Related papers: Modelling matrix time series via a tensor CP-decom…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

Time series forecasting presents significant challenges in real-world applications across various domains. Building upon the decomposition of the time series, we enhance the architecture of machine learning models for better multivariate…

Higher-order tensors are well-suited for representing multi-dimensional data, such as images and videos, which typically characterize low-rank structures. Low-rank tensor decomposition has become essential in machine learning and computer…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

We propose a new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch. We then extend this approach to the tensor interpolative decomposition problem introduced by Biagioni et al. (J. Comput.…

We prove a generalization to Jennrich's uniqueness theorem for tensor decompositions in the undercomplete setting. Our uniqueness theorem is based on an alternative definition of the standard tensor decomposition, which we call…

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…

Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…

Matrices can be decomposed via rank-one approximations: the best rank-one approximation is a singular vector pair, and the singular value decomposition writes a matrix as a sum of singular vector pairs. The singular vector tuples of a…

In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition…

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…