[Paper Review] DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning

Siqi Xu, Lin Liu+1 more|arXiv (Cornell University)|Oct 10, 2022

Bayesian Modeling and Causal Inference7 citations

TL;DR

DeepMed proposes a deep learning-based method for semiparametric causal mediation analysis that uses debiased deep neural networks (DNNs) to estimate nuisance functions in the efficient influence function of natural direct and indirect effects (NDE/NIE). It achieves semiparametric efficiency without requiring sparse DNN architectures and adapts to low-dimensional structures, advancing theory and practice in DNN-based causal inference.

ABSTRACT

Causal mediation analysis can unpack the black box of causality and is therefore a powerful tool for disentangling causal pathways in biomedical and social sciences, and also for evaluating machine learning fairness. To reduce bias for estimating Natural Direct and Indirect Effects in mediation analysis, we propose a new method called DeepMed that uses deep neural networks (DNNs) to cross-fit the infinite-dimensional nuisance functions in the efficient influence functions. We obtain novel theoretical results that our DeepMed method (1) can achieve semiparametric efficiency bound without imposing sparsity constraints on the DNN architecture and (2) can adapt to certain low dimensional structures of the nuisance functions, significantly advancing the existing literature on DNN-based semiparametric causal inference. Extensive synthetic experiments are conducted to support our findings and also expose the gap between theory and practice. As a proof of concept, we apply DeepMed to analyze two real datasets on machine learning fairness and reach conclusions consistent with previous findings.

Motivation & Objective

• To address the gap in theoretical guarantees for DNN-based causal mediation analysis, especially for complex, high-dimensional nuisance functions.
• To develop a method that achieves semiparametric efficiency without imposing sparsity on DNN architectures, which are common in practice.
• To bridge the gap between theory and practice by designing synthetic experiments that simulate nearly infinite-dimensional nuisance functions.
• To provide a practical, user-friendly R package for reproducible causal mediation analysis in biomedical and fairness applications.

Proposed method

• DeepMed uses V-fold cross-fitting with fully connected ReLU-activated feedforward DNNs to estimate nuisance functions (propensity scores, outcome regressions, mediator regressions).
• It leverages the multiply-robust property of the efficient influence function (EIF) for NDE/NIE, enabling bias cancellation when at least one nuisance function is consistently estimated.
• The method employs a debiased estimator based on the EIF, ensuring asymptotic normality and semiparametric efficiency under weak regularity conditions.
• It avoids Donsker-type empirical process assumptions by using sample-splitting, enhancing finite-sample performance.
• The framework is extended to total effect estimation via a special case of NDE/NIE, and applies to functionals with mixed-bias structure.
• An R package is provided for reproducible implementation, supporting real-world applications in fairness and biomedicine.

Experimental results

Research questions

• RQ1 Can DNN-based causal mediation estimators achieve semiparametric efficiency without requiring sparse DNN architectures?
• RQ2 How do DNNs perform in estimating high-dimensional nuisance functions when the true functions are not sparse?
• RQ3 Can the theoretical guarantees of DNN-based causal inference be validated in realistic, complex simulation settings?
• RQ4 Does DeepMed recover known findings in real-world fairness applications, such as algorithmic recidivism prediction?
• RQ5 To what extent does the method adapt to low-dimensional structures in nuisance functions, avoiding the curse of dimensionality?

Key findings

• DeepMed achieves the semiparametric efficiency bound for NDE/NIE estimation without imposing sparsity constraints on the DNN architecture.
• The method adapts to low-dimensional structures in nuisance functions, significantly reducing estimation error and mitigating the curse of dimensionality.
• Synthetic experiments with nearly infinite-dimensional nuisance functions demonstrate that theoretical guarantees hold even in complex, high-dimensional settings.
• The method maintains asymptotic normality and valid inference under weak regularity conditions, with convergence rates driven by DNN estimation error.
• In real-world applications to algorithmic fairness, DeepMed recovers conclusions consistent with prior work, validating its practical relevance.
• The R package implementation ensures reproducibility and facilitates adoption in biomedical and fairness research.