论文标题
使用边缘化退火重要性抽样的自由能评估
Free Energy Evaluation Using Marginalized Annealed Importance Sampling
论文作者
论文摘要
在物理学和机器学习的各个领域，对随机模型的自由能的评估被认为是一个重要问题。但是，确切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棘手的分区函数。退火重要性采样（AIS）是基于马尔可夫链蒙特卡洛方法的一种重要性采样，类似于模拟退火，并且可以有效地近似自由能。这项研究提出了一种基于AIS的方法，该方法称为边缘化的AI（MAI）。 MAI的统计效率根据理论和数值观点进行了详细研究。根据调查，证明MAI在某种条件下比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.
