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Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard,…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
It is known that the Kesten-Stigum reconstruction bound is tight for roughly symmetric binary channels. In this paper, we will adopt a refined analysis of moment recursion on a weighted version of the magnetization, which is engaged in Sly…
A sparse stochastic block model (SBM) with two communities is defined by the community probability $\pi_0,\pi_1$, and the connection probability between communities $a,b\in\{0,1\}$, namely $q_{ab} = \frac{\alpha_{ab}}{n}$. When $q_{ab}$ is…
Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD does not admit a unique solution. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and…
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a $q$-state Potts model coupled to an $r$-state Potts model in two dimensions. For integer values of $q$ and $r$ the fixed point…
Broadcasting on trees is a fundamental model from statistical physics that plays an important role in information theory, noisy computation and phylogenetic reconstruction within computational biology and linguistics. While this model…
We study the problem of exact community recovery in the Geometric Stochastic Block Model (GSBM), where each vertex has an unknown community label as well as a known position, generated according to a Poisson point process in $\mathbb{R}^d$.…
We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…
We give a criterion of the form Q(d)c(M)<1 for the non-reconstructability of tree-indexed q-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix M. Here c(M) is an explicit function, which is…
Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for…
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP)…
The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study…
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities $a/n$ and $b/n$ for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better…
Exact recovery in stochastic block models (SBMs) is well understood in undirected settings, but remains considerably less developed for directed and sparse networks, particularly when the number of communities diverges. Spectral methods for…
We introduce the Poisson Binomial mechanism (PBM), a discrete differential privacy mechanism for distributed mean estimation (DME) with applications to federated learning and analytics. We provide a tight analysis of its privacy guarantees,…
The framework of statistical inference has been successfully used to detect the meso-scale structures in complex networks, such as community structure, core-periphery (CP) structure. The main principle is that the stochastic block model…
For the model of communication through a discrete memoryless channel using i.i.d. random block codes, where the channel is changing slowly from block to block, we propose a stochastic algorithm for adaptation of the generating distribution…
The stochastic block model is a natural model for studying community detection in random networks. Its clustering properties have been extensively studied in the statistics, physics and computer science literature. Recently this area has…
Belief propagation is known to perform extremely well in many practical statistical inference and learning problems using graphical models, even in the presence of multiple loops. The iterative use of belief propagation algorithm on loopy…