Distributional CNN-LSTM, KDE, and Copula Approaches for Multimodal Multivariate Data: Assessing Conditional Treatment Effects

We introduce a distributional CNN-LSTM framework for probabilistic multivariate modeling and heterogeneous treatment effect (HTE) estimation. The model jointly captures complex dependencies among multiple outcomes and enables precise estimation of individual-level conditional average treatment effects (CATEs). In simulation studies with multivariate Gaussian mixtures, the CNN-LSTM demonstrates robust density estimation and strong CATE recovery, particularly as mixture complexity increases, while classical methods such as Kernel Density Estimation (KDE) and Gaussian Copulas may achieve higher log-likelihood or coverage in simpler scenarios. On real-world datasets, including Iris and Criteo Uplift, the CNN-LSTM achieves the lowest CATE RMSE, confirming its practical utility for individualized prediction, although KDE and Gaussian Copula approaches may perform better on global likelihood or coverage metrics. These results indicate that the CNN-LSTM can be trained efficiently on moderate-sized datasets while maintaining stable predictive performance. Overall, the framework is particularly valuable in applications requiring accurate individual-level effect estimation and handling of multimodal heterogeneity—such as personalized medicine, economic policy evaluation, and environmental risk assessment—with its primary strength being superior CATE recovery under complex outcome distributions, even when likelihood-based metrics favor simpler baselines.