标题： 受限玻尔兹曼机中存在缺失观测的逆伊辛问题的有效方法 显示英文标题

标题： Effective Method for Inverse Ising Problem under Missing Observations in Restricted Boltzmann Machines

摘要： 受限玻尔兹曼机（RBMs）是类似于伊辛模型的能量模型，在统计机器学习中得到了广泛应用。 具有完整数据集的标准逆伊辛问题需要同时计算数据期望和模型期望，这在计算上极具挑战性，因为模型期望存在组合爆炸的问题。 此外，在许多应用中，可用的数据集部分是不完整的，使得即使计算数据期望也变得困难。 在本研究中，我们提出了一种针对实际逆伊辛问题中这些期望的近似框架，该框架结合了平均场近似或持久对比散度来生成精炼的初始点，并使用空间蒙特卡罗积分来提高估计器的准确性。 我们证明，与传统方法相比，所提出的方法能够更有效地且准确地调整模型参数。 显示英文摘要

摘要： 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.