Related papers: A Random Matrix Perspective on Random Tensors
We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Large language models have become ubiquitous in modern life, finding applications in various domains such as natural language processing, language translation, and speech recognition. Recently, a breakthrough work [Zhao, Panigrahi, Ge, and…
This work finds its place in the statistical mechanical approach to light amplification in disordered media, namely Random Lasers (RLs). The problem of going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory employed to…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…
We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…
In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data…
We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and…
We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian…
In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…