# What to Expect of Classifiers? Reasoning about Logistic Regression with Missing Features

arXiv: https://arxiv.org/abs/1903.01620 · HTML: https://mlsanity.com/paper/1903.01620/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 12 of 12)

- [Probabilistic Sufficient Explanations](https://mlsanity.com/paper/2105.10118/) (2021)
- [Efficient Explanations With Relevant Sets](https://mlsanity.com/paper/2106.00546/) (2021)
- [A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queries](https://mlsanity.com/paper/2102.06137/) (2021)
- [Bayesian Structure Scores for Probabilistic Circuits](https://mlsanity.com/paper/2302.12130/) (2023)
- [MisConv: Convolutional Neural Networks for Missing Data](https://mlsanity.com/paper/2110.14010/) (2021)
- [Semantic Probabilistic Control of Language Models](https://mlsanity.com/paper/2505.01954/) (2025)
- [When is the Computation of a Feature Attribution Method Tractable?](https://mlsanity.com/paper/2501.02356/) (2025)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Tractable Computation of Expected Kernels](https://mlsanity.com/paper/2102.10562/) (2021)
- [Even More Guarantees for Variational Inference in the Presence of Symmetries](https://mlsanity.com/paper/2604.21407/) (2026)
- [On Logic-Based Explainability with Partially Specified Inputs](https://mlsanity.com/paper/2306.15803/) (2023)
- [Learning from Uncertain Data: From Possible Worlds to Possible Models](https://mlsanity.com/paper/2405.18549/) (2024)

## Abstract (arXiv)

While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were trained on. In this paper, we propose a novel framework that classifies examples with missing features by computing the expected prediction with respect to a feature distribution. Moreover, we use geometric programming to learn a naive Bayes distribution that embeds a given logistic regression classifier and can efficiently take its expected predictions. Empirical evaluations show that our model achieves the same performance as the logistic regression with all features observed, and outperforms standard imputation techniques when features go missing during prediction time. Furthermore, we demonstrate that our method can be used to generate "sufficient explanations" of logistic regression classifications, by removing features that do not affect the classification.