Sum-Product Graphical Models

TL;DR

Sum-Product Graphical Models (SPGMs) integrate the interpretability of graphical models with the computational efficiency of Sum-Product Networks, enabling tractable inference and effective density estimation.

Contribution

The paper introduces SPGMs, a novel probabilistic architecture that combines the semantics of graphical models with the efficiency of SPNs, along with a new learning algorithm.

Findings

SPGMs enable tractable inference with context-specific independence.

The proposed learning algorithm effectively estimates structure and parameters.

Empirical results show competitive density estimation performance.

Abstract

This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence. Like GMs, SPGMs provide a high-level model interpretation in terms of conditional independence assumptions and corresponding factorizations. Thus, the new architecture represents a class of probability distributions that combines, for the first time, the semantics of graphical models with the evaluation efficiency of SPNs. We also propose a novel algorithm for learning both the structure and the parameters of SPGMs. A comparative empirical evaluation demonstrates competitive performances of our approach in density estimation.