# Adaptive Optimization for Prediction with Missing Data

arXiv: https://arxiv.org/abs/2402.01543 · HTML: https://mlsanity.com/paper/2402.01543/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Linear predictor on linearly-generated data with missing values: non consistency and solutions](https://mlsanity.com/paper/2002.00658/) (2020)
- [The Missing Indicator Method: From Low to High Dimensions](https://mlsanity.com/paper/2211.09259/) (2022)
- [What Is Meant by "Missing at Random"?](https://mlsanity.com/paper/1306.2812/) (2013)
- [An improved column-generation-based matheuristic for learning classification trees](https://mlsanity.com/paper/2308.11477/) (2023)
- [Black-Box Optimization in Machine Learning with Trust Region Based Derivative Free Algorithm](https://mlsanity.com/paper/1703.06925/) (2017)

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

- [Learning Data-Driven Uncertainty Set Partitions for Robust and Adaptive Energy Forecasting with Missing Data](https://mlsanity.com/paper/2503.20410/) (2025)
- [Probabilistic Prediction Markets with Intermittent Contributions](https://mlsanity.com/paper/2510.13385/) (2025)

## Abstract (arXiv)

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with missing data as a two-stage adaptive optimization problem and propose a new class of models, adaptive linear regression models, where the regression coefficients adapt to the set of observed features. We show that some adaptive linear regression models are equivalent to learning an imputation rule and a downstream linear regression model simultaneously instead of sequentially. We leverage this joint-impute-then-regress interpretation to generalize our framework to non-linear models. In settings where data is strongly not missing at random, our methods achieve a 2-10% improvement in out-of-sample accuracy.