The masked sample covariance estimator: an analysis using matrix concentration inequalities

Chen, Richard Y.; Gittens, Alex; Tropp, Joel A.

doi:10.1093/imaiai/ias001

Cited by 44 publications

(59 citation statements)

References 29 publications

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“…This work collects bounds for the expected value of the spectral norm of a random matrix and bounds for the expectation of the smallest and largest eigenvalues of a random symmetric matrix. Some of these useful results have appeared piecemeal in the literature [40,118], but they have not been included in a unified presentation.…”

Section: About This Monographmentioning

confidence: 99%

An Introduction to Matrix Concentration Inequalities

Tropp

2015

FNT in Machine Learning

335

159

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Section: About This Monographmentioning

confidence: 99%

An Introduction to Matrix Concentration Inequalities

Tropp

2015

FNT in Machine Learning

335

159

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“…Theorem A.3 (Matrix moment inequality, Theorem A.1 in Chen et al (2012)). Suppose that q ≥ 2 and fix r ≥ max(q, 2 log p).…”

Section: Proofs Of Results Of Sectionmentioning

confidence: 99%

“…Suppose that q ≥ 2 and fix r ≥ max(q, 2 log p). Consider a finite sequence {Y i } of independent, symmetric, random, self-adjoint matrices with dimension p × p. Then A proof can be found in Chen et al (2012).…”

Section: Proofs Of Results Of Sectionmentioning

confidence: 99%

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Laguerre deconvolution with unknown matrix operator

Comte

Mabon

2017

Math. Meth. Stat.

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Abstract. In this paper we consider the convolution model Z = X + Y with X of unknown density f , independent of Y , when both random variables are nonnegative. Our goal is to estimate the unknown density f of X from n independent, identically, distributed observations of Z, when the law of the additive process Y is unknown. When the density of Y is known, a solution to the problem has been proposed in Mabon (2016b). To make the problem identifiable for unknown density of Y , we assume that we have access to a preliminary sample of the nuisance process Y . The question is to propose a solution to an inverse problem with unknown operator. To that aim, we build a family of projection estimators of f on the Laguerre basis, particularly adapted to the non-negativeness of both random variables. The dimension of the projection space is chosen thanks to a model selection procedure by penalization. At last we prove that the final estimator satisfies an oracle inequality. It can be noted that the study of the mean integrated square risk is based on Bernstein's type concentration inequalities developed for random matrices in Tropp (2015). Finally we illustrate our method on some simulated data.

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“…This is quantified by a symmetric mask matrix M ∈ R d×d , whence the goal is to estimate the matrix M Σ that "downweights" the entries of Σ that are deemed less important, or incorporates the prior information on Σ. This problem formulation has been introduced in [30], and later studied in a number of papers including [12] and [26]. We will be interested in finding an estimator Σ M such that Σ M * −M Σ is small with high probability, and specifically in dependence of the estimation error on the mask matrix M .…”

Section: Masked Covariance Estimationmentioning

confidence: 99%

Robust modifications of U-statistics and applications to covariance estimation problems

Minsker¹,

Wei²

2020

Bernoulli

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Let Y be a d-dimensional random vector with unknown mean µ and covariance matrix Σ. This paper is motivated by the problem of designing an estimator of Σ that admits tight deviation bounds in the operator norm under minimal assumptions on the underlying distribution, such as existence of only 4th moments of the coordinates of Y . To address this problem, we propose robust modifications of the operator-valued U-statistics, obtain non-asymptotic guarantees for their performance, and demonstrate the implications of these results to the covariance estimation problem under various structural assumptions.

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The masked sample covariance estimator: an analysis using matrix concentration inequalities

Cited by 44 publications

References 29 publications

An Introduction to Matrix Concentration Inequalities

An Introduction to Matrix Concentration Inequalities

Laguerre deconvolution with unknown matrix operator

Robust modifications of U-statistics and applications to covariance estimation problems

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