A Density Ratio Super Learner

TL;DR

This paper introduces a super learner ensemble method for estimating density ratios, crucial in statistics and causal inference, demonstrating improved performance through simulations.

Contribution

It develops a novel super learning-based ensemble estimator for density ratios with a new loss function, advancing causal inference methods.

Findings

Effective in mediation analysis scenarios

Performs well in longitudinal modified treatment policy contexts

Shows empirical improvements over existing methods

Abstract

The estimation of the ratio of two density probability functions is of great interest in many statistics fields, including causal inference. In this study, we develop an ensemble estimator of density ratios with a novel loss function based on super learning. We show that this novel loss function is qualified for building super learners. Two simulations corresponding to mediation analysis and longitudinal modified treatment policy in causal inference, where density ratios are nuisance parameters, are conducted to show our density ratio super learner's performance empirically.