  Sum-Product Networks (SPNs) are hierarchical, graphical models that combine
benefits of deep learning and probabilistic modeling. SPNs offer unique
advantages to applications demanding exact probabilistic inference over
high-dimensional, noisy inputs. Yet, compared to convolutional neural nets,
they struggle with capturing complex spatial relationships in image data. To
alleviate this issue, we introduce Deep Generalized Convolutional Sum-Product
Networks (DGC-SPNs), which encode spatial features in a way similar to CNNs,
while preserving the validity of the probabilistic SPN model. As opposed to
existing SPN-based image representations, DGC-SPNs allow for overlapping
convolution patches through a novel parameterization of dilations and strides,
resulting in significantly improved feature coverage and feature resolution.
DGC-SPNs substantially outperform other SPN architectures across several visual
datasets and for both generative and discriminative tasks, including image
inpainting and classification. These contributions are reinforced by the first
simple, scalable, and GPU-optimized implementation of SPNs, integrated with the
widely used Keras/TensorFlow framework. The resulting model is fully
probabilistic and versatile, yet efficient and straightforward to apply in
practical applications in place of traditional deep nets.
