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

• URL: http://arxiv.org/abs/2408.07394v2
• Date: Sun, 18 Aug 2024 12:01:38 GMT
• Title: Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs
• Authors: Milan Papež, Martin Rektoris, Tomáš Pevný, Václav Šmídl,
• Abstract summary: We propose sum-product-set networks, an extension of probabilistic circuits from unstructured data to tree-structured graph data. We demonstrate that our tractable model performs comparably to various intractable models based on neural networks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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