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We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…

This work describes probabilistic methods for utilizing random spanning trees generated via a random walk process. Goyal et al. showed that the union of random spanning trees approximates the expansion of every cut of a graph. First, we…

This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random…

Fast distributed algorithms that output a feasible solution for constraint satisfaction problems, such as maximal independent sets, have been heavily studied. There has been much less research on distributed sampling problems, where one…

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…

In multivariate data analysis, it is often important to estimate a graph characterizing dependence among (p) variables. A popular strategy uses the non-zero entries in a (p\times p) covariance or precision matrix, typically requiring…

Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants…

Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems…

Bayesian approaches provide a principled solution to the exploration-exploitation trade-off in Reinforcement Learning. Typical approaches, however, either assume a fully observable environment or scale poorly. This work introduces the…

This technical note presents a new approach to carrying out the kind of exploration achieved by Thompson sampling, but without explicitly maintaining or sampling from posterior distributions. The approach is based on a bootstrap technique…

In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs…

We consider a class of pursuit-evasion problems where an evader enters a directed acyclic graph and attempts to reach one of the terminal nodes. A pursuer enters the graph at a later time and attempts to capture the evader before it reaches…

We present a novel extension of Thompson Sampling for stochastic sequential decision problems with graph feedback, even when the graph structure itself is unknown and/or changing. We provide theoretical guarantees on the Bayesian regret of…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

We consider the problem of estimating the expected time to find a maximum degree node on a graph using a (parameterized) biased random walk. For assortative graphs the positive degree correlation serves as a local gradient for which a bias…

We propose MDP-GapE, a new trajectory-based Monte-Carlo Tree Search algorithm for planning in a Markov Decision Process in which transitions have a finite support. We prove an upper bound on the number of calls to the generative models…

We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…

We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of…

The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…