Related papers: Broadcasting with Random Matrices
We introduce a spectral approach to characterizing the three-dimensional Edwards-Anderson spin glass. By analyzing the eigenvalue statistics of overlap matrices constructed from two-dimensional cross-sections, we identify a crossover from…
We study a class of random matrices that appear in several communication and signal processing applications, and whose asymptotic eigenvalue distribution is closely related to the reconstruction error of an irregularly sampled bandlimited…
Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample…
The directed L-distance minimal dominating set (MDS) problem has wide practical applications in the fields of computer science and communication networks. Here, we study this problem from the perspective of purely theoretical interest. We…
Strongly Rayleigh distributions are a class of negatively dependent distributions of binary-valued random variables [Borcea, Branden, Liggett JAMS 09]. Recently, these distributions have played a crucial role in the analysis of algorithms…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on…
We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Markov random fields are common prior distributions used in Bayesian inverse imaging problems. In particular, difference priors assign probability distributions to differences between neighbouring pixels, such as Gaussian, Laplace, or…
The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its…
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…
We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
Due to inappropriate sample selection and limited training data, a distribution shift often exists between the training and test sets. This shift can adversely affect the test performance of Graph Neural Networks (GNNs). Existing approaches…
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$…
In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth $r$ (up to isomorphism) for some $r\geq 1$ and we wish to recover the underlying graph up to isomorphism. When the underlying…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…