  In several domains obtaining class annotations is expensive while at the same
time unlabelled data are abundant. While most semi-supervised approaches
enforce restrictive assumptions on the data distribution, recent work has
managed to learn semi-supervised models in a non-restrictive regime. However,
so far such approaches have only been proposed for linear models. In this work,
we introduce semi-supervised parameter learning for Sum-Product Networks
(SPNs). SPNs are deep probabilistic models admitting inference in linear time
in number of network edges. Our approach has several advantages, as it (1)
allows generative and discriminative semi-supervised learning, (2) guarantees
that adding unlabelled data can increase, but not degrade, the performance
(safe), and (3) is computationally efficient and does not enforce restrictive
assumptions on the data distribution. We show on a variety of data sets that
safe semi-supervised learning with SPNs is competitive compared to
state-of-the-art and can lead to a better generative and discriminative
objective value than a purely supervised approach.
