Multi-Task CNN-LSTM Modeling of Zero-Inflated Count and Time-to-Event Outcomes for Causal Inference with Functional Representation of Features

We propose a novel deep learning framework for counterfactual inference on the COMPAS dataset, utilizing a multi-task CNN-LSTM architecture. The model jointly predicts multiple outcome types: (i) count outcomes with zero inflation, modeled using zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and negative binomial (NB) distributions; (ii) time-to-event outcomes, modeled via the Cox proportional hazards model. To effectively leverage the structure in high-dimensional tabular data, we integrate functional data analysis (FDA) techniques by transforming covariates into smooth functional representations using B-spline basis expansions. Specifically, we construct a pseudo-temporal index over predictor variables and fit basis expansions to each subject’s feature vector, yielding a low-dimensional set of coefficients that preserve smooth variation while reducing noise. This functional representation enables the CNN-LSTM model to capture both local and global temporal patterns in the data, including treatment-covariate interactions. Our approach estimates both population-average and individual-level treatment effects (ATE and CATE) for each outcome and evaluates predictive performance using metrics such as Poisson deviance, root mean squared error (RMSE), and the concordance index (C-index). Statistical inference on treatment effects is supported via bootstrap-based confidence intervals and hypothesis testing. Overall, this comprehensive framework facilitates flexible modeling of heterogeneous treatment effects in structured, high-dimensional data, advancing causal inference methodologies in criminal justice and related domains.