mlsanityData to 7 Oct 2026

Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination

arXiv 2512.09266 ↗First posted 10 Dec 2025stat.ML cs.LGcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 18 of its 49 references that are in the map. First posted on arXiv 10 Dec 2025.

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References · 18

  1. 2016Robust Estimators in High Dimensions without the Computational Intractabilitycited by 209
  2. 2016Agnostic Estimation of Mean and Covariancecited by 131
  3. 2020Telescoping Density-Ratio Estimationcited by 108
  4. 2021Density Ratio Estimation via Infinitesimal Classificationcited by 59
  5. 2015Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Modelcited by 47
  6. 2020Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimationcited by 43
  7. 2021Featurized Density Ratio Estimationcited by 33
  8. 2019Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimatorcited by 31
  9. 2018High Dimensional Robust Sparse Regressioncited by 29
  10. 2017Robust Regression via Mutivariate Regression Depthcited by 20
  11. 2023Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regressioncited by 17
  12. 2017Trimmed Density Ratio Estimationcited by 15
6 more
  1. 2023Adapting to Continuous Covariate Shift via Online Density Ratio Estimationcited by 15
  2. 2019Two-sample inference for high-dimensional Markov networkscited by 7
  3. 2019Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivitycited by 7
  4. 2014Support Consistency of Direct Sparse-Change Learning in Markov Networkscited by 6
  5. 2013Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimationcited by 3
  6. 2017Learning Sparse Structural Changes in High-dimensional Markov Networks: A Review on Methodologies and Theoriescited by 3

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