Continuous Treatment Effect Estimation with Cauchy-Schwarz Divergence Information Bottleneck

Abstract

Estimating conditional average treatment effects (CATE) for continuous and multivariate treatments remains a fundamental yet underexplored problem in causal inference, as most existing methods are confined to binary treatment settings. In this paper, we make two key theoretical contributions. First, we derive a novel counterfactual error bound based on the Cauchy–Schwarz (CS) divergence, which is provably tighter than prior bounds derived from the Kullback–Leibler (KL) divergence. Second, we strengthen this bound by integrating the Information Bottleneck principle, introducing a compression regularization on latent representations to enhance generalization. Building on these insights, we propose a new neural framework that operationalizes our theory. Extensive experiments on three benchmarks show that our method consistently outperforms state-of-the-art baselines and remains robust under biased treatment assignments.