Value-Based Abstraction Functions for Abstraction Sampling

Bobak Pezeshki, Kalev Kask, Alexander Ihler, Rina Dechter

Keywords: Abstraction, Sampling, Z, Partition Function, Normalizing Constant, Graphical Models, Bayesian Networks, Probability

TL;DR: This work introduces new abstraction methodologies to Abstraction Sampling (a Stratified Importance Sampling-like Monte Carlo method over graphical models), three of which show significant performance gains over the existing state-of-the-art.

Abstract: Monte Carlo methods are powerful tools for solving problems involving complex probability distributions. Despite their versatility, these methods often suffer from inefficiencies, especially when dealing with rare events. As such, importance sampling emerged as a prominent technique for alleviating these challenges. Recently, a new scheme called Abstraction Sampling was developed that incorporated stratification to importance sampling over graphical models. However, existing work only explored a limited set of abstraction functions that guide stratification. This study introduces three new classes of abstraction functions combined with seven distinct partitioning schemes, resulting in twenty-one new abstraction functions, each motivated by theory and intuition from both search and sampling domains. An extensive empirical analysis on over 400 problems compares these new schemes highlighting several well-performing candidates.

List Of Authors: Pezeshki, Bobak and Kask, Kalev and Ihler, Alexander and Dechter, Rina

Code Url: https://github.com/dechterlab-publications/uai2024-abstraction-sampling

Submission Number: 724