  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 leave distributions together with novel nonparametric decomposition
and conditioning steps using the Hirschfeld-Gebelein-R\'enyi 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 continuous distribution and permits efficient
learning and inference. Our empirical evidence shows that the architecture,
called Mixed SPNs, can indeed capture complex distributions across a wide range
of hybrid domains.
