Free Energy Evaluation Using Marginalized Annealed Importance Sampling

TL;DR

This paper introduces marginalized annealed importance sampling (mAIS), a novel method for more efficiently estimating free energy in stochastic models, outperforming traditional AIS under certain conditions.

Contribution

The paper proposes and analyzes marginalized AIS (mAIS), demonstrating its improved efficiency over AIS through theoretical and numerical evaluations.

Findings

mAIS is more effective than AIS under specific conditions

Theoretical analysis confirms increased efficiency of mAIS

Numerical experiments support the superiority of mAIS

Abstract

The evaluation of the free energy of a stochastic model is considered a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because the free energy expression includes an intractable partition function. Annealed importance sampling (AIS) is a type of importance sampling based on the Markov chain Monte Carlo method that is similar to a simulated annealing and can effectively approximate the free energy. This study proposes an AIS-based approach, which is referred to as marginalized AIS (mAIS). The statistical efficiency of mAIS is investigated in detail based on theoretical and numerical perspectives. Based on the investigation, it is proved that mAIS is more effective than AIS under a certain condition.