Estimating Structural Target Functions using Machine Learning and Influence Functions

TL;DR

This paper introduces a flexible machine learning framework called 'IF-learning' that leverages influence functions to estimate a wide range of target parameters in statistical models, especially with incomplete data.

Contribution

It proposes a new, problem- and model-agnostic framework for estimating target functions using influence functions, including two novel algorithms for bias removal and confidence estimation.

Findings

The 'IF-learner' effectively estimates target functions without confidence bands.

The 'Group-IF-learner' provides confidence estimates with sufficient coarsening information.

Simulation results demonstrate the methods' effectiveness in treatment effect inference.

Abstract

We aim to construct a class of learning algorithms that are of practical value to applied researchers in fields such as biostatistics, epidemiology and econometrics, where the need to learn from incompletely observed information is ubiquitous. We propose a new framework for statistical machine learning of target functions arising as identifiable functionals from statistical models, which we call `IF-learning' due to its reliance on influence functions (IFs). This framework is problem- and model-agnostic and can be used to estimate a broad variety of target parameters of interest in applied statistics: we can consider any target function for which an IF of a population-averaged version exists in analytic form. Throughout, we put particular focus on so-called coarsening at random/doubly robust problems with partially unobserved information. This includes problems such as treatment effect estimation and inference in the presence of missing outcome data. Within this framework, we propose two general learning algorithms that build on the idea of nonparametric plug-in bias removal via IFs: the 'IF-learner' which uses pseudo-outcomes motivated by uncentered IFs for regression in large samples and outputs entire target functions without confidence bands, and the 'Group-IF-learner', which outputs only approximations to a function but can give confidence estimates if sufficient information on coarsening mechanisms is available. We apply both in a simulation study on inferring treatment effects.