  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.
