Related papers: Convergence Analysis of the Random Bisection Metho…
The planted bisection model is a random graph model in which the nodes are divided into two equal-sized communities and then edges are added randomly in a way that depends on the community membership. We establish necessary and sufficient…
The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
In the planted bisection model a random graph $G(n,p_+,p_- )$ with $n$ vertices is created by partitioning the vertices randomly into two classes of equal size (up to $\pm1$). Any two vertices that belong to the same class are linked by an…
In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients $\{\binom{n}{k} \}_{k=0,...,n}$ and include a table with the results for all $n\le 154$. Connections with previous work on…
Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…
In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the…
We present a novel distributed probabilistic bisection algorithm using social learning with application to target localization. Each agent in the network first constructs a query about the target based on its local information and obtains a…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
If a line cuts randomly two sides of a triangle, the length of the segment determined by the points of intersection is also random. The object of this study, applied to a particular case, is to calculate the probability that the length of…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
We present an approximate sampling framework and discuss how risk-limiting audits can compensate for these approximations, while maintaining their "risk-limiting" properties. Our framework is general and can compensate for counting mistakes…
In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple…
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.
The aim of this paper is the study of the bisection method in $\mathbb{R}^n$. In this work we propose a multivariate bisection method supported by the Poincar\'e-Miranda theorem in order to solve non-linear system of equations. Given an…
We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called…
We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in…