Representation Learning for Semiparametric Causal Mediation Analysis under No Essential Heterogeneity

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.

Mediation analysis has traditionally focused on outcome-level summary contrasts, such as mean effects, which may obscure substantial distributional changes induced by complex and nonlinear causal mechanisms. We propose Distributional Causal Mediation Analysis (DCMA), a generative learning framework for identifying and estimating treatment effects on entire outcome distributions transmitted through multiple mediators. DCMA learns conditional generative models for the mediators and the outcome, recovering the relevant conditional distributions from observational data. Leveraging the identification formulas, it reconstructs interventional outcome distributions via Monte Carlo forward simulation by noise resampling, enabling the capture of both classical summary effects and rich distributional contrasts such as energy distance and the Wasserstein distance. Analytical error bounds are derived to decompose how estimation errors in the learned conditional models propagate to the reconstructed interventional outcome distributions. The empirical effectiveness of DCMA is demonstrated through numerical experiments and real-world data applications.

In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.