  Local structure such as context-specific independence (CSI) has received much
attention in the probabilistic graphical model (PGM) literature, as it
facilitates the modeling of large complex systems, as well as for reasoning
with them. In this paper, we provide a new perspective on how to learn CSIs
from data. We propose to first learn a functional and parameterized
representation of a conditional probability table (CPT), such as a neural
network. Next, we quantize this continuous function, into an arithmetic circuit
representation that facilitates efficient inference. In the first step, we can
leverage the many powerful tools that have been developed in the machine
learning literature. In the second step, we exploit more recently-developed
analytic tools from explainable AI, for the purposes of learning CSIs. Finally,
we contrast our approach, empirically and conceptually, with more traditional
variable-splitting approaches, that search for CSIs more explicitly.
