Related papers: Efficient randomized tensor-based algorithms for f…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
We present a sequential version of the multilinear Nystr\"om algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random sketches of…
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,…
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…
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,…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…
Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…
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…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…