SumProduct Networks: A New Deep Architecture
Abstract
The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sumproduct networks (SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and products as internal nodes, and weighted edges. We show that if an SPN is complete and consistent it represents the partition function and all marginals of some graphical model, and give semantics to its nodes. Essentially all tractable graphical models can be cast as SPNs, but SPNs are also strictly more general. We then propose learning algorithms for SPNs, based on backpropagation and EM. Experiments show that inference and learning with SPNs can be both faster and more accurate than with standard deep networks. For example, SPNs perform image completion better than stateoftheart deep networks for this task. SPNs also have intriguing potential connections to the architecture of the cortex.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 arXiv:
 arXiv:1202.3732
 Bibcode:
 2012arXiv1202.3732P
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Artificial Intelligence;
 Statistics  Machine Learning