  Probabilistic representations, such as Bayesian and Markov networks, are
fundamental to much of statistical machine learning. Thus, learning
probabilistic representations directly from data is a deep challenge, the main
computational bottleneck being inference that is intractable. Tractable
learning is a powerful new paradigm that attempts to learn distributions that
support efficient probabilistic querying. By leveraging local structure,
representations such as sum-product networks (SPNs) can capture high tree-width
models with many hidden layers, essentially a deep architecture, while still
admitting a range of probabilistic queries to be computable in time polynomial
in the network size. While the progress is impressive, numerous data sources
are incomplete, and in the presence of missing data, structure learning methods
nonetheless revert to single distributions without characterizing the loss in
confidence. In recent work, credal sum-product networks, an imprecise extension
of sum-product networks, were proposed to capture this robustness angle. In
this work, we are interested in how such representations can be learnt and thus
study how the computational machinery underlying tractable learning and
inference can be generalized for imprecise probabilities.
