  We present a novel tractable generative model that extends Sum-Product
Networks (SPNs) and significantly boosts their power. We call it
Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate
conditional distributions into the model by direct computation using quotient
nodes, e.g. $P(A|B) = \frac{P(A,B)}{P(B)}$. We provide sufficient conditions
for the tractability of SPQNs that generalize and relax the decomposable and
complete tractability conditions of SPNs. These relaxed conditions give rise to
an exponential boost to the expressive efficiency of our model, i.e. we prove
that there are distributions which SPQNs can compute efficiently but require
SPNs to be of exponential size. Thus, we narrow the gap in expressivity between
tractable graphical models and other Neural Network-based generative models.
