Summary of Optimal Transport For Probabilistic Circuits, by Adrian Ciotinga and Yoojung Choi
Optimal Transport for Probabilistic Circuits
by Adrian Ciotinga, YooJung Choi
First submitted to arxiv on: 16 Oct 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)
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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 optimal transport framework is proposed for probabilistic circuits (PCs), enabling tractable computation of the Wasserstein distance between probability distributions represented as PCs. The approach restricts the coupling measure to be a probabilistic circuit and develops an algorithm for computing this distance by solving small linear programs. The optimal transport plan can be retrieved from these solutions. Additionally, the empirical Wasserstein distance between a PC and dataset is studied, allowing estimation of PC parameters to minimize this distance through an efficient iterative algorithm. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to compare probability distributions using “circuit” calculations is introduced. This method helps solve a long-standing problem in understanding how different probability distributions relate to each other. The approach uses a combination of mathematical optimization techniques and simple calculations involving circuits. By solving smaller problems, the full calculation can be done efficiently. This research has potential applications in estimating parameters for these circuit-based models. |
Keywords
» Artificial intelligence » Optimization » Probability
