Statistical Estimation from Dependent Data
Talkat Algorithmic Advances for Statistical Inference with Combinatorial Structure · 2021-10-11..10-15·
summary
Model sets labels Y as an Ising with feature-dependent external fields: each node’s external field equals f_theta(x_i) and labels have network coupling beta·A, observations include node features and A but only one joint sample of Y. Estimator maximizes the single-sample pseudo-likelihood (convex, tractable) and gives provable error bounded by the function-class metric-entropy divided by ||A||_F^2, with exponential dependence on beta; proofs require new low-temperature concentration/anti-concentration tools and yield polytime rates for linear and sparse classes.
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chapters (10)
- 0:00Statistical estimation intro
- 4:49Drop independence assumption
- 8:05Regression with dependencies
- 12:29Estimation challenges
- 18:47Learning Ising models
- 24:17Main result implications
- 30:20Corollaries for linear/sparse models
- 35:53Proof sketch
- 48:25Summary and future work
- 49:12Q&A
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