# Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weights

arXiv: https://arxiv.org/abs/2605.10654 · HTML: https://mlsanity.com/paper/2605.10654/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 18 of 18)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Scalable Thompson Sampling using Sparse Gaussian Process Models](https://mlsanity.com/paper/2006.05356/) (2020)
- [Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2506.16471/) (2025)
- [Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers](https://mlsanity.com/paper/2106.11719/) (2021)
- [Transductive Active Learning: Theory and Applications](https://mlsanity.com/paper/2402.15898/) (2024)
- [Incorporating Unlabeled Data into Distributionally Robust Learning](https://mlsanity.com/paper/1912.07729/) (2019)
- [Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials](https://mlsanity.com/paper/2210.04225/) (2022)
- [Tanimoto Random Features for Scalable Molecular Machine Learning](https://mlsanity.com/paper/2306.14809/) (2023)
- [BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching](https://mlsanity.com/paper/2409.09787/) (2024)
- [Distributionally Robust Active Learning for Gaussian Process Regression](https://mlsanity.com/paper/2502.16870/) (2025)
- [Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization](https://mlsanity.com/paper/2401.05716/) (2024)

## Abstract (arXiv)

We consider the active learning problem where the goal is to learn an unknown function with low prediction error under an unknown Boltzmann distribution induced by the function itself. This self-induced weighting arises naturally in problems such as potential energy surface (PES) modeling in computational chemistry, yet poses unique challenges as the target distribution is unknown and its partition function is intractable. We propose textttAB-SID-iVAR, a Gaussian Process-based acquisition function that approximates the intractable Bayesian target distribution in closed form while avoiding partition function estimation, and is applicable to both discrete and continuous input domains. We also analyze a Thompson sampling alternative (textttTS-SID-iVAR) as a higher variance Monte Carlo variant. Despite the unknown target, under mild conditions, we establish that the terminal prediction error vanishes with high probability, and provide a tighter average-case guarantee. We demonstrate consistent improvements over existing approaches in this setting on synthetic benchmarks and real-world PES modeling and drug discovery tasks.