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

## TL;DR

This paper introduces a novel framework for handling missing features in classifiers by computing expected predictions over feature distributions, using geometric programming to embed logistic regression, and providing explanations for classifications.

## Contribution

It proposes a new method that accurately predicts with missing features, embedding logistic regression into a probabilistic model and offering feature importance explanations.

## Key findings

- Achieves performance comparable to full-feature logistic regression.
- Outperforms standard imputation techniques with missing features.
- Provides interpretable feature removal explanations.

## Abstract

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.