Density Ratio Estimation and Neyman Pearson Classification with Missing Data
This addresses the problem of biased DRE and classification in MNAR settings for machine learning practitioners, offering a novel adaptation with theoretical guarantees.
The paper tackled density ratio estimation (DRE) with missing not at random (MNAR) data, showing that standard methods are biased while their proposed M-KLIEP method restores consistency and achieves minimax optimal error bounds. They also adapted Neyman-Pearson classification to MNAR, controlling Type I error and achieving high power with promising empirical results on synthetic and real-world data.
Density Ratio Estimation (DRE) is an important machine learning technique with many downstream applications. We consider the challenge of DRE with missing not at random (MNAR) data. In this setting, we show that using standard DRE methods leads to biased results while our proposal (M-KLIEP), an adaptation of the popular DRE procedure KLIEP, restores consistency. Moreover, we provide finite sample estimation error bounds for M-KLIEP, which demonstrate minimax optimality with respect to both sample size and worst-case missingness. We then adapt an important downstream application of DRE, Neyman-Pearson (NP) classification, to this MNAR setting. Our procedure both controls Type I error and achieves high power, with high probability. Finally, we demonstrate promising empirical performance both synthetic data and real-world data with simulated missingness.