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We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove a celebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also allows us to prove…

Functional Analysis · Mathematics 2024-04-09 Yongtao Li

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Machine Learning · Statistics 2021-02-03 Malik Tiomoko , Florent Bouchard , Guillaume Ginholac , Romain Couillet

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…

Functional Analysis · Mathematics 2007-05-23 Leonid Kontorovich

We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…

Probability · Mathematics 2020-06-02 Richard Aoun , Marwa Banna , Pierre Youssef

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

Optimization and Control · Mathematics 2020-01-30 Mootta Prangprakhon , Nimit Nimana , Narin Petrot

In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…

Functional Analysis · Mathematics 2017-09-27 Christian Engström , Axel Torshage

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…

Machine Learning · Statistics 2025-07-04 Dali Liu , Haolei Weng

We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of…

Probability · Mathematics 2007-05-23 Sourav Chatterjee

This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate…

General Mathematics · Mathematics 2023-10-24 Branko Malesevic , Milos Micovic

The aim of this paper is to discuss various concentration inequalities for U-statistics and most recent results. A special focus will be on providing proofs for bounds on the U-statistics using classical concentration inequalities, which,…

Statistics Theory · Mathematics 2019-03-18 Yannik Pitcan

Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss…

Applications · Statistics 2023-03-23 Marco Morucci , Cynthia Rudin

Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…

Computers and Society · Computer Science 2021-09-09 A. Feder Cooper , Ellen Abrams

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

Neural and Evolutionary Computing · Computer Science 2020-03-10 Quan Quan , Kai-Yuan Cai

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Computer Vision and Pattern Recognition · Computer Science 2018-02-26 D. Khuê Lê-Huu , Nikos Paragios

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…

Probability · Mathematics 2019-06-17 Bernard Bercu , Taieb Touati

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these…

Probability · Mathematics 2007-06-13 Christian Houdré , Hua Xu

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

Symbolic Computation · Computer Science 2020-10-15 Dong Lu , Dingkang Wang , Fanghui Xiao

Since there exist several completion methods to estimate the missing entries of pairwise comparison matrices, practitioners face a difficult task in choosing the best technique. Our paper contributes to this issue: we consider a special set…

Optimization and Control · Mathematics 2023-11-14 László Csató

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…

Artificial Intelligence · Computer Science 2014-04-24 Mathias Niepert , Guy Van den Broeck

The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results…

Functional Analysis · Mathematics 2021-03-11 Bo-Yan Xi , Fuzhen Zhang