A New Perspective on High-Dimensional Causal Inference
summary
Paper proves a new central limit theorem for a three‑split cross‑fit AIPW estimator in a proportional regime (p/n → constant) without sparsity, explicitly computing a larger variance than classical theory and identifying non‑negligible negative cross‑covariances between fold estimators. Results assume logistic propensity, linear outcome, Gaussian covariates; simulations (n=10,000, p=700) match the variance inflation. Proof uses leave-one-out (cavity), approximate message passing and deterministic equivalents, runs ~100 pages, and yields formulas needed to tune inference‑aware regularization.
AI-written summary · about
chapters (13)
- 0:00Start
- 0:18Causal Inference
- 1:29Rajesh Mkhirji
- 4:33Framework of Potential Outcomes
- 6:41Causal Identification
- 7:52Nuisance Functions
- 20:47Sample Splitting
- 23:29Main Hurdles
- 25:31Formal Setting
- 37:21Cavity Method
- 38:19Approximate Message Passing Theory
- 46:28Introduce a Suitable Iterative Algorithm
- 50:25Summary
related talks
43mRobustness in High-Dimensional Inference Tasks
01h 11mStatistical Limits of Causal Inference
01h 02mUnmeasured Confounding and More Recent Developments/Challenges in Causal Discovery
33mSimple Yet Efficient Estimators For Network Causal Inference...
44mA Modern Maximum-Likelihood Theory for High-Dimensional Logistic Regression
42mBypassing the Impossibility of Online Learning Thresholds: Unbounded Losses and Transductive Priors
31mLearning And Testing Causal Models: A Property Testing Viewpoint
01h 02mPrediction, Generalization, Complexity: Revisiting the Classical View from Statistics Part 2