Visualizing and Understanding Sum-Product Networks

TL;DR

This paper explores the inner representations of Sum-Product Networks (SPNs) using visualization techniques, evaluates their effectiveness as feature extractors, and compares them with other models in classification tasks.

Contribution

It provides new insights into SPN internal workings, introduces visualization methods for their interpretability, and empirically assesses their utility in feature extraction and model comparison.

Findings

SPNs' node activations can be visualized to understand their representations.

SPNs' embeddings are competitive with popular feature extractors like RBMs.

Random probabilistic queries can be used to compare different tractable models.

Abstract

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.