional Flow Cytometric Data
stat.ML
In systems biomedicine, an experimenter encounters different potential sources of variation in data such as individual samples, multiple experimental conditions, and multi-variable network-level responses. In multiparametric cytometry, which is often used for analyzing patient samples, such issues are critical. While c...
computer science
21,846
Forward-Backward Greedy Algorithms for General Convex Smooth Functions over A Cardinality Constraint
stat.ML
We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems...
computer science
21,847
Online Matrix Completion Through Nuclear Norm Regularisation
stat.ML
It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the ...
computer science
21,848
Multiscale Shrinkage and Lévy Processes
stat.ML
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The me...
computer science
21,849
A variational Bayes framework for sparse adaptive estimation
stat.ML
Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a ...
computer science
21,850
Detection of Anomalous Crowd Behavior Using Spatio-Temporal Multiresolution Model and Kronecker Sum Decompositions
stat.ML
In this work we consider the problem of detecting anomalous spatio-temporal behavior in videos. Our approach is to learn the normative multiframe pixel joint distribution and detect deviations from it using a likelihood based approach. Due to the extreme lack of available training samples relative to the dimension of t...
computer science
21,851
Survey On The Estimation Of Mutual Information Methods as a Measure of Dependency Versus Correlation Analysis
stat.ML
In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus correlation analysis, which is only optimal in case of linear dependencies. First, w...
computer science
21,852
Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learning
stat.ML
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or...
computer science
21,853
Embedding Graphs under Centrality Constraints for Network Visualization
stat.ML
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding appro...
computer science
21,854
Marginal Pseudo-Likelihood Learning of Markov Network structures
stat.ML
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In ge...
computer science
21,855
Hilbert Space Methods for Reduced-Rank Gaussian Process Regression
stat.ML
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of $\mathbb{R}^d$. On this approximate eigenbasis the eigenvalues of the c...
computer science
21,856
Identifiability of an Integer Modular Acyclic Additive Noise Model and its Causal Structure Discovery
stat.ML
The notion of causality is used in many situations dealing with uncertainty. We consider the problem whether causality can be identified given data set generated by discrete random variables rather than continuous ones. In particular, for non-binary data, thus far it was only known that causality can be identified exce...
computer science
21,857
The EM algorithm and the Laplace Approximation
stat.ML
The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient ...
computer science
21,858
Near-Ideal Behavior of Compressed Sensing Algorithms
stat.ML
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose $y = Az + \eta$ where $A$ satisfies the restricted isometry property (RIP) with a sufficiently small constant, and $\Vert \eta \Vert_2 \leq \epsilon$. Then minimizing $\Vert z \Vert_1$ subject to $\Ve...
computer science
21,859
Safe Sample Screening for Support Vector Machines
stat.ML
Sparse classifiers such as the support vector machines (SVM) are efficient in test-phases because the classifier is characterized only by a subset of the samples called support vectors (SVs), and the rest of the samples (non SVs) have no influence on the classification result. However, the advantage of the sparsity has...
computer science
21,860
Tempering by Subsampling
stat.ML
In this paper we demonstrate that tempering Markov chain Monte Carlo samplers for Bayesian models by recursively subsampling observations without replacement can improve the performance of baseline samplers in terms of effective sample size per computation. We present two tempering by subsampling algorithms, subsampled...
computer science
21,861
Sparse Bayesian Unsupervised Learning
stat.ML
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of relevant variables $S$ using a generalized Bayesian posterior with a sparsity indu...
computer science
21,862
A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning
stat.ML
This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a structured input space and a structured output space. Our formulation encompasses both Vector-valued Manifold Regularization and Co-regularized Multi-view...
computer science
21,863
Marginal and simultaneous predictive classification using stratified graphical models
stat.ML
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have b...
computer science
21,864
Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models - a Gentle Tutorial
stat.ML
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias & Lawrence (2010) is brief, hence getting a full picture of it requires collecting resul...
computer science
21,865
An Algorithmic Framework for Computing Validation Performance Bounds by Using Suboptimal Models
stat.ML
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model validation errors without actually training the model itself. A key idea behind ou...
computer science
21,866
Justifying Information-Geometric Causal Inference
stat.ML
Information Geometric Causal Inference (IGCI) is a new approach to distinguish between cause and effect for two variables. It is based on an independence assumption between input distribution and causal mechanism that can be phrased in terms of orthogonality in information space. We describe two intuitive reinterpretat...
computer science
21,867
Performance Limits of Dictionary Learning for Sparse Coding
stat.ML
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of the dictionary learning problem which governs the mean squared error (MSE) perf...
computer science
21,868
A Kernel Independence Test for Random Processes
stat.ML
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when compu...
computer science
21,869
High Dimensional Semiparametric Scale-Invariant Principal Component Analysis
stat.ML
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three as...
computer science
21,870
Le Cam meets LeCun: Deficiency and Generic Feature Learning
stat.ML
"Deep Learning" methods attempt to learn generic features in an unsupervised fashion from a large unlabelled data set. These generic features should perform as well as the best hand crafted features for any learning problem that makes use of this data. We provide a definition of generic features, characterize when it i...
computer science
21,871
Novel Deviation Bounds for Mixture of Independent Bernoulli Variables with Application to the Missing Mass
stat.ML
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity...
