Related papers: Ising Model on Locally Tree-like Graphs: Uniquenes…
In the study of sparse stochastic block models (SBMs) one often needs to analyze a distributional recursion, known as the belief propagation (BP) recursion. Uniqueness of the fixed point of this recursion implies several results about the…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
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…
Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles.…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…
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 provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…
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 fixed-magnetization ferromagnetic Ising model on random $d$-regular graphs for $d\ge 3$ and inverse temperature below the tree reconstruction threshold. Our main result is that for each magnetization $\eta$, the free energy…
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…
We consider noisy binary channels on regular trees and introduce periodic enhancements consisting of locally self-correcting the signal in blocks without break of the symmetry of the model. We focus on the realistic class of within-descent…
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…
We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration…
We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…
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 study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables…
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Their fundamental result…
We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…
The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…