Spatial Monte Carlo integration with annealed importance sampling
| Autor: | Kaiji Sekimoto, Muneki Yasuda |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Computer science Boltzmann machine FOS: Physical sciences Machine Learning (stat.ML) 01 natural sciences Machine Learning (cs.LG) 010305 fluids & plasmas symbols.namesake Quality (physics) Statistics - Machine Learning 0103 physical sciences Statistical physics 010306 general physics Sampling (statistics) Probability and statistics Markov chain Monte Carlo Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Physics - Data Analysis Statistics and Probability symbols Ising model Monte Carlo integration Data Analysis Statistics and Probability (physics.data-an) Importance sampling |
| Zdroj: | Physical review. E. 103(5-1) |
| ISSN: | 2470-0053 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|