Your Dreams May Come True with MTP2

on YouTube ↗51m

" summary

Defines MTP2 by the pointwise inequality p(x)p(y) ≤ p(x∧y)p(x∨y) and shows concrete consequences: Simpson's paradox cannot occur, MTP2 is closed under conditioning and marginalization, and for Gaussians inverse covariance is an M‑matrix (off‑diagonals ≤ 0). Gives real data hits (stock correlations, symptom tables), proves Gaussian MLE under MTP2 exists with as few as two samples via an ultrametric construction and yields sparsity where sample covariances are negative. For nonparametric MTP2+log‑concave MLE often reduces to a tent function; whether that holds in full generality remains open.

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" chapters (16)

1. 0:00Introduction
2. 1:05What is MTP2
3. 2:13Why were they introduced
4. 3:37Simpsons Paradox
5. 10:21MTP2 Distribution
6. 17:31Density Estimation
7. 19:43Optimization Problem
8. 24:10Multipage Proof
9. 30:10Shape Constraints
10. 33:22Questions
11. 33:47What is LLC
12. 34:29Why is LLC important
13. 36:02When does the Emily exist
14. 37:10Support
15. 38:58Example
16. 45:57Conclusion

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