Related papers: Stochastic Trace and Diagonal Estimator for Tensor…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on…
When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. Therefore, among the second-order optimization methods, it is common to bypass the…
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…
Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…
The problem of testing whether a signal lies within a given subspace, also named matched subspace detection, has been well studied when the signal is represented as a vector. However, the matched subspace detection methods based on vectors…
There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…
The determination of the maximal ranks of a set of a given type of tensors is a basic problem both in theory and application. In statistical applications, the maximal rank is related to the number of necessary parameters to be built in a…
Contemporary applications, such as recommendation systems and mobile health monitoring, require real-time processing and analysis of sequentially arriving high-dimensional tensor data. Traditional offline learning, involving the storage and…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
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,…
A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or the trace of a symmetric positive semi-definite matrix. Several such probabilistic…
A first order trace formula is obtained for a higher-order differential operator on a segment in the case where the perturbation is an operator of multiplication by a finite complex-valued measure. For the operators of even order $n\ge4$ a…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…