Varying Coefficient Neural Network with Functional Targeted Regularization for Estimating Continuous Treatment Effects
With the rising abundance of observational data with continuous treatments, we investigate the problem of estimating average dose-response curve (ADRF). Available parametric methods are limited in model space, while previous attempts in leveraging neural network to enhance model expressiveness rely on partitioning continuous treatment into blocks and using separate heads for each block, which, however, produce discontinuous ADRF in practice. Thus, the question of how to adapt the structure and training of neural network to estimate ADRF is still open. This paper provides an answer to this question by making two contributions. First, we propose a novel varying coefficient neural network (VCNet) which improves model expressiveness while preserving continuity of the estimated ADRF. Second, in order to improve finite sample performance, we generalize targeted regularization to obtain a doubly robust estimator of the whole ADRF curve, whereas its predecessor is only for estimating a scalar quantity.
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