论文标题
空间蒙特卡洛与退火重要性取样
Spatial Monte Carlo Integration with Annealed Importance Sampling
论文作者
论文摘要
评估对ISING模型（或Boltzmann机器）的期望对于包括统计机器学习在内的各种应用程序至关重要。但是，通常，评估在计算上很难，因为它涉及棘手的多个总结或集成。因此，它需要近似。蒙特卡洛整合（MCI）是一种众所周知的近似方法。最近提出了一种更有效的MCI样近似方法，称为空间蒙特卡洛整合（SMCI）。但是，由于采样质量的降解，使用SMCI（和MCI）获得的估计在低温下显示出较低的精度。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，可以抑制具有重要性权重的低温区域的性能降解。在这项研究中，提出了一种新方法来评估对AIS和SMCI结合的ISING模型的期望。所提出的方法在高温和低温区域都有效地执行，这在理论上和数值上都得到了证明。
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 new 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.
