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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07394 |
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| _version_ | 1866913470797053952 |
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| author | Papež, Milan Rektoris, Martin Pevný, Tomáš Šmídl, Václav |
| author_facet | Papež, Milan Rektoris, Martin Pevný, Tomáš Šmídl, Václav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs Papež, Milan Rektoris, Martin Pevný, Tomáš Šmídl, Václav Machine Learning Artificial Intelligence 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. |
| title | Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2408.07394 |