Multi-Treatment Effect Estimation with Proxy: Contrastive Learning and Rank Weighting

Minqin Zhu, Anpeng Wu, Ruoxuan Xiong, Kun Kuang

Abstract: We study the treatment effect estimation problem for continuous and multi-dimensional treatments, in the setting with unobserved confounders, but high-dimension proxy variables for unobserved confounders are available. Existing methods either directly adjust the relationship between observed covariates and treatments or recover the hidden confounders by probabilistic models. However, they either rely on a correctly specified treatment assignment model or require strong prior of the unobserved confounder distribution. To relax these requirements, we propose a Contrastive Regularizer (CR) to learn the proxy representation that contains all the relevant information in unobserved confounders. Based on the CR, we propose a novel ranked weighting method (Rw) to de-bias the treatment assignment. Combining Cr and Rw, we propose a neural network framework named CRNet to estimate the effects of multiple continuous treatments under unobserved confounders, evaluated by the Average Dose-Response Function. Empirically, we demonstrate that CRNet achieves state-of-the-art performance on both synthetic and semi-synthetic datasets.

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