Spatial Monte Carlo integration with annealed importance sampling

Evaluating expectations on an Ising model (or Boltzmann machine) is essential for various applications, including statistical machine learning. However, in general, the evaluation computationally difficult because it involves intractable multiple summations or integrations; therefore, requires approximation. Monte Carlo integration (MCI) a well-known approximation method; more effective MCI-like method was proposed recently, called spatial (SMCI). estimations obtained using SMCI (and MCI) exhibit low accuracy models under temperature owing to degradation of sampling quality. Annealed importance (AIS) type based Markov chain methods that can suppress performance low-temperature regions with force weights. In this study, new evaluate combining AIS and SMCI. The performs efficiently both high- regions, which demonstrated theoretically numerically.