Related papers: Recent results on matrix weighted norm inequalitie…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
Robust Principal Component Analysis (RPCA) and its associated non-convex relaxation methods constitute a significant component of matrix completion problems, wherein matrix factorization strategies effectively reduce dimensionality and…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via…
In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…
In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great…
We prove that the class of convolution-type kernels satisfying suitable decay conditions of the Fourier transform, appearing in the works of Christ, Christ-Rubio de Francia, and Duoandikoetxea-Rubio de Francia gives rise to maximally…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.
We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
These notes cover a few calculations regarding the sum-rank weight of a matrix in relation to its rank. In particular, a formula and lower bounds are given on the probability that a matrix of rank $t$ consisting of $\ell$ blocks has…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
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…