# A Density Ratio Super Learner

arXiv: https://arxiv.org/abs/2408.04796 · HTML: https://mlsanity.com/paper/2408.04796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 2 of 2)

- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Non-parametric causal effects based on longitudinal modified treatment policies](https://mlsanity.com/paper/2006.01366/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)

## Abstract (arXiv)

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.