# High-dimensional logistic regression with missing data: Imputation, regularization, and universality

arXiv: https://arxiv.org/abs/2410.01093 · HTML: https://mlsanity.com/paper/2410.01093/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 1 Oct 2024.

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

- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [A framework to characterize performance of LASSO algorithms](https://mlsanity.com/paper/1303.7291/) (2013)
- [The Lasso with general Gaussian designs with applications to hypothesis testing](https://mlsanity.com/paper/2007.13716/) (2020)
- [The Impact of Regularization on High-dimensional Logistic Regression](https://mlsanity.com/paper/1906.03761/) (2019)
- [The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime](https://mlsanity.com/paper/1911.01544/) (2019)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [Imputation for High-Dimensional Linear Regression](https://mlsanity.com/paper/2001.09180/) (2020)
- [Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspective](https://mlsanity.com/paper/2109.09859/) (2021)
- [Estimation and inference in metabolomics with non-random missing data and latent factors](https://mlsanity.com/paper/1909.02644/) (2019)

## Built on by (most cited first, 5 of 5)

- [When Pattern-by-Pattern Works: Theoretical and Empirical Insights for Logistic Models with Missing Values](https://mlsanity.com/paper/2507.13024/) (2025)
- [Optimal Transport with Heterogeneously Missing Data](https://mlsanity.com/paper/2505.17291/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Increasing Missingness to Reduce Bias: Richardson-SGD with Missing Data](https://mlsanity.com/paper/2605.19641/) (2026)
- [Beyond Second-Order Information: Paid Logistic Regression with Noisy Features](https://mlsanity.com/paper/2610.12919/) (2026)

## Abstract (arXiv)

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we provide exact characterizations of both the prediction error as well as the estimation error. Moreover, we show that these characterizations are universal: as long as the entries of the data matrix satisfy a set of independence and moment conditions, our guarantees continue to hold. Universality, in turn, enables the detailed study of several imputation-based strategies when the covariates are missing completely at random. We ground our study by comparing the performance of these strategies with the conjectured performance -- stemming from replica theory in statistical physics -- of the Bayes optimal procedure. Our analysis yields several insights including: (i) a distinction between single imputation and a simple variant of multiple imputation and (ii) that adding a simple ridge regularization term to single-imputed logistic regression can yield an estimator whose prediction error is nearly indistinguishable from the Bayes optimal prediction error. We supplement our findings with extensive numerical experiments.