Related papers: Improved bounds for randomized Schatten norm estim…
Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its…
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…
This paper studies the Schatten-$q$ error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
We consider the twin problems of estimating the effective rank and the Schatten norms $\|{\bf A}\|_{s}$ of a rectangular $p\times q$ matrix ${\bf A}$ from noisy observations. When $s$ is an even integer, we introduce a polynomial-time…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or the trace of a symmetric positive semi-definite matrix. Several such probabilistic…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
The Schatten quasi-norm was introduced to bridge the gap between the trace norm and rank function. However, existing algorithms are too slow or even impractical for large-scale problems. Motivated by the equivalence relation between the…
We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate…
We report on the use of a stochastic trace estimator algorithm, based on mutually unbiased bases, for evaluating the trace of a matrix differential operator appearing in the context of lattice simulations for the discretized superstring…
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the…
This article is concerned with Monte-Carlo methods for the estimation of the trace of an implicitly given matrix $A$ whose information is only available through matrix-vector products. Such a method approximates the trace by an average of…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as…
We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models. The estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples, is consistent,…