Related papers: Estimation under matrix quadratic loss and matrix …

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…

We consider the additive version of the matrix denoising problem, where a random symmetric matrix $S$ of size $n$ has to be inferred from the observation of $Y=S+Z$, with $Z$ an independent random matrix modeling a noise. For prior…

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion…

Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…

We consider a statistical model for matrix factorization in a regime where the rank of the two hidden matrix factors grows linearly with their dimension and their product is corrupted by additive noise. Despite various approaches,…

We consider a minimal realization of a rational matrix functions. We perturb the polynomial part and one of the constant matrices from the realization part. We derive explicit computable expressions of backward errors of approximate…

Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between…

Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ be independent p-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on only observing $X=x$, we consider the problem of obtaining a predictive…

This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…

We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…

In this paper, we study the low-rank matrix completion problem, a class of machine learning problems, that aims at the prediction of missing entries in a partially observed matrix. Such problems appear in several challenging applications…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…