Spatial Monte Carlo integration with annealed importance sampling
Spatial Monte Carlo integration with annealed importance sampling
复制标题
空间蒙特卡罗积分与退火重要性采样
DOI：
10.1103/physreve.103.052118
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发表时间：
2021
影响因子：
2.4
通讯作者：
Muneki Yasuda and Kaiji Sekimoto
中科院分区：
文献类型：
--
作者：
原田魁成;寒河江雅彦;Muneki Yasuda and Kaiji Sekimoto
评估对伊辛模型(或波尔兹曼机器)的预期对于包括统计机器学习在内的各种应用至关重要。然而，一般而言，求值在计算上是困难的，因为它涉及到难以处理的多重求和或积分；因此，它需要近似。蒙特卡罗积分(MCI)是一种著名的近似方法，最近提出了一种更有效的类MCI近似方法，称为空间蒙特卡罗积分(SMCI)。然而，在Ising模型中，由于抽样质量的降低，用SMCI(和MCI)得到的估计在低温下的精度很低。退火重要度抽样(AIS)是一种基于马尔可夫链蒙特卡罗方法的重要度抽样方法，它可以用重要度权重力来抑制低温区域的性能退化。在这项研究中，提出了一种结合AIS和SMCI的Ising模型的预期评估方法。理论和数值结果表明，该方法在高温区和低温区都能有效地进行数值模拟。
Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation is computationally difficult because it involves intractable multiple summations or integrations; therefore, it requires approximation. Monte Carlo integration (MCI) is a well-known approximation method; a more effective MCI-like approximation method was proposed recently, called spatial Monte Carlo integration (SMCI). However, the estimations obtained using SMCI (and MCI) exhibit a low accuracy in Ising models under a low temperature owing to degradation of the sampling quality. Annealed importance sampling (AIS) is a type of importance sampling based on Markov chain Monte Carlo methods that can suppress performance degradation in low-temperature regions with the force of importance weights. In this study, a method is proposed to evaluate the expectations on Ising models combining AIS and SMCI. The proposed method performs efficiently in both high- and low-temperature regions, which is demonstrated theoretically and numerically.