The two main types of deep learning are function approximation and probability estimation. Function approximators like convolutional neural networks are robust and allow for real-time inference, but are very inflexible, requiring fixed inputs and outputs and detailed supervision. Probability estimators like deep Boltzmann machines allow arbitrary inputs and outputs and require no supervision, but are not robust and do not allow real-time inference. Both are very opaque. Sum-product networks (SPNs) are a new class of deep models that are suitable for both function approximation and probability estimation. SPNs allow for real-time inference, are robust and comprehensible, and are highly flexible, with any choice of inputs and outputs and any amount of supervision. I will present generative and discriminative algorithms for learning SPN weights, and an algorithm for learning SPN structure. SPNs have achieved impressive results in a wide variety of domains, including object recognition, image completion, activity recognition, language modeling, collaborative filtering, and click prediction, and are arguably the most powerful class of deep models available today. (Joint work with Abe Friesen, Rob Gens, Mathias Niepert and Hoifung Poon.)

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