Related papers: Large Degree Asymptotics and the Reconstruction Th…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$ descendants. The…
The information reconstruction problem on an infinite tree, is to collect and analyze massive data samples at the $n$th level of the tree to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. This…
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…
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…
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…
Motivated by the theory of spin-glasses in physics, we study the so-called reconstruction problem for the related distributions on the tree, and on the sparse random graph $G(n,d/n)$. Both cases, reduce naturally to studying broadcasting…
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…
We study the low-degree hardness of broadcasting on trees. Broadcasting on trees has been extensively studied in statistical physics, in computational biology in relation to phylogenetic reconstruction and in statistics and computer science…
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 broadcasting models on trees arise in many contexts such as discrete mathematics, biology statistical physics and cs. In this work, we consider the colouring model. A basic question here is whether the root's assignment affects the…
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…
We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The root of the tree takes a random value 0…
The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…
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…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
In this paper we study the nonasymptotic bounds of a special Joint Source-Channel Coding system with hierarchical source, where an observable source and an unobservable indirect source are required to be reconstructed. Namely, we focus on…
The tree reconstruction problem is to collect and analyze massive data at the $n$th level of the tree, to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. Its connection to the clustering problem in…
We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…
We study the weak recovery problem on the $r$-uniform hypergraph stochastic block model ($r$-HSBM) with two balanced communities. In this model, $n$ vertices are randomly divided into two communities, and size-$r$ hyperedges are added…