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.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical ModelsData Mining & Knowledge Management: Data Compression

Application Category

Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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