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. (Formula presented.). 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.
|Original language||American English|
|Number of pages||9|
|State||Published - 2018|
|Event||21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018 - Playa Blanca, Lanzarote, Canary Islands, Spain|
Duration: 9 Apr 2018 → 11 Apr 2018
|Conference||21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018|
|City||Playa Blanca, Lanzarote, Canary Islands|
|Period||9/04/18 → 11/04/18|
Bibliographical noteFunding Information:
This work is supported by Intel grant ICRI-CI #9-2012-6133, by ISF Center grant 1790/12 and by the European Research Council (TheoryDL project).
Copyright 2018 by the author(s).