A1772
Title: Asymptotically optimal change detection for unnormalized pre- and post-change distributions
Authors: Arman Adibi - Augusta University (United States) [presenting]
Abstract: The problem of detecting changes when only unnormalized pre- and post-change distributions are accessible is addressed. This situation occurs in many scenarios in physics such as in ferromagnetism, crystallography, magneto-hydrodynamics, and thermodynamics, where the energy models are difficult to normalize. The approach is based on the estimation of the Cumulative Sum (CUSUM) statistics, which is known to produce optimal performance. First, an intuitively appealing Approximation method is presented. Unfortunately, this produces a biased estimator of the CUSUM statistics and may cause performance degradation. The Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm is then proposed, 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 asymptotically optimal performance. Moreover, a relationship between the required sample size for thermodynamic integration and the desired detection delay performance is derived, offering guidelines for practical parameter selection. Numerical studies demonstrate the efficacy of the approach.
