# Assumption-lean logistic regression with missing covariates

arXiv: https://arxiv.org/abs/2610.07292 · HTML: https://mlsanity.com/paper/2610.07292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 75 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 7 of 7)

- [Prediction-Powered Inference with Imputed Covariates and Nonuniform Sampling](https://mlsanity.com/paper/2501.18577/) (2025)
- [Imputation for High-Dimensional Linear Regression](https://mlsanity.com/paper/2001.09180/) (2020)
- [A Unified Framework for Inference with General Missingness Patterns and Machine Learning Imputation](https://mlsanity.com/paper/2508.15162/) (2025)
- [Imputation-Powered Inference](https://mlsanity.com/paper/2509.13778/) (2025)
- [Semi-supervised linear regression with missing covariates](https://mlsanity.com/paper/2602.13729/) (2026)
- [Towards Efficient Inference under Nonmonotone Missingness with General Imputation](https://mlsanity.com/paper/2509.24158/) (2025)
- [Instance-optimal stochastic convex optimization: Can we improve upon sample-average and robust stochastic approximation?](https://mlsanity.com/paper/2603.25657/) (2026)

## Abstract (arXiv)

Missing covariates are frequently encountered in supervised learning problems, and classical methods for estimation using such data use carefully chosen imputation schemes for missing data, or likelihood approximations that lead to nonconvex M-estimation problems. These methods and their relatives are suitable for scenarios in which the covariate distribution is known, and more broadly, have enjoyed tremendous success in linear models. But even in basic nonlinear problems such as logistic regression in moderate dimensions, such methods can experience drastic failure modes when the covariate distribution is unknown. Motivated by the need for reliable alternatives, we consider the problem of parameter estimation in logistic regression with missing covariates. Crucially, we operate in the assumption-lean setting where the covariate distribution is unknown (but bounded). We design a stochastic approximation method that is based on Z-estimation with a novel monotone operator, and establish that our algorithm is computationally efficient and achieves provable signal recovery at parametric rates under the hypothesis that covariates are missing completely at random. Our theory sharply characterizes the ℓ22 risk of the estimator in terms of the missingness profile, accommodating heterogeneous observation probabilities. Importantly, it shows that our method always outperforms the de facto ``complete-case'' estimator that ignores observations with any missing data. Even in the setting with homogeneous missingness (in which each covariate is observed independently with probability q), our bounds exhibit intricate and nonstandard dependence on q that can yield significant improvements over using only complete cases. We complement our upper bounds with new information-theoretic lower bounds that show that this intricate dependence on q is fundamental in a minimax sense.