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Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…

Statistics Theory · Mathematics 2023-02-02 Collin Cademartori , Cynthia Rush

Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…

Machine Learning · Computer Science 2020-01-22 Baoyuan Wu , Li Shen , Tong Zhang , Bernard Ghanem

The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that…

Statistical Mechanics · Physics 2015-06-11 Avik Halder , Ansuman Adhikary

Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…

Information Theory · Computer Science 2018-09-14 Amelia Perry , Alexander S. Wein , Afonso S. Bandeira , Ankur Moitra

Approximate message passing (AMP) algorithms are iterative methods for signal recovery in noisy linear systems. In some scenarios, AMP algorithms need to operate within a distributed network. To address this challenge, the distributed…

Signal Processing · Electrical Eng. & Systems 2024-07-26 Jun Lu , Lei Liu , Shunqi Huang , Ning Wei , Xiaoming Chen

We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total…

Machine Learning · Computer Science 2023-04-10 Donghao Ying , Yuhao Ding , Javad Lavaei

Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…

Statistics Theory · Mathematics 2017-08-16 Jelena Bradic

The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…

Data Structures and Algorithms · Computer Science 2022-08-25 Etienne Bamas , Marina Drygala , Ola Svensson

In this paper, we consider the maximum a posteriori (MAP) estimation for the multiple measurement vectors (MMV) problem with application to direction-of-arrival (DOA) estimation, which is classically formulated as a regularized…

Signal Processing · Electrical Eng. & Systems 2024-10-21 Tianyi Liu , Frederic Matter , Alexander Sorg , Marc E. Pfetsch , Martin Haardt , Marius Pesavento

We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…

Machine Learning · Statistics 2022-06-10 Ramji Venkataramanan , Kevin Kögler , Marco Mondelli

We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…

Statistics Theory · Mathematics 2025-09-09 Rishabh Dudeja , Songbin Liu , Junjie Ma

The paper proposes a numerically stable recursive algorithm for the exact computation of the linear-chain conditional random field gradient. It operates as a forward algorithm over the log-domain expectation semiring and has the purpose of…

Artificial Intelligence · Computer Science 2012-05-31 Velimir M. Ilic , Dejan I. Mancev , Branimir T. Todorovic , Miomir S. Stankovic

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…

Information Theory · Computer Science 2018-10-23 Ali Çivril

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…

Information Theory · Computer Science 2012-12-04 Ulugbek S. Kamilov , Sundeep Rangan , Alyson K. Fletcher , Michael Unser

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…

Physics and Society · Physics 2023-09-27 George T. Cantwell , Alec Kirkley , Filippo Radicchi

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

Artificial Intelligence · Computer Science 2012-06-18 Branislav Kveton , Milos Hauskrecht

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID)…

Information Theory · Computer Science 2021-06-07 Lei Liu , Shunqi Huang , Brian M. Kurkoski

This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design…

Information Theory · Computer Science 2021-01-05 Weifeng Zhu , Meixia Tao , Xiaojun Yuan , Yunfeng Guan

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs…

Computer Vision and Pattern Recognition · Computer Science 2018-10-29 Thomas Joy , Alban Desmaison , Thalaiyasingam Ajanthan , Rudy Bunel , Mathieu Salzmann , Pushmeet Kohli , Philip H. S. Torr , M. Pawan Kumar

We propose an efficient dual algorithm for ELP based on Fast Gradient Method. The basic idea - to solve properly regularized dual problem.

Optimization and Control · Mathematics 2016-02-05 Alexander Gasnikov , Evgenia Gasnikova , Yurii Nesterov , Alexey Chernov