A Neural Mean Embedding Approach for Back-door and Front-door Adjustment

TL;DR

This paper introduces a neural mean embedding method for estimating treatment effects under back-door and front-door adjustments, avoiding density estimation and effectively handling high-dimensional data.

Contribution

It proposes a novel neural network-based approach that directly computes conditional expectations for causal effect estimation, improving convergence and performance over existing methods.

Findings

Method converges to true causal parameters.

Outperforms state-of-the-art on high-dimensional benchmarks.

Effective in settings with complex data like images.

Abstract

We consider the estimation of average and counterfactual treatment effects, under two settings: back-door adjustment and front-door adjustment. The goal in both cases is to recover the treatment effect without having an access to a hidden confounder. This objective is attained by first estimating the conditional mean of the desired outcome variable given relevant covariates (the "first stage" regression), and then taking the (conditional) expectation of this function as a "second stage" procedure. We propose to compute these conditional expectations directly using a regression function to the learned input features of the first stage, thus avoiding the need for sampling or density estimation. All functions and features (and in particular, the output features in the second stage) are neural networks learned adaptively from data, with the sole requirement that the final layer of the first stage should be linear. The proposed method is shown to converge to the true causal parameter, and outperforms the recent state-of-the-art methods on challenging causal benchmarks, including settings involving high-dimensional image data.