Related papers: Self-Correction of Transmission on Regular Trees
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…
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…
In this paper, we consider a broadcasting process in which information is propagated from a given root node on a noisy tree network, and answer the question that whether the symbols at the nth level of the tree contain non-vanishing…
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…
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…
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between…
Despite significant progress in text-to-image diffusion models, achieving precise spatial control over generated outputs remains challenging. ControlNet addresses this by introducing an auxiliary conditioning module, while ControlNet++…
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…
We investigate the inner vertex-isoperimetric problem on the $d$-regular tree $T_d$. We first determine the exact value of the inner vertex-isoperimetric profile $I_d(k) = \min\{ |\partial D| \mid D\subset T_d \text{ finite and connected},\…
Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
Recently deep neural networks have been successfully used for various classification tasks, especially for problems with massive perfectly labeled training data. However, it is often costly to have large-scale credible labels in real-world…
We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…
Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on…
A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix…
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…
Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
Strong Disorder Renormalization for the Random Transverse Field Ising model leads to a complicated topology of surviving clusters as soon as $d>1$. Even if one starts from a Cayley tree, the network of surviving renormalized clusters will…