Causal Matrix Completion

on YouTube ↗29m

" summary

Provides a causal model (potential outcomes) for matrix completion under MNAR, shows entries can be identified even when observation probability is zero, and builds an estimator called synthetic nearest neighbors that combines nearest neighbors and synthetic controls. Proves finite-sample consistency and asymptotic normality, gives entry-wise (max-norm) bounds (error scaling like R^{3/2}/√K under assumptions), supplies a variance estimator via second-moment de-noising, and demonstrates in simulations that SNN recovers distributions where USVT and softImpute fail for MCAR, LMNAR and MNAR.

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" chapters (22)

1. 0:00Intro
2. 2:04Formal setup for matrix completion
3. 2:54State-of-the-art: NO unified approach to different sparsity patterns
4. 4:35Overview
5. 5:13Does the sparsity pattern matter? An empirical example
6. 6:45Missing completely at random (MCAR) data
7. 8:14Limited-missing not at random (L-MNAR) data
8. 8:54Missing not at random (MNAR) data
9. 10:12MNAR data is abundant
10. 10:47Nearest neighbors (NN)
11. 11:26Synthetic controls (SC)
12. 12:37SNN = SC + NN l'Academic Sudoku
13. 14:47In general, we cannot infer missing entries...
14. 15:21What type of missing is allowed?—selection on latent factors
15. 17:01Other operating assumptions
16. 18:33Simplifying assumption
17. 19:00Theoretical results
18. 23:08Optimal observation pattern
19. 23:53Towards heteroskedastic variance estimation
20. 25:01Heteroskedastic variance estimation algorithm
21. 25:34Statistical guarantees
22. 26:26An important connection

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