Summary of On the Expressive Power Of Tree-structured Probabilistic Circuits, by Lang Yin et al.
On the Expressive Power of Tree-Structured Probabilistic Circuits
by Lang Yin, Han Zhao
First submitted to arxiv on: 7 Oct 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates the expressiveness of probabilistic circuits (PCs) with directed acyclic graphs (DAGs) versus trees. PCs have been shown to efficiently represent probability distributions, and DAG-structured PCs are particularly effective. However, existing algorithms for learning PC structures often rely on tree-structured intermediaries. The authors pose an intriguing question: does an exponential gap exist between DAGs and trees in terms of PC structure? They provide a negative answer by demonstrating that a quasi-polynomial upper bound exists for the size of equivalent trees computing the same probability distribution, whereas a super-polynomial separation exists when considering depth-restricted trees. This work contributes to understanding the expressive power of tree-structured PCs, with implications for structure learning algorithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper is about a new way to understand and work with special kinds of mathematical structures called probabilistic circuits (PCs). PCs are used to efficiently calculate probabilities and make predictions. The authors are trying to figure out how these PC structures compare when they’re in tree-like forms versus more complex, branch-like forms. They found that even though the simpler trees might seem less powerful, there’s a limit to how big and complicated they can get before they start to struggle with certain calculations. This discovery can help us better understand and use PCs for different tasks. |
Keywords
» Artificial intelligence » Probability
