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On the Relationship between SumProduct Networks and Bayesian Networks
"... In this paper, we establish some theoretical connections between SumProduct Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compac ..."
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In this paper, we establish some theoretical connections between SumProduct Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the local conditional probability distributions at each node in the resulting BN by exploiting contextspecific independence (CSI). The generated BN has a simple directed bipartite graphical structure. We show that by applying the Variable Elimination algorithm (VE) to the generated BN with ADD representations, we can recover the original SPN where the SPN can be viewed as a history record or caching of the VE inference process. To help state the proof clearly, we introduce the notion of normal SPN and present a theoretical analysis of the consistency and decomposability properties. We conclude the paper with some discussion of the implications of the proof and establish a connection between the depth of an SPN and a lower bound of the treewidth of its corresponding BN. 1.
On Theoretical Properties of SumProduct Networks
"... Abstract Sumproduct networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show ..."
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Abstract Sumproduct networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show that the weights of any complete and consistent SPN can be transformed into locally normalized weights without changing the SPN distribution. Second, we show that consistent SPNs cannot model distributions significantly (exponentially) more compactly than decomposable SPNs. As a third contribution, we extend the inference mechanisms known for SPNs with finite states to generalized SPNs with arbitrary input distributions.
Dynamic Sum Product Networks for Tractable Inference on Sequence Data
"... Abstract SumProduct Networks (SPN) have recently emerged as a new class of tractable probabilistic models. Unlike Bayesian networks and Markov networks where inference may be exponential in the size of the network, inference in SPNs is in time linear in the size of the network. Since SPNs represen ..."
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Abstract SumProduct Networks (SPN) have recently emerged as a new class of tractable probabilistic models. Unlike Bayesian networks and Markov networks where inference may be exponential in the size of the network, inference in SPNs is in time linear in the size of the network. Since SPNs represent distributions over a fixed set of variables only, we propose dynamic sum product networks (DSPNs) as a generalization of SPNs for sequence data of varying length. A DSPN consists of a template network that is repeated as many times as needed to model data sequences of any length. We present a local search technique to learn the structure of the template network. In contrast to dynamic Bayesian networks for which inference is generally exponential in the number of variables per time slice, DSPNs inherit the linear inference complexity of SPNs. We demonstrate the advantages of DSPNs over DBNs and other models on several datasets of sequence data.