# Sharing pattern submodels for prediction with missing values

arXiv: https://arxiv.org/abs/2206.11161 · HTML: https://mlsanity.com/paper/2206.11161/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [Linear predictor on linearly-generated data with missing values: non consistency and solutions](https://mlsanity.com/paper/2002.00658/) (2020)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [What Is Meant by "Missing at Random"?](https://mlsanity.com/paper/1306.2812/) (2013)
- [Interpreting Classifiers through Attribute Interactions in Datasets](https://mlsanity.com/paper/1707.07576/) (2017)
- [Robust Prediction when Features are Missing](https://mlsanity.com/paper/1912.07226/) (2019)
- [Missing Data and Prediction](https://mlsanity.com/paper/1704.08192/) (2017)

## Built on by (most cited first, 7 of 7)

- [Interpretable Generalized Additive Models for Datasets with Missing Values](https://mlsanity.com/paper/2412.02646/) (2024)
- [Leveraging Predictive Equivalence in Decision Trees](https://mlsanity.com/paper/2506.14143/) (2025)
- [MINTY: Rule-based Models that Minimize the Need for Imputing Features with Missing Values](https://mlsanity.com/paper/2311.14108/) (2023)
- [HgbNet: predicting hemoglobin level/anemia degree from EHR data](https://mlsanity.com/paper/2401.12002/) (2024)
- [Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR](https://mlsanity.com/paper/2602.06713/) (2026)
- [Prediction Models That Learn to Avoid Missing Values](https://mlsanity.com/paper/2505.03393/) (2025)
- [Hypernetworks for Dynamic Feature Selection](https://mlsanity.com/paper/2605.12278/) (2026)

## Abstract (arXiv)

Missing values are unavoidable in many applications of machine learning and present challenges both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as a solution. However, fitting models independently does not make efficient use of all available data. Conversely, fitting a single shared model to the full data set relies on imputation which often leads to biased results when missingness depends on unobserved factors. We propose an alternative approach, called sharing pattern submodels, which i) makes predictions that are robust to missing values at test time, ii) maintains or improves the predictive power of pattern submodels, and iii) has a short description, enabling improved interpretability. Parameter sharing is enforced through sparsity-inducing regularization which we prove leads to consistent estimation. Finally, we give conditions for when a sharing model is optimal, even when both missingness and the target outcome depend on unobserved variables. Classification and regression experiments on synthetic and real-world data sets demonstrate that our models achieve a favorable tradeoff between pattern specialization and information sharing.