提出一种在严重污染下仍能稀疏准确估计密度比的新方法。
Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contamination
- 通过加权策略实现对异常值的双重稳健性
- 在重污染条件下仍能保证稀疏一致性
- 适合处理含大量异常数据的密度估计场景
我们研究了在污染环境下鲁棒密度比估计（DRE）的非渐近性质。加权DRE是现有方法中最具前景的，从渐近角度看具有双重强稳健性。本研究证明，在非渐近框架下，加权DRE在重污染条件下仍能实现稀疏一致性。该方法解决了密度比估计与鲁棒估计中的两个关键挑战：对于密度比估计，在加权密度比函数有界的假设下，给出了无界密度比的非渐近性质；对于鲁棒估计，引入了在重污染下的非渐近双重强稳健性框架，前提是满足以下任一条件：(i) 污染比例小，(ii) 异常值的加权值小。这是首次在重污染下对强稳健性进行非渐近分析。
原文摘要 · Abstract (English)
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.
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