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The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic…

Information Theory · Computer Science 2015-08-27 Andrei Giurgiu , Nicolas Macris , Rüdiger Urbanke

We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…

Statistics Theory · Mathematics 2025-11-10 Curtis Grant , Aukosh Jagannath , Justin Ko

This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…

Information Theory · Computer Science 2015-11-06 Jean Barbier

We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work [1]. We use heuristic statistical-physics-based tools such as the cavity and the…

Information Theory · Computer Science 2017-07-17 Jean Barbier , Florent Krzakala

In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…

Machine Learning · Statistics 2023-11-07 Hao Zhang

In spite of considerable practical importance, current algorithmic fairness literature lacks technical methods to account for underlying geographic dependency while evaluating or mitigating bias issues for spatial data. We initiate the…

Applications · Statistics 2022-01-31 Subhabrata Majumdar , Cheryl Flynn , Ritwik Mitra

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…

Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a "threshold saturation"…

Information Theory · Computer Science 2010-10-29 Shrinivas Kudekar , Henry D. Pfister

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Information Theory · Computer Science 2026-05-12 Frédéric Zheng , Yassir Jedra , Alexandre Proutiere

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Machine Learning · Statistics 2010-09-07 Mehryar Mohri , Ameet Talwalkar

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…

Computation · Statistics 2023-07-19 Yoann Altmann , Marcelo Pereyra , Jose Bioucas-Dias

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

Numerical Analysis · Mathematics 2014-08-12 Ming Gu

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

Machine Learning · Computer Science 2013-01-16 Joonseok Lee , Seungyeon Kim , Guy Lebanon , Yoram Singer

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…

Machine Learning · Statistics 2018-05-25 Ricardo Pio Monti , Aapo Hyvärinen

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing…

Statistical Mechanics · Physics 2013-09-03 Fabrizio Altarelli , Alfredo Braunstein , Abolfazl Ramezanpour , Riccardo Zecchina

Robotic affordance estimation is challenging due to visual, geometric, and semantic ambiguities in sensory input. We propose a method that disambiguates these signals using two coupled recursive estimators for sub-aspects of affordances:…

Robotics · Computer Science 2026-03-17 Patrick Lowin , Vito Mengers , Oliver Brock

We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…

Statistics Theory · Mathematics 2026-01-29 Zhangsong Li

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Machine Learning · Statistics 2020-03-03 Bradley S. Price , Aaron J. Molstad , Ben Sherwood

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

Machine Learning · Statistics 2024-03-04 Xumei Xi , Christina Lee Yu , Yudong Chen

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…

Statistics Theory · Mathematics 2016-04-20 Ilya Soloveychik , Ami Wiesel