Summary of Sum Of Squares Circuits, by Lorenzo Loconte et al.
Sum of Squares Circuits
by Lorenzo Loconte, Stefan Mengel, Antonio Vergari
First submitted to arxiv on: 21 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Algebraic Geometry (math.AG)
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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 A novel framework for designing expressive generative models that support exact and efficient inference is presented, focusing on probabilistic circuits (PCs) with negative parameters. The study explores the trade-off between tractability and expressiveness, building upon recent advances in squared PCs. The authors prove that squared PCs can be less expressive than monotonic PCs, while also introducing a new class of PCs called sum of squares PCs, which can be exponentially more expressive than both squared and monotonic PCs. An expressiveness hierarchy is constructed around sum of squares PCs, unifying and separating various tractable model classes, including Born Machines and PSD models. The effectiveness of these circuits in performing distribution estimation is empirically demonstrated. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Expressive generative models are important in machine learning. This paper looks at a special type of model called probabilistic circuits (PCs) that can generate data that matches a certain probability distribution. PCs with negative parameters, also known as squared PCs, have been shown to be very expressive. However, this study finds that squared PCs can actually be less expressive than another type of PC called monotonic PCs. The authors also introduce a new class of PCs called sum of squares PCs that are even more expressive. They show how these circuits can be used for tasks like estimating probability distributions and demonstrate their effectiveness in an experiment. |
Keywords
» Artificial intelligence » Inference » Machine learning » Probability
