Learning Kolmogorov Models for Binary Random Variables

Hadi Ghauch, Hossein S. Ghadikolaei, Mikael Skoglund, Carlo Fischione

Abstract: We propose a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link (in the sense of implications in mathematical logic) outcomes of specific random variables and extract valuable relations from the data. We also propose an efficient algorithm for computing the model and show its first-order optimality, despite the combinatorial nature of the learning problem. We exemplify our general framework to recommendation systems and gene expression data. We believe that the work is a significant step toward interpretable machine learning.

Keywords: Kolmogorov model, interpretable models, causal relations mining, non-convex optimization, relaxations