# Density Ratio Estimation and Neyman Pearson Classification with Missing Data

arXiv: https://arxiv.org/abs/2302.10655 · HTML: https://mlsanity.com/paper/2302.10655/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 9 of 9)

- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Sub-sampled Cubic Regularization for Non-convex Optimization](https://mlsanity.com/paper/1705.05933/) (2017)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [Neyman-Pearson (NP) classification algorithms and NP receiver operating characteristics (NP-ROC)](https://mlsanity.com/paper/1608.03109/) (2016)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Trimmed Density Ratio Estimation](https://mlsanity.com/paper/1703.03216/) (2017)
- [Subsampling Generative Adversarial Networks: Density Ratio Estimation in Feature Space with Softplus Loss](https://mlsanity.com/paper/1909.10670/) (2019)

## Built on by (most cited first, 2 of 2)

- [Minimizing f-Divergences by Interpolating Velocity Fields](https://mlsanity.com/paper/2305.15577/) (2023)
- [One-Step Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2604.10672/) (2026)

## Abstract (arXiv)

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.