A Copula-Tensor Neural Network Framework for High-Dimensional Causal Inference
TL;DR
It is suggested that copula-based feature representations combined with deep learning provide a flexible approach for heterogeneous treatment effect estimation, particularly in high-dimensional settings with complex covariate dependence.
Abstract
Estimating conditional average treatment effects (CATEs) in high-dimensional causal inference problems remains challenging because complex nonlinear relationships, heterogeneous feature distributions, and dependence among covariates can limit the effectiveness of conventional machine learning approaches. To address this challenge, we propose a copula-enhanced neural learning framework that integrates empirical copula transformations, manifold-based feature augmentation, structured treatment–covariate interaction representations, and deep neural networks for flexible CATE estimation. The empirical copula transformation does not introduce additional dependence information; instead, it provides a rank-based feature representation that normalizes marginal distributions, reduces sensitivity to heterogeneous feature scales and extreme observations, and offers a dependence-aware representation for subsequent learning. The proposed framework is evaluated through Monte Carlo simulations under diverse data-generating mechanisms and a real-world application using the Criteo uplift dataset. The simulation study examines the contribution of individual model components through ablation experiments and compares the proposed approach with established causal learning methods. Results demonstrate that the proposed framework achieves competitive CATE estimation accuracy while providing stable policy evaluation based on Inverse Propensity Scoring (IPS) and Doubly Robust (DR) estimators. In the Criteo application, the proposed method exhibits predictive performance comparable to conventional neural-network approaches while producing more stable Doubly Robust policy value estimates. These findings suggest that copula-based feature representations combined with deep learning provide a flexible approach for heterogeneous treatment effect estimation, particularly in high-dimensional settings with complex covariate dependence. The benefits of the proposed framework depend on data characteristics, including sample size, dimension, dependence structure, and treatment assignment mechanisms.