Recent work has leveraged the popular distributionally robust optimization
paradigm to combat overfitting in classical logistic regression. While the resulting
classification scheme displays a promising performance in numerical experiments,
it is inherently limited to numerical features. In this paper, we show that distri-
butionally robust logistic regression with mixed (i.e., numerical and categorical)
features, despite amounting to an optimization problem of exponential size, ad-
mits a polynomial-time solution scheme. We subsequently develop a practically
efficient column-and-constraint approach that solves the problem as a sequence of
polynomial-time solvable exponential conic programs. Our model retains many
of the desirable theoretical features of previous works, but—in contrast to the
literature—it does not admit an equivalent representation as a regularized logistic
regression, that is, it represents a genuinely novel variant of logistic regression.
We show that our method outperforms both the unregularized and the regularized
logistic regression on categorical as well as mixed-feature benchmark instances.