computer science
21,872
Addendum on the scoring of Gaussian directed acyclic graphical models
stat.ML
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
computer science
21,873
New Perspectives on k-Support and Cluster Norms
stat.ML
The $k$-support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the $k$-support norm to matrices, and we observe that it is a special ...
computer science
21,874
A reversible infinite HMM using normalised random measures
stat.ML
We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Mark...
computer science
21,875
On the Sensitivity of the Lasso to the Number of Predictor Variables
stat.ML
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a deterministic choice of the regularization parameter. These bounds tend to zero if ...
computer science
21,876
On The Sample Complexity of Sparse Dictionary Learning
stat.ML
In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this would be achieved by optimizing the expectation of the factors over the underlyin...
computer science
21,877
Sparse Learning over Infinite Subgraph Features
stat.ML
We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, ...
computer science
21,878
First Order Methods for Robust Non-negative Matrix Factorization for Large Scale Noisy Data
stat.ML
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or rows) [1]. In real applications, however, such separability assumption is hard t...
computer science
21,879
Optimal Schatten-q and Ky-Fan-k Norm Rate of Low Rank Matrix Estimation
stat.ML
In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_{\lambda}^d$ or matrix-version LASSO estimator $\hat{A}_{\lambda}^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. ...
computer science
21,880
Systematic Ensemble Learning for Regression
stat.ML
The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression problems. We propose two extensions to the standard stacking approach. In the fir...
computer science
21,881
Characteristic Kernels and Infinitely Divisible Distributions
stat.ML
We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is two-fold. First, we show, usi...
computer science
21,882
A Rank-SVM Approach to Anomaly Detection
stat.ML
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a rank-SVM using this ranked data. A test-point is declared as an anomaly at alpha-...
computer science
21,883
The Falling Factorial Basis and Its Statistical Applications
stat.ML
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria...
computer science
21,884
PAC-Bayes Mini-tutorial: A Continuous Union Bound
stat.ML
When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the PAC-Bayesian bounds, there is actually a very close relation, and the main innovation is a cont...
computer science
21,885
Learning rates for the risk of kernel based quantile regression estimators in additive models
stat.ML
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel ...
computer science
21,886
Fast Ridge Regression with Randomized Principal Component Analysis and Gradient Descent
stat.ML
We propose a new two stage algorithm LING for large scale regression problems. LING has the same risk as the well known Ridge Regression under the fixed design setting and can be computed much faster. Our experiments have shown that LING performs well in terms of both prediction accuracy and computational efficiency co...
computer science
21,887
A convergence and asymptotic analysis of the generalized symmetric FastICA algorithm
stat.ML
This contribution deals with the generalized symmetric FastICA algorithm in the domain of Independent Component Analysis (ICA). The generalized symmetric version of FastICA has been shown to have the potential to achieve the Cram\'er-Rao Bound (CRB) by allowing the usage of different nonlinearity functions in its paral...
computer science
21,888
A Bayesian estimation approach to analyze non-Gaussian data-generating processes with latent classes
stat.ML
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the non-Gaussianity of external influences has been proposed to estimate the data-generating ...
computer science
21,889
L0 Sparse Inverse Covariance Estimation
stat.ML
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm. However, the best estimator performance is not always achieved with this penalty. The ...
computer science
21,890
On the Generalization of the C-Bound to Structured Output Ensemble Methods
stat.ML
This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second stat...
computer science
21,891
Learning From Non-iid Data: Fast Rates for the One-vs-All Multiclass Plug-in Classifiers
stat.ML
We prove new fast learning rates for the one-vs-all multiclass plug-in classifiers trained either from exponentially strongly mixing data or from data generated by a converging drifting distribution. These are two typical scenarios where training data are not iid. The learning rates are obtained under a multiclass vers...
computer science
21,892
Beta diffusion trees and hierarchical feature allocations
stat.ML
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogou...
computer science
21,893
On the Sample Complexity of Subspace Learning
stat.ML
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and der...
computer science
21,894
A Wild Bootstrap for Degenerate Kernel Tests
stat.ML
A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on...
computer science
21,895
Kernel-based Information Criterion
stat.ML
This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Expe...
computer science
21,896
A study of the fixed points and spurious solutions of the FastICA algorithm
stat.ML
The FastICA algorithm is one of the most popular iterative algorithms in the domain of linear independent component analysis. Despite its success, it is observed that FastICA occasionally yields outcomes that do not correspond to any true solutions (known as demixing vectors) of the ICA problem. These outcomes are comm...
computer science
21,897
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
stat.ML
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic dimensionality reduct...
computer science
21,898
Learning Planar Ising Models
stat.ML
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of ...
computer science
21,899
Sparse Representation Classification Beyond L1 Minimization and the Subspace Assumption
stat.ML
The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence t...
computer science
21,900
Provable Sparse Tensor Decomposition
stat.ML
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family ...
computer science
21,901
Active Function Cross-Entropy Clustering
stat.ML
Gaussian Mixture Models (GMM) have found many applications in density estimation and data clustering. However, the model does not adapt well to curved and strongly nonlinear data. Recently there appeared an improvement called AcaGMM (Active curve axis Gaussian Mixture Model), which fits Gaussians along curves using an ...
computer science