Free Energy Evaluation Using Marginalized Annealed Importance Sampling
Free Energy Evaluation Using Marginalized Annealed Importance Sampling
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DOI：
10.1103/physreve.106.024127
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发表时间：
2022-04
期刊：
影响因子：
--
通讯作者：
Muneki Yasuda;Chako Takahashi
中科院分区：
文献类型：
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作者：
Muneki Yasuda;Chako Takahashi
随机模型自由能的评估被认为是物理和机器学习各个领域的一个重要问题。然而，精确的自由能评估在计算上是不可行的，因为自由能表达式包括难以处理的配分函数。退火重要性采样（AIS）是一种基于马尔可夫链蒙特卡罗方法的重要性采样，类似于模拟退火，可以有效地逼近自由能。本研究提出了一种基于 AIS 的方法，称为边缘化 AIS (mAIS)。基于理论和数值的角度详细研究了 mAIS 的统计效率。经调查证明，在一定条件下mAIS比AIS更有效。
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.