Related papers: Structured Matrix Estimation and Completion
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…
We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix by a…
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…
In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system - a problem known as sample complexity analysis in computer science. Motivated by the…
Last decade witnesses significant methodological and theoretical advances in estimating large precision matrices. In particular, there are scientific applications such as longitudinal data, meteorology and spectroscopy in which the ordering…
Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…