A First Step Towards Even More Sparse Encodings of Probability Distributions

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.

Figures (1)

• Figure 1: Hellinger distances from the original to the noised and mapped models

Theorems & Definitions (3)

• definition 1: Parfactor model
• definition 2: Hellinger distance
• definition 3: MLN