Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs

TL;DR

This paper introduces sum-product-set networks, a novel probabilistic model that efficiently performs exact inference on tree-structured graph data like XML and JSON, addressing limitations of neural network-based models.

Contribution

The paper extends probabilistic circuits to tree-structured graphs using random finite sets, enabling tractable inference on complex graph data.

Findings

Performs comparably to neural network models in experiments

Enables exact and efficient inference on tree-structured graphs

Addresses computational challenges of neural models on graph data

Abstract

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution over undirected cyclic graphs. This assumption of a generic graph structure brings various computational challenges, and, more importantly, the presence of non-linearities in neural networks does not permit tractable probabilistic inference. We address these problems by proposing sum-product-set networks, an extension of probabilistic circuits from unstructured tensor data to tree-structured graph data. To this end, we use random finite sets to reflect a variable number of nodes and edges in the graph and to allow for exact and efficient inference. We demonstrate that our tractable model performs comparably to various intractable models based on neural networks.