针对缺失数据的RBM逆伊辛问题，提出高效参数优化方法。
Effective Method for Inverse Ising Problem under Missing Observations in Restricted Boltzmann Machines
- 结合均场近似与持续对比散度生成初始点，降低计算复杂度。
- 采用空间蒙特卡洛积分提升期望估计精度，参数调优更准确。
- 适合处理不完整数据下的能量模型参数学习，适用于机器学习建模场景。
受限玻尔兹曼机（RBMs）是类伊辛的能量模型，在统计机器学习中广泛应用。标准逆伊辛问题需计算数据与模型期望，但模型期望存在组合爆炸，计算困难。此外，实际应用中数据常部分缺失，导致数据期望也难以计算。本文提出一种近似框架，将均场近似或持续对比散度用于生成精炼初始点，结合空间蒙特卡洛积分提升估计器精度。实验表明，该方法在参数调优上比传统方法更有效且准确。
原文摘要 · Abstract (English)
Restricted Boltzmann machines (RBMs) are energy-based models analogous to the Ising model and are widely applied in statistical machine learning. The standard inverse Ising problem with a complete dataset requires computing both data and model expectations and is computationally challenging because model expectations have a combinatorial explosion. Furthermore, in many applications, the available datasets are partially incomplete, making it difficult to compute even data expectations. In this study, we propose a approximation framework for these expectations in the practical inverse Ising problems that integrates mean-field approximation or persistent contrastive divergence to generate refined initial points and spatial Monte Carlo integration to enhance estimator accuracy. We demonstrate that the proposed method effectively and accurately tunes the model parameters in comparison to the conventional method.
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