# Projection Pursuit Density Ratio Estimation

arXiv: https://arxiv.org/abs/2506.00866 · HTML: https://mlsanity.com/paper/2506.00866/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2008.10581/) (2020)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [On regularized Radon-Nikodym differentiation](https://mlsanity.com/paper/2308.07887/) (2023)
- [Inverse Density as an Inverse Problem: The Fredholm Equation Approach](https://mlsanity.com/paper/1304.5575/) (2013)
- [Support Consistency of Direct Sparse-Change Learning in Markov Networks](https://mlsanity.com/paper/1407.0581/) (2014)
- [Overcoming Saturation in Density Ratio Estimation by Iterated Regularization](https://mlsanity.com/paper/2402.13891/) (2024)
- [A Projection Pursuit Forest Algorithm for Supervised Classification](https://mlsanity.com/paper/1807.07207/) (2018)

## Built on by (most cited first, 5 of 5)

- [Domain-Shift-Aware Conformal Prediction for Large Language Models](https://mlsanity.com/paper/2510.05566/) (2025)
- [Diffusion Secant Alignment for Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2509.04852/) (2025)
- [A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2602.00834/) (2026)
- [One-Step Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2604.10672/) (2026)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)

## Abstract (arXiv)

Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for estimating the density ratio possibly lead to biased results if models are misspecified, while conventional non-parametric methods suffer from the curse of dimensionality when the dimension of data is large. To address these challenges, in this paper, we propose a novel approach for DRE based on the projection pursuit (PP) approximation. The proposed method leverages PP to mitigate the impact of high dimensionality while retaining the model flexibility needed for the accuracy of DRE. We establish the consistency and the convergence rate for the proposed estimator. Experimental results demonstrate that our proposed method outperforms existing alternatives in various applications.