Regularized Targeted Maximum Likelihood Estimation in Highly Adaptive Lasso Implied Working Models

2025-06-20

AI Summary

To address the instability, slow convergence, and inaccurate efficient influence curve (EIC) estimation of the Highly Adaptive Lasso–Targeted Minimum Loss Estimation (HAL-TMLE) in high-dimensional causal inference—particularly in survival analysis and longitudinal mediation analysis—this paper introduces two novel regularization strategies: the Delta method and the projection method. Both operate within HAL’s implicit finite-dimensional working model to perform targeted updates, thereby avoiding nonparametric iteration and explicit EIC computation, and substantially reducing computational cost. Theoretically and through simulation studies, the proposed methods retain double robustness and achieve efficient asymptotic normality. They markedly improve estimation stability and convergence speed in complex settings such as survival curve estimation. This work establishes a scalable, robust, and computationally feasible paradigm for high-dimensional semiparametric causal inference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Humans and AI: Human-in-the-loop Machine Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We address the challenge of performing Targeted Maximum Likelihood Estimation (TMLE) after an initial Highly Adaptive Lasso (HAL) fit. Existing approaches that utilize the data-adaptive working model selected by HAL-such as the relaxed HAL update-can be simple and versatile but may become computationally unstable when the HAL basis expansions introduce collinearity. Undersmoothed HAL may fail to solve the efficient influence curve (EIC) at the desired level without overfitting, particularly in complex settings like survival-curve estimation. A full HAL-TMLE, which treats HAL as the initial estimator and then targets in the nonparametric or semiparametric model, typically demands costly iterative clever-covariate calculations in complex set-ups like survival analysis and longitudinal mediation analysis. To overcome these limitations, we propose two new HAL-TMLEs that operate within the finite-dimensional working model implied by HAL: Delta-method regHAL-TMLE and Projection-based regHAL-TMLE. We conduct extensive simulations to demonstrate the performance of our proposed methods.

Problem

• Address computational instability in HAL-based TMLE methods
• Improve efficiency in solving influence curves without overfitting
• Reduce cost of iterative calculations in complex analyses

Innovation

• Delta-method regHAL-TMLE for efficient estimation
• Projection-based regHAL-TMLE to avoid instability
• Utilizes HAL-implied working models for TMLE