Estimation Beyond the IID Setting (Two Vignettes)

on YouTube ↗01h 02m

" summary

Two vignettes show concrete claims and tools: the worst‑case squared‑error estimator for a coin with one flip predicts quarter/three-quarters rule and for k flips regularizes the empirical mean toward 1/2 with 1/sqrt(k+1) shrinkage (classical result traced to 1950). For general sampling from a known distribution P over subsets, a polynomial‑time SDP (Goemans–Williamson style) gives a pi/2 SDP approximation to the minimax expected error over bounded data, restricted to semi-linear estimators; the SDP is implementable, yields consistent constant‑factor gains over reweighting and subgroup baselines in importance/snowball/forecasting examples.

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" chapters (12)

1. 0:00Introduction
2. 0:49Warmup
3. 11:50Alternate Formulation
4. 15:45Sampling
5. 17:36Estimation and Learning
6. 18:48Framework
7. 27:09Examples
8. 29:01Theorems
9. 31:24Problem Explanation
10. 32:03Special Case
11. 45:35Use Cases
12. 46:45Open Questions

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