  A sum-product network (SPN) is a graphical model that allows several types of
inferences to be drawn efficiently. There are two types of learning for SPNs:
Learning the architecture of the model, and learning the parameters. In this
paper, we tackle the second problem: We show how to learn the weights for the
sum nodes, assuming the architecture is fixed, and the data is horizontally
partitioned between multiple parties. The computations will preserve the
privacy of each participant. Furthermore, we will use secret sharing instead of
(homomorphic) encryption, which allows fast computations and requires little
computational resources. To this end, we use a novel integer division to
compute approximate real divisions. We also show how simple and private
evaluations can be performed using the learned SPN.
