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.

中文翻译：

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失配作为增强蒙特卡罗方法算法性能的工具，用于种植集团模型

过度参数化是推理和机器学习领域近期发展的关键因素。然而，仍然缺乏一个很好的理论来解释这种成功。在本文中，我们研究了一个非常简单的不匹配超参数化算法案例，该算法应用于研究最多的推理问题之一：种植集团问题。我们分析了与著名的 Jerrum 算法属于同一类的蒙特卡洛 (MC) 算法。我们展示了这种 MC 算法对于种植集团的恢复通常是如何次优的。然而，我们展示了如何通过添加（不匹配的）参数来增强其性能：温度；我们在数值上发现该算法的这种过度参数化版本可以达到种植集团问题的假定算法阈值。