Mismatching as a tool to enhance algorithmic performances of Monte Carlo methods for the planted clique model

TL;DR

This paper investigates how introducing a mismatched parameter, temperature, into a Monte Carlo algorithm can improve its performance in solving the planted clique problem, reaching the theoretical algorithmic threshold.

Contribution

It demonstrates that over-parametrization via a mismatched parameter can enhance Monte Carlo algorithms for inference problems like the planted clique.

Findings

Adding temperature improves algorithm performance

Over-parametrized algorithm reaches the planted clique threshold

Mismatched parameters can optimize inference algorithms

Abstract

Over-parametrization was a crucial ingredient for recent developments in inference and machine-learning fields. However a good theory explaining this success is still lacking. In this paper we study a very simple case of mismatched over-parametrized algorithm applied to one of the most studied inference problem: the planted clique problem. We analyze a Monte Carlo (MC) algorithm in the same class of the famous Jerrum algorithm. We show how this MC algorithm is in general suboptimal for the recovery of the planted clique. We show however how to enhance its performances by adding a (mismatched) parameter: the temperature; we numerically find that this over-parametrized version of the algorithm can reach the supposed algorithmic threshold for the planted clique problem.