# Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination

arXiv: https://arxiv.org/abs/2512.09266 · HTML: https://mlsanity.com/paper/2512.09266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model](https://mlsanity.com/paper/1506.00691/) (2015)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimator](https://mlsanity.com/paper/1904.06288/) (2019)
- [High Dimensional Robust Sparse Regression](https://mlsanity.com/paper/1805.11643/) (2018)
- [Robust Regression via Mutivariate Regression Depth](https://mlsanity.com/paper/1702.04656/) (2017)
- [Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression](https://mlsanity.com/paper/2305.00869/) (2023)
- [Trimmed Density Ratio Estimation](https://mlsanity.com/paper/1703.03216/) (2017)
- [Adapting to Continuous Covariate Shift via Online Density Ratio Estimation](https://mlsanity.com/paper/2302.02552/) (2023)
- [Two-sample inference for high-dimensional Markov networks](https://mlsanity.com/paper/1905.00466/) (2019)
- [Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity](https://mlsanity.com/paper/1909.05892/) (2019)
- [Support Consistency of Direct Sparse-Change Learning in Markov Networks](https://mlsanity.com/paper/1407.0581/) (2014)
- [Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation](https://mlsanity.com/paper/1304.6803/) (2013)
- [Learning Sparse Structural Changes in High-dimensional Markov Networks: A Review on Methodologies and Theories](https://mlsanity.com/paper/1701.01582/) (2017)

## Abstract (arXiv)

We examine the non-asymptotic properties of robust density ratio estimation (DRE) in contaminated settings. Weighted DRE is the most promising among existing methods, exhibiting doubly strong robustness from an asymptotic perspective. This study demonstrates that Weighted DRE achieves sparse consistency even under heavy contamination within a non-asymptotic framework. This method addresses two significant challenges in density ratio estimation and robust estimation. For density ratio estimation, we provide the non-asymptotic properties of estimating unbounded density ratios under the assumption that the weighted density ratio function is bounded. For robust estimation, we introduce a non-asymptotic framework for doubly strong robustness under heavy contamination, assuming that at least one of the following conditions holds: (i) contamination ratios are small, and (ii) outliers have small weighted values. This work provides the first non-asymptotic analysis of strong robustness under heavy contamination.