Related papers: Exactness of Belief Propagation for Some Graphical…
Sudderth, Wainwright, and Willsky have conjectured that the Bethe approximation corresponding to any fixed point of the belief propagation algorithm over an attractive, pairwise binary graphical model provides a lower bound on the true…
The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
We investigate the question of tightness of linear programming (LP) relaxation for finding a maximum weight independent set (MWIS) in sparse random weighted graphs. We show that an edge-based LP relaxation is asymptotically tight for…
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…
The Bradley-Terry-Luce (BTL) model is a popular statistical approach for estimating the global ranking of a collection of items using pairwise comparisons. To ensure accurate ranking, it is essential to obtain precise estimates of the model…
Predicting with missing inputs challenges even parametric models, as parameter estimation alone is insufficient for prediction on incomplete data. While several works study prediction in linear models, we focus on logistic models, where…
Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and…
Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. Our…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal…
We study the theoretical limits of the $\ell_0$ (quasi) norm based optimization algorithms when employed for solving classical compressed sensing or sparse regression problems. Considering standard contexts with deterministic signals and…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…
This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled…
In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE…