Free Energy Evaluation Using Marginalized Annealed Importance Sampling
This work addresses a computational bottleneck in physics and machine learning for researchers and practitioners, but it appears incremental as it builds on existing AIS methods.
The paper tackles the problem of evaluating free energy in stochastic models, which is computationally challenging due to intractable partition functions, by proposing marginalized Annealed Importance Sampling (mAIS) and showing it is more effective than standard AIS under certain conditions.
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.