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Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

Machine Learning · Statistics 2020-12-15 Chanwoo Lee , Miaoyan Wang

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Information Theory · Computer Science 2016-11-17 Jin Tan , Danielle Carmon , Dror Baron

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Numerical Analysis · Computer Science 2017-04-13 Nematollah Zarmehi , Farokh Marvasti

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…

Numerical Analysis · Computer Science 2018-04-24 Cuiping Li , Xiao-Yang Liu , Yue Sun

We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…

Data Structures and Algorithms · Computer Science 2017-10-04 Samuel B. Hopkins , David Steurer

The theory of low-rank tensor-train approximation is well understood when the approximation error is measured in the Frobenius norm. The entrywise maximum norm is equally important but is significantly weaker for large tensors, making the…

Numerical Analysis · Mathematics 2025-04-09 Stanislav Budzinskiy

Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…

Numerical Analysis · Mathematics 2021-09-23 Mark A. Iwen , Deanna Needell , Michael Perlmutter , Elizaveta Rebrova

Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…

Machine Learning · Computer Science 2023-04-28 L. Mars Gao , Urban Fasel , Steven L. Brunton , J. Nathan Kutz

Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…

Statistics Theory · Mathematics 2022-03-25 Bertrand Michel , Anthony Nouy

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Machine Learning · Computer Science 2025-11-03 Hiroki Hasegawa , Yukihiko Okada

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…

Signal Processing · Electrical Eng. & Systems 2018-08-01 Mario Coutino , Sundeep Prabhakar Chepuri , Geert Leus

We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…

Information Theory · Computer Science 2017-05-22 Robert F. H. Fischer , Susanne Sparrer

We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…

Information Theory · Computer Science 2015-06-02 Vipul Gupta , Bhavya Kailkhura , Thakshila Wimalajeewa , Pramod K. Varshney

In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly…

Statistics Theory · Mathematics 2024-10-10 Joshua Agterberg , Anru Zhang

Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…

Optimization and Control · Mathematics 2018-12-12 Wen Huang , Paul Hand , Reinhard Heckel , Vladislav Voroninski

We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are…

Information Theory · Computer Science 2022-06-23 Chongwen Huang , Lei Liu , Chau Yuen , Sumei Sun

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

Machine Learning · Statistics 2026-04-15 Angelo Giorgio Cavaliere , Riki Nagasawa , Shuta Yokoi , Tomoyuki Obuchi , Hajime Yoshino

In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…

Information Theory · Computer Science 2014-12-18 V. Meena , G. Abhilash

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…

Methodology · Statistics 2022-04-15 Jian-Feng Cai , Jingyang Li , Dong Xia