  Many learning algorithms require categorical data to be transformed into real
vectors before it can be used as input. Often, categorical variables are
encoded as one-hot (or dummy) vectors. However, this mode of representation can
be wasteful since it adds many low-signal regressors, especially when the
number of unique categories is large. In this paper, we investigate simple
alternative solutions for universally consistent estimators that rely on
lower-dimensional real-valued representations of categorical variables that are
"sufficient" in the sense that no predictive information is lost. We then
compare preexisting and proposed methods on simulated and observational
datasets.
