Related papers: Tensor distributions with covariance tensor or cor…

Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…

A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…

Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…

In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…

Conformal fluctuations of the metric tensor at the Planck scale are considered. They give rise to a lower bound of the proper length. This leads to finite expressions for quantities related to propagators without the need of renormalization…

We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any…

We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed…

It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…

The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…

We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$.

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…

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 as Communications, Signal Processing, Machine learning,…