Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya–Watson Regression

Abstract

A new method for estimating the conditional average treatment effect is proposed in this paper. It is called TNW-CATE (the Trainable Nadaraya–Watson regression for CATE) and based on the assumption that the number of controls is rather large and the number of treatments is small. TNW-CATE uses the Nadaraya–Watson regression for predicting outcomes of patients from control and treatment groups. The main idea behind TNW-CATE is to train kernels of the Nadaraya–Watson regression by using a weight sharing neural network of a specific form. The network is trained on controls, and it replaces standard kernels with a set of neural subnetworks with shared parameters such that every subnetwork implements the trainable kernel, but the whole network implements the Nadaraya–Watson estimator. The network memorizes how the feature vectors are located in the feature space. The proposed approach is similar to transfer learning when domains of source and target data are similar, but the tasks are different. Various numerical simulation experiments illustrate TNW-CATE and compare it with the well-known T-learner, S-learner, and X-learner for several types of control and treatment outcome functions. The code of proposed algorithms implementing TNW-CATE is publicly available.

Keywords

• treatment effect
• Nadaraya–Watson regression
• neural network
• shared weights
• meta-learner
• regression