From interpretability to inference: an estimation framework for universal approximators

TL;DR

This paper introduces a comprehensive estimation and inference framework for universal approximators using Shapley values, enabling better understanding and uncovering of true data generating processes, including in complex models.

Contribution

It develops a novel framework leveraging Shapley values for estimation and inference in universal approximators, extending linear regression insights to broader models.

Findings

Shapley value estimation is asymptotically unbiased.

Shapley regressions can uncover true data generating processes.

Framework applicable to heterogeneous treatment effects.

Abstract

We present a novel framework for estimation and inference with the broad class of universal approximators. Estimation is based on the decomposition of model predictions into Shapley values. Inference relies on analyzing the bias and variance properties of individual Shapley components. We show that Shapley value estimation is asymptotically unbiased, and we introduce Shapley regressions as a tool to uncover the true data generating process from noisy data alone. The well-known case of the linear regression is the special case in our framework if the model is linear in parameters. We present theoretical, numerical, and empirical results for the estimation of heterogeneous treatment effects as our guiding example.