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Related papers: Tensor Recovery in High-Dimensional Ising Models

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In multivariate regression, a $K$-dimensional response vector is regressed upon a common set of $p$ covariates, with a matrix $B^*\in\mathbb{R}^{p\times K}$ of regression coefficients. We study the behavior of the multivariate group Lasso,…

Machine Learning · Statistics 2011-03-08 Guillaume Obozinski , Martin J. Wainwright , Michael I. Jordan

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…

Statistical Mechanics · Physics 2021-01-26 Satoshi Morita , Naoki Kawashima

We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…

Statistics Theory · Mathematics 2019-09-24 David Gamarnik , Ilias Zadik

This paper proposes a new methodology to predict and update the residual useful lifetime of a system using a sequence of degradation images. The methodology integrates tensor linear algebra with traditional location-scale regression widely…

Applications · Statistics 2017-06-13 Xiaolei Fang , Kamran Paynabar , Nagi Gebraeel

Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…

Statistical Mechanics · Physics 2025-10-14 Xia-Ze Xu , Tong-Yu Lin , Guang-Ming Zhang

Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…

Machine Learning · Computer Science 2022-09-13 Arya Mazumdar , Soumyabrata Pal

Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…

Optimization and Control · Mathematics 2016-12-30 Mateo Díaz , Mauricio Junca , Felipe Rincón , Mauricio Velasco

We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed…

Machine Learning · Computer Science 2022-06-13 Chuyang Ke , Jean Honorio

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…

Computer Vision and Pattern Recognition · Computer Science 2017-07-04 Fujiao Ju , Yanfeng Sun , Junbin Gao , Yongli Hu , Baocai Yin

We propose a scalable and noise-resilient protocol for the detection of the entanglement transition in a projective version of the transverse field Ising model. Entanglement transitions are experimentally difficult to observe due to the…

Quantum Physics · Physics 2025-11-24 Felix Roser , Etienne M. Springer , Hans Peter Büchler , Nicolai Lang

Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…

Information Theory · Computer Science 2015-05-14 Robert Calderbank , Stephen Howard , Sina Jafarpour

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal…

Numerical Analysis · Computer Science 2017-06-27 Yaru Fan , Yilun Wang , Tingzhu Huang

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…

Information Theory · Computer Science 2013-02-06 Galen Reeves , Michael Gastpar

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and…

Methodology · Statistics 2026-02-10 Ruihan Liu , Zhenggang Wang , Jianfeng Yao

Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…

Numerical Analysis · Mathematics 2019-09-24 Mike Espig , Wolfgang Hackbusch , Alexander Litvinenko , Hermann G. Matthies , Elmar Zander

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…

Methodology · Statistics 2024-07-19 Yuefeng Han , Rong Chen , Dan Yang , Cun-Hui Zhang

We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured…

Computational Engineering, Finance, and Science · Computer Science 2026-02-10 Rémi Cloarec , Sebastian Rodriguez , Xavier Kestelyn , Francisco Chinesta

The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…

Optimization and Control · Mathematics 2014-04-09 Min Zhang , Lei Yang , Zheng-Hai Huang

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

Information Theory · Computer Science 2009-10-18 Robert Calderbank , Stephen Howard , Sina Jafarpour

Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…

Machine Learning · Statistics 2018-05-30 Takashi Sano