Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination
This work addresses challenges in density ratio and robust estimation for statistical learning, providing foundational non-asymptotic analysis, though it is incremental in extending existing methods.
The paper tackles robust density ratio estimation under heavy contamination, demonstrating that Weighted DRE achieves sparse consistency with non-asymptotic properties for unbounded density ratios and doubly strong robustness.
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.