# Free Energy Evaluation Using Marginalized Annealed Importance Sampling

arXiv: https://arxiv.org/abs/2204.03784 · HTML: https://mlsanity.com/paper/2204.03784/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 8 Apr 2022.

## Builds on (most cited first, 2 of 2)

- [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)

## Built on by (most cited first, 5 of 5)

- [Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond](https://mlsanity.com/paper/2502.04575/) (2025)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [Improving Interpretability of Scores in Anomaly Detection Based on Gaussian-Bernoulli Restricted Boltzmann Machine](https://mlsanity.com/paper/2403.12672/) (2024)
- [Dataset-Free Weight-Initialization on Restricted Boltzmann Machine](https://mlsanity.com/paper/2409.07708/) (2024)
- [Nonlocal Transition Kernel for Efficient Learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2608.17450/) (2026)

## Abstract (arXiv)

The evaluation of the free energy of a stochastic model is considered a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because the free energy expression includes an intractable partition function. Annealed importance sampling (AIS) is a type of importance sampling based on the Markov chain Monte Carlo method that is similar to a simulated annealing and can effectively approximate the free energy. This study proposes an AIS-based approach, which is referred to as marginalized AIS (mAIS). The statistical efficiency of mAIS is investigated in detail based on theoretical and numerical perspectives. Based on the investigation, it is proved that mAIS is more effective than AIS under a certain condition.