A First Step Towards Even More Sparse Encodings of Probability Distributions

2026-03-31

AI Summary

Traditional probabilistic distribution encodings require exponential storage and struggle to efficiently represent lifted probability distributions encountered in real-world scenarios. This work proposes a novel approach that, for the first time, integrates numerical compression with first-order logical formula extraction. The method first reduces the number of distinct values in the distribution and then generates minimizable logical formulas for each remaining value, yielding a sparse yet generalizable encoding. Experimental results demonstrate that only a small number of concise logical formulas are sufficient to substantially enhance sparsity while effectively preserving the key statistical properties of the original distribution.

Abstract

Real world scenarios can be captured with lifted probability distributions. However, distributions are usually encoded in a table or list, requiring an exponential number of values. Hence, we propose a method for extracting first-order formulas from probability distributions that require significantly less values by reducing the number of values in a distribution and then extracting, for each value, a logical formula to be further minimized. This reduction and minimization allows for increasing the sparsity in the encoding while also generalizing a given distribution. Our evaluation shows that sparsity can increase immensely by extracting a small set of short formulas while preserving core information.

Problem

• sparse encoding
• probability distributions
• lifted representation
• exponential complexity

Innovation

• sparse encoding
• probability distributions
• first-order logic
• formula extraction
• distribution generalization