Tractable Probabilistic Circuits

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" summary

Introduces tractable probabilistic circuits as sum‑product DAGs learned via Chow‑Liu → hidden tree → circuit and trained with mini‑batch EM on GPUs; achieves state‑of‑the‑art likelihood on full MNIST and yields image compression that is 5–40× faster than neural baselines. Proves that determinantal point processes require new syntax, gives probability generating circuits that represent DPPs in polynomial size, and shows KL/cross‑entropy are tractable when circuits are smooth, decomposable and deterministic; practical marginal‑MAP solver outperforms prior methods.

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" chapters (16)

1. 0:00Start
2. 4:15Tractable marginals
3. 7:04Outline
4. 7:41Learning Expressive Probabilistic Circuits Hidden Chow-Liu Trees
5. 12:57Probabilistic circuits seem awfully general.
6. 13:32Enter: Determinantal Point Processes DPPST
7. 17:22Probability Generating Functions
8. 21:46Example
9. 22:17Experiment Results: Amazon Baby Registries
10. 24:37Queries as pipelines: Cross Entropy
11. 25:31Tractable circuit operations
12. 26:03Inference by tractable operations systematically derive tractable inference algorithm of complex queries
13. 27:41Pruning circuits
14. 29:46Tractable Computation of Expected Kernels: Applications Reasoning about support vector regression (SVR) with missing features
15. 30:36Conclusion
16. 34:16Even harder queries

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