A Bayesian Approach To Graph Partitioning

TL;DR

This paper introduces a Bayesian inference-based algorithm utilizing Gaussian Processes and MCMC techniques to efficiently learn and analyze local conductance in weighted graphs, enhancing scalability and convergence speed.

Contribution

It presents a novel scalable algorithm combining Gaussian Processes and advanced MCMC methods for graph conductance learning, improving convergence and uncertainty estimation.

Findings

Effective learning of graph conductance behavior

Scalable and fast convergence to stationary distribution

Uncertainty quantification of hyper-parameters

Abstract

A new algorithm based on bayesian inference for learning local graph conductance based on Gaussian Process(GP) is given that uses advanced MCMC convergence ideas to create a scalable and fast algorithm for convergence to stationary distribution which is provided to learn the bahavior of conductance when traversing the indirected weighted graph. First metric embedding is used to represent the vertices of the graph. Then, uniform induced conductance is calculated for training points. Finally, in the learning step, a gaussian process is used to approximate the uniform induced conductance. MCMC is used to measure uncertainty of estimated hyper-parameters.