Related papers: Structured Matrix Estimation and Completion
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate…
Social trust prediction addresses the significant problem of exploring interactions among users in social networks. Naturally, this problem can be formulated in the matrix completion framework, with each entry indicating the trustness or…
In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…
In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank target matrix with auxiliary data available. We propose a transfer learning procedure given prior…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…
Finite Mixture Regression (FMR) refers to the mixture modeling scheme which learns multiple regression models from the training data set. Each of them is in charge of a subset. FMR is an effective scheme for handling sample heterogeneity,…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…
In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…
This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…
We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…