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Related papers: Regression for matrix-valued data via Kronecker pr…

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We introduce \underline{F}actor-\underline{A}ugmented \underline{Ma}trix \underline{R}egression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and…

Methodology · Statistics 2024-05-29 Elynn Chen , Jianqing Fan , Xiaonan Zhu

In this technical report, we consider an approach that combines the PPO objective and K-FAC natural gradient optimization, for which we call PPOKFAC. We perform a range of empirical analysis on various aspects of the algorithm, such as…

Artificial Intelligence · Computer Science 2018-01-18 Jiaming Song , Yuhuai Wu

Reducing the test time resource requirements of a neural network while preserving test accuracy is crucial for running inference on resource-constrained devices. To achieve this goal, we introduce a novel network reparameterization based on…

Machine Learning · Computer Science 2019-05-16 Chaoqi Wang , Roger Grosse , Sanja Fidler , Guodong Zhang

We consider the numerical approximation of $f({\cal A})b$ where $b\in{\mathbb R}^{N}$ and $\cal A$ is the sum of Kronecker products, that is ${\cal A}=M_2 \otimes I + I \otimes M_1\in{\mathbb R}^{N\times N}$. Here $f$ is a regular function…

Numerical Analysis · Mathematics 2015-03-10 Michele Benzi , Valeria Simoncini

Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…

Disordered Systems and Neural Networks · Physics 2025-03-17 Jean Barbier , Francesco Camilli , Justin Ko , Koki Okajima

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

Econometrics · Economics 2025-08-25 Degui Li , Yayi Yan , Qiwei Yao

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…

Applications · Statistics 2011-12-01 Nicholas Arcolano , Patrick J. Wolfe

This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…

Signal Processing · Electrical Eng. & Systems 2024-12-03 Yanbin He , Geethu Joseph

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate…

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

Machine Learning · Statistics 2015-05-14 Xinyang Yi , Zhaoran Wang , Constantine Caramanis , Han Liu

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Machine Learning · Computer Science 2019-05-31 Liu Liu , Yanyao Shen , Tianyang Li , Constantine Caramanis

We propose a new framework for modeling high-dimensional matrix-variate time series by a two-way transformation, where the transformed data consist of a matrix-variate factor process, which is dynamically dependent, and three other blocks…

Econometrics · Economics 2021-08-19 Zhaoxing Gao , Ruey S. Tsay

The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…

Numerical Analysis · Mathematics 2018-01-17 John Harlim , Haizhao Yang

This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex, elliptically symmetric (CES) distributions…

Signal Processing · Electrical Eng. & Systems 2022-02-08 Lei Xie , Zishu He , Jun Tong , Tianle Liu , Jun Li , Jiangtao Xi

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…

Statistics Theory · Mathematics 2017-08-28 Thibault Lesieur , Florent Krzakala , Lenka Zdeborová

We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality, we impose an additional assumption on the structure of the covariance matrix $\Sigma$. To be more…

Statistics Theory · Mathematics 2026-02-11 Artsiom Patarusau , Nikita Puchkin , Maxim Rakhuba , Fedor Noskov

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

Machine Learning · Statistics 2016-03-02 Milad Kharratzadeh , Mark Coates

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product…

Machine Learning · Statistics 2016-10-31 Aaron J. Molstad , Adam J. Rothman