Decision Diagrams for Efficient Inference and Optimization in Expressive Discrete+Continuous Domains

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Extends the algebraic decision diagram to continuous variables as the extended ADD (XADD) and represents arbitrary piecewise polynomial functions, with implemented plus/times/max/integral and symbolic substitution so marginals, means and Bellman backups evaluate in closed form. Works on hybrid graphical models, parametric constrained optimization and continuous MDPs, and collapses bilinear learning+decision problems via symbolic variable elimination to solve Smart Predict+Optimize exactly. Operations can blow up (worst‑case exponential) but XADDs compress structure; decision‑ordering and canonicity versus minimality remain practical hurdles.

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" chapters (14)

1. 0:00Introduction
2. 2:42Discrete to continuous HMMs
3. 7:47Case statements in closed form
4. 15:57Inference challenges
5. 18:31Decision diagrams for discrete
6. 21:29Extending to continuous
7. 25:27Decision ordering in XADDs
8. 28:23Minimality in XADDs
9. 33:04XADD operations
10. 34:55Mixed MDPs
11. 38:29Inventory control with XADDs
12. 39:55Smart Predict+Optimize
13. 41:45Recap and conclusion
14. 43:00Q&A