Nonparametric Inverse Probability Weighted Estimators Based on the Highly Adaptive Lasso

• Activity Number: 422 - Recent Development of Machine Learning Methods in Causal Inference
• Type: Invited
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Ashkan Ertefaie* and Nima Hejazi and Mark Van Der Laan
• Companies: University of Rochester and University of California, Berkeley and University of California
• Keywords: Adaptive estimation; Causal inference; Efficient influence function

Abstract

Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudo-population in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse probability weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at $n^{-1/3}$-rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model.