# Prediction with Incomplete Data under Agnostic Mask Distribution Shift

arXiv: https://arxiv.org/abs/2305.11197 · HTML: https://mlsanity.com/paper/2305.11197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 13 of 13)

- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [Stable Prediction with Model Misspecification and Agnostic Distribution Shift](https://mlsanity.com/paper/2001.11713/) (2020)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [Stable Prediction across Unknown Environments](https://mlsanity.com/paper/1806.06270/) (2018)
- [Learning from Irregularly-Sampled Time Series: A Missing Data Perspective](https://mlsanity.com/paper/2008.07599/) (2020)
- [Causally Regularized Learning with Agnostic Data Selection Bias](https://mlsanity.com/paper/1708.06656/) (2017)
- [A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization](https://mlsanity.com/paper/2111.02355/) (2021)

## Abstract (arXiv)

Data with missing values is ubiquitous in many applications. Recent years have witnessed increasing attention on prediction with only incomplete data consisting of observed features and a mask that indicates the missing pattern. Existing methods assume that the training and testing distributions are the same, which may be violated in real-world scenarios. In this paper, we consider prediction with incomplete data in the presence of distribution shift. We focus on the case where the underlying joint distribution of complete features and label is invariant, but the missing pattern, i.e., mask distribution may shift agnostically between training and testing. To achieve generalization, we leverage the observation that for each mask, there is an invariant optimal predictor. To avoid the exponential explosion when learning them separately, we approximate the optimal predictors jointly using a double parameterization technique. This has the undesirable side effect of allowing the learned predictors to rely on the intra-mask correlation and that between features and mask. We perform decorrelation to minimize this effect. Combining the techniques above, we propose a novel prediction method called StableMiss. Extensive experiments on both synthetic and real-world datasets show that StableMiss is robust and outperforms state-of-the-art methods under agnostic mask distribution shift.