# Asymptotically Optimal Change Detection for Unnormalized Pre- and Post-Change Distributions

arXiv: https://arxiv.org/abs/2410.14615 · HTML: https://mlsanity.com/paper/2410.14615/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds](https://mlsanity.com/paper/1911.03043/) (2019)
- [Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation](https://mlsanity.com/paper/2303.03237/) (2023)
- [Sampling from Arbitrary Functions via PSD Models](https://mlsanity.com/paper/2110.10527/) (2021)
- [Sum-of-Squares Relaxations for Information Theory and Variational Inference](https://mlsanity.com/paper/2206.13285/) (2022)
- [Quickest Change Detection for Unnormalized Statistical Models](https://mlsanity.com/paper/2302.00250/) (2023)
- [Sequential Multivariate Change Detection with Calibrated and Memoryless False Detection Rates](https://mlsanity.com/paper/2108.00883/) (2021)
- [A Faster Approximation Algorithm for the Gibbs Partition Function](https://mlsanity.com/paper/1608.04223/) (2016)
- [Fast Doubly-Adaptive MCMC to Estimate the Gibbs Partition Function with Weak Mixing Time Bounds](https://mlsanity.com/paper/2111.07372/) (2021)

## Abstract (arXiv)

This paper addresses the problem of detecting changes when only unnormalized pre- and post-change distributions are accessible. This situation happens in many scenarios in physics such as in ferromagnetism, crystallography, magneto-hydrodynamics, and thermodynamics, where the energy models are difficult to normalize. Our approach is based on the estimation of the Cumulative Sum (CUSUM) statistics, which is known to produce optimal performance. We first present an intuitively appealing approximation method. Unfortunately, this produces a biased estimator of the CUSUM statistics and may cause performance degradation. We then propose the Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration (TI) in order to estimate the log-ratio of normalizing constants of pre- and post-change distributions. It is proved that this approach gives an unbiased estimate of the log-partition function and the CUSUM statistics, and leads to an asymptotically optimal performance. Moreover, we derive a relationship between the required sample size for thermodynamic integration and the desired detection delay performance, offering guidelines for practical parameter selection. Numerical studies are provided demonstrating the efficacy of our approach.