Many applications seek to recover low-rank approximations of noisy tensor data. We
consider several practical and effective matricization strategies which construct specific …

This review paper utilizes renormalization group techniques for signal detection in nearly
continuous positive spectra. We emphasize the universal aspects of the analogue field …

Under a simplified data model, this paper provides a theoretical analysis of learning from
data that have an underlying low-rank tensor structure in both supervised and unsupervised …

We pursue the current developments in random tensor theory by laying the foundations of a
free probability theory for tensors and establish its relevance in the study of random tensors …

We study the performance of a Bayesian statistician who estimates a rank-one signal
corrupted by non-symmetric rotationally invariant noise with a generic distribution of singular …

We study adjacency and Laplacian matrices of Erd\H {o} sR\'{e} nyi $ r $-uniform
hypergraphs on $ n $ vertices with hyperedge inclusion probability $ p $, in the setting …

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 …

We study the estimation of a planted signal hidden in a recently introduced nested matrix-
tensor model, which is an extension of the classical spiked rank-one tensor model …

This work considers the notion of random tensors and reviews some fundamental concepts
in statistics when applied to a tensor based data or signal. In several engineering fields such …

We consider two hypothesis testing problems for low-rank and high-dimensional tensor
signals, namely the tensor signal alignment and tensor signal matching problems. These …