# Trimmed Density Ratio Estimation

arXiv: https://arxiv.org/abs/1703.03216 · HTML: https://mlsanity.com/paper/1703.03216/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2017.

## Built on by (most cited first, 15 of 15)

- [Mandoline: Model Evaluation under Distribution Shift](https://mlsanity.com/paper/2107.00643/) (2021)
- [A Short Survey on Importance Weighting for Machine Learning](https://mlsanity.com/paper/2403.10175/) (2024)
- [Multiply Robust Federated Estimation of Targeted Average Treatment Effects](https://mlsanity.com/paper/2309.12600/) (2023)
- [Meta-Learning for Relative Density-Ratio Estimation](https://mlsanity.com/paper/2107.00801/) (2021)
- [A Unified Framework for Multi-distribution Density Ratio Estimation](https://mlsanity.com/paper/2112.03440/) (2021)
- [General Frameworks for Conditional Two-Sample Testing](https://mlsanity.com/paper/2410.16636/) (2024)
- [Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts](https://mlsanity.com/paper/2605.02072/) (2026)
- [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)
- [Estimation of Local Average Treatment Effect by Data Combination](https://mlsanity.com/paper/2109.05175/) (2021)
- [Density Ratio Estimation and Neyman Pearson Classification with Missing Data](https://mlsanity.com/paper/2302.10655/) (2023)
- [Towards Disentangled Preference Optimization Dynamics: Suppress the Loser, Preserve the Winner](https://mlsanity.com/paper/2604.18239/) (2026)
- [Unsupervised Change Detection using DRE-CUSUM](https://mlsanity.com/paper/2201.11678/) (2022)
- [One-Step Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2604.10672/) (2026)
- [Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination](https://mlsanity.com/paper/2512.09266/) (2025)

## Abstract (arXiv)

Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator which automatically identifies and trims outliers. The proposed estimator has a convex formulation, and the global optimum can be obtained via subgradient descent. We analyze the parameter estimation error of this estimator under high-dimensional settings. Experiments are conducted to verify the effectiveness of the estimator.