Related papers: On low-rank approximability of solutions to high-d…

The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based…

To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…

Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding…

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

The substantial computational demands of modern large-scale deep learning present significant challenges for efficient training and deployment. Recent research has revealed a widespread phenomenon wherein deep networks inherently learn…

We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale,…

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…