2/4/2025 | 9:10 AM - 10:30 AM | Regency B

Asymptotically efficient simulation and modeling of rare binary images

Author(s)

Jiaxuan Xu | Purdue University
Mary Comer | Purdue University

Abstract

Characterization of rare events is often of critical importance, and is an especially difficult task when rare image data are needed. To the best of our knowledge, there has been no published work that simulates rare images and then uses those images to estimate probabilities of associated rare events. We present a novel approach that performs asymptotically efficient importance sampling of images modeled by Gibbs distributions, or equivalently Markov random fields (MRFs), and estimates rare event probabilities, providing unprecedented capabilities for characterizing rare events in images. Theoretically, the AEIS sampling distribution gives an unbiased estimator with the lowest variance asymptotically from a class of admissible importance sampling distributions. We will first give a precise definition of a rare event, in terms of a rare event statistic and a rare event region. For the given rare event, we estimate the asymptotically efficient importance sampling (AEIS) distribution, which is based on a large deviation principle; draw samples of rare images from this AEIS distribution, for the special case of binary images; and estimate rare event probabilities for several different rare event regions. Finally, we fit large deviations rate functions from simulations and a small number of probability estimates for a given rare event statistic. This allows us to compute probability estimates associated with a particular rare event statistic for any rare event region of interest without requiring further simulations. We apply these methods to two binary MRF models. The first problem we address is the magnetization of a ferromagnet, which is modeled using an Ising model, in the absence of an external field. The second problem regards the density of clusters in a NiAlCr super-alloy, for which we use a Strauss model.