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Motivated by the rising abundance of observational data with continuoustreatments, we investigate the problem of estimating the average dose-responsecurve (ADRF). Available parametric methods are limited in their model space,and previous attempts in leveraging neural network to enhance modelexpressiveness relied on partitioning continuous treatment into blocks andusing separate heads for each block; this however produces in practicediscontinuous ADRFs. Therefore, the question of how to adapt the structure andtraining of neural network to estimate ADRFs remains open. This paper makes twoimportant contributions. First, we propose a novel varying coefficient neuralnetwork (VCNet) that improves model expressiveness while preserving continuityof the estimated ADRF. Second, to improve finite sample performance, wegeneralize targeted regularization to obtain a doubly robust estimator of thewhole ADRF curve.

VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments