Summary of Polynomial Semantics Of Tractable Probabilistic Circuits, by Oliver Broadrick et al.
Polynomial Semantics of Tractable Probabilistic Circuits
by Oliver Broadrick, Honghua Zhang, Guy Van den Broeck
First submitted to arxiv on: 14 Feb 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: None
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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 Probabilistic circuits compute multilinear polynomials representing multivariate probability distributions. They support efficient marginal inference, but various polynomial semantics have been considered in the literature. This paper proves that for binary distributions, each probabilistic circuit model is equivalent, meaning any circuit can be transformed into another with a polynomial increase in size. They are all tractable for marginal inference on the same class of distributions. We also explore the extension of one such polynomial semantics to categorical random variables, showing that inference becomes #P-hard. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Probabilistic circuits help us understand probability distributions. They can do complex calculations quickly, but there’s been confusion about how different ways of representing these distributions are related. This paper shows that for certain types of distributions, all these different representations are essentially the same thing. You can turn one into another by adding a little extra information. This makes them all useful for doing quick calculations on the same type of data. It also shows that using these circuits to do even more complex calculations becomes really hard. |
Keywords
» Artificial intelligence » Inference » Probability » Semantics
