Medizinische Universität Graz Austria/Österreich  Forschungsportal  Medical University of Graz
Gewählte Publikation:
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Neuro
Krebs
Kardio
Lipid
Peharz, R; Gens, R; Pernkopf, F; Domingos, P.
On the Latent Variable Interpretation in SumProduct Networks
IEEE T PATTERN ANAL. 2017; 39(10): 20302044.
Web of Science
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 Autor/innen der Med Uni Graz:

Peharz Robert
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 Abstract:
 One of the central themes in SumProduct networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM algorithm and to efficiently perform MPE inference. In literature, the LV interpretation was justified by explicitly introducing the indicator variables corresponding to the LVs' states. However, as pointed out in this paper, this approach is in conflict with the completeness condition in SPNs and does not fully specify the probabilistic model. We propose a remedy for this problem by modifying the original approach for introducing the LVs, which we call SPN augmentation. We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sumweights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbistyle algorithm for MPE proposed in literature was never proven to be correct. We show that this is indeed a correct algorithm, when applied to selective SPNs, and in particular when applied to augmented SPNs. Our theoretical results are confirmed in experiments on synthetic data and 103 realworld datasets.
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Sumproduct networks

latent variables

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MPE inference