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

arXiv: https://arxiv.org/abs/2504.05643 · HTML: https://mlsanity.com/paper/2504.05643/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 24 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Restricted Boltzmann Machine, recent advances and mean-field theory](https://mlsanity.com/paper/2011.11307/) (2020)
- [A Generalization of Spatial Monte Carlo Integration](https://mlsanity.com/paper/2009.02165/) (2020)
- [Robust Multi-Output Learning with Highly Incomplete Data via Restricted Boltzmann Machines](https://mlsanity.com/paper/1912.09382/) (2019)

## Abstract (arXiv)

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.