Related papers: Uniqueness of BP fixed point for the Potts model a…
In the study of Ising models on large locally tree-like graphs, in both rigorous and non-rigorous methods one is often led to understanding the so-called belief propagation distributional recursions and its fixed points. We prove that there…
Many inference problems, notably the stochastic block model (SBM) that generates a random graph with a hidden community structure, undergo phase transitions as a function of the signal-to-noise ratio, and can exhibit hard phases in which…
The limit of the entropy in the stochastic block model (SBM) has been characterized in the sparse regime for the special case of disassortative communities [COKPZ17] and for the classical case of assortative communities but in the dense…
Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…
We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions…
Consider a tree network $T$, where each edge acts as an independent copy of a given channel $M$, and information is propagated from the root. For which $T$ and $M$ does the configuration obtained at level $n$ of $T$ typically contain…
The paper concerns the $q$-state Potts model (i.e., with spin values in $\{1,\dots,q\}$) on a Cayley tree $\mathbb{T}^k$ of degree $k\geq 2$ (i.e., with $k+1$ edges emanating from each vertex) in an external (possibly random) field. We…
Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and…
Belief propagation (BP) is a popular method for performing probabilistic inference on graphical models. In this work, we enhance BP and propose self-guided belief propagation (SBP) that incorporates the pairwise potentials only gradually.…
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…
We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair…
Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block model with $q$ groups, average degree $d$, and connection…
We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this…
New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide…
The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity…
The reconstruction problem on the tree has been studied in numerous contexts including statistical physics, information theory and computational biology. However, rigorous reconstruction thresholds have only been established in a small…
We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…