Sum-product networks: A survey

TL;DR

This survey comprehensively reviews sum-product networks (SPNs), their structure, inference algorithms, learning methods, applications, and software tools, highlighting their advantages in building tractable probabilistic models for various tasks.

Contribution

It provides the first extensive overview of SPNs, detailing their definitions, algorithms, applications, and comparisons with related probabilistic models.

Findings

SPNs enable efficient inference proportional to graph size.

They are applicable to image processing and natural language tasks.

Software libraries facilitate SPN implementation and experimentation.

Abstract

A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and products of probability functions. They are closely related to probabilistic graphical models, in particular to Bayesian networks with multiple context-specific independencies. Their main advantage is the possibility of building tractable models from data, i.e., models that can perform several inference tasks in time proportional to the number of links in the graph. They are somewhat similar to neural networks and can address the same kinds of problems, such as image processing and natural language understanding. This paper offers a survey of SPNs, including their definition, the main algorithms for inference and learning from data, the main applications, a brief review of software libraries, and a comparison with related models