  Computing expected predictions of discriminative models is a fundamental task
in machine learning that appears in many interesting applications such as
fairness, handling missing values, and data analysis. Unfortunately, computing
expectations of a discriminative model with respect to a probability
distribution defined by an arbitrary generative model has been proven to be
hard in general. In fact, the task is intractable even for simple models such
as logistic regression and a naive Bayes distribution. In this paper, we
identify a pair of generative and discriminative models that enables tractable
computation of expectations, as well as moments of any order, of the latter
with respect to the former in case of regression. Specifically, we consider
expressive probabilistic circuits with certain structural constraints that
support tractable probabilistic inference. Moreover, we exploit the tractable
computation of high-order moments to derive an algorithm to approximate the
expectations for classification scenarios in which exact computations are
intractable. Our framework to compute expected predictions allows for handling
of missing data during prediction time in a principled and accurate way and
enables reasoning about the behavior of discriminative models. We empirically
show our algorithm to consistently outperform standard imputation techniques on
a variety of datasets. Finally, we illustrate how our framework can be used for
exploratory data analysis.
