Learning Optimized Or's of And's
  Or's of And's (OA) models are comprised of a small number of disjunctions of
conjunctions, also called disjunctive normal form. An example of an OA model is
as follows: If ($x_1 = $ `blue' AND $x_2=$ `middle') OR ($x_1 = $ `yellow'),
then predict $Y=1$, else predict $Y=0$. Or's of And's models have the advantage
of being interpretable to human experts, since they are a set of conditions
that concisely capture the characteristics of a specific subset of data. We
present two optimization-based machine learning frameworks for constructing OA
models, Optimized OA (OOA) and its faster version, Optimized OA with
Approximations (OOAx). We prove theoretical bounds on the properties of
patterns in an OA model. We build OA models as a diagnostic screening tool for
obstructive sleep apnea, that achieves high accuracy with a substantial gain in
interpretability over other methods.
