Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains

Authors

  • Alejandro Molina TU Dortmund
  • Antonio Vergari University of Bari
  • Nicola Di Mauro University of Bari
  • Sriraam Natarajan Indiana University
  • Floriana Esposito University of Bari
  • Kristian Kersting TU Darmstadt

Keywords:

sum-product networks, non-parametric density estimation, non-parameteric independency test, hybrid domains, mixed graphical models

Abstract

While all kinds of mixed data---from personal data, over panel and scientific data, to public and commercial data---are collected and stored, building probabilistic graphical models for these hybrid domains becomes more difficult. Users spend significant amounts of time in identifying the parametric form of the random variables (Gaussian, Poisson, Logit, etc.) involved and learning the mixed models. To make this difficult task easier, we propose the first trainable probabilistic deep architecture for hybrid domains that features tractable queries. It is based on Sum-Product Networks (SPNs) with piecewise polynomial leaf distributions together with novel nonparametric decomposition and conditioning steps using the Hirschfeld-Gebelein-Renyi Maximum Correlation Coefficient. This relieves the user from deciding a-priori the parametric form of the random variables but is still expressive enough to effectively approximate any distribution and permits efficient learning and inference.Our experiments show that the architecture, called Mixed SPNs, can indeed capture complex distributions across a wide range of hybrid domains.

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Published

2018-04-29

How to Cite

Molina, A., Vergari, A., Di Mauro, N., Natarajan, S., Esposito, F., & Kersting, K. (2018). Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1). Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/11731