A First Step Towards Even More Sparse Encodings of Probability Distributions

TL;DR

The paper introduces a method to encode probability distributions more sparsely by extracting logical formulas, reducing data requirements and enhancing generalization.

Contribution

It proposes a novel approach to derive first-order formulas from distributions, significantly increasing sparsity while maintaining essential information.

Findings

Sparsity of distribution encoding can be greatly increased.

Short formulas can preserve core distribution information.

Method reduces the number of values needed for representation.

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.