Effective Method for Inverse Ising Problem under Missing Observations in Restricted Boltzmann Machines
This work addresses a computational bottleneck for researchers and practitioners using RBMs in statistical machine learning, though it appears incremental as it builds on existing approximations.
The authors tackled the inverse Ising problem in Restricted Boltzmann Machines with missing data by proposing an approximation framework that combines mean-field approximation or persistent contrastive divergence with spatial Monte Carlo integration, resulting in effective and accurate parameter tuning compared to conventional methods.
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.