Primary Submission Category: Machine Learning and Causal Inference
Super Ensemble Learning Using the Highly-Adaptive-Lasso: Imaging Data in Causal Inference
Authors: Zeyi Wang, Wenxin Zhang, Mark van der Laan,
Presenting Author: Zeyi Wang*
Imaging-based models have great potential to enable more powerful and efficient causal analysis. However, it is challenging to incorporate high-dimensional models into causal inference under different scientific contexts. In this paper, we present a novel minimum loss estimation framework with meta-learning and the Highly Adaptive Lasso (HAL). For a true functional parameter defined as the minimizer of the expectation of a loss function, we consider ensemble estimators that are compositions of a cadlag function and a data adaptive coordinate-transformation. Meta-HAL minimum loss estimator is defined as the cadlag function that minimizes the cross-validated empirical risk of the ensemble estimator, over all cadlag functions with a uniform bound on the sectional variation norm. The average of the resulted ensemble estimators across folds is called meta-HAL super-learner. We show that under regularity conditions, the meta-HAL super-learner converges to the true function at a rate n^{−2/3} up till log n-factor in the excess risk, and by choosing the sectional variation norm large enough the target feature of the meta-HAL super-learner is an asymptotically linear estimator for the target feature of the true function. This leads to effective dimension reduction for which we provide theoretical guarantees, simulation evidence with concrete examples including average treatment effects, and real-world evidence of natural indirect effects of functional brain images in pain studies.