PCs are a class of tractable models that allow efficient computations (such as conditional and marginal probabilities) while achieving state-of-the-art performance in some domains. The proposed approach takes both a PC and constraints as inputs, and outputs a new PC that satisfies the constraints. This is done efficiently via convex optimization without the need to retrain the entire model. Empirical evaluations indicate that the combination of constraints and PCs can have multiple use cases, including the improvement of model performance under scarce or incomplete data, as well as the enforcement of machine learning fairness measures into the model without compromising model fitness. We believe that these ideas will open possibilities for multiple other applications involving the combination of logics and deep probabilistic models.

Unsupervised anomaly detection models which are trained solely by healthy data, have gained importance in the recent years, as the annotation of medical data is a tedious task. Autoencoders and generative adversarial networks are the standard anomaly detection methods that are utilized to learn the data distribution. However, they fall short when it comes to inference and evaluation of the likelihood of test samples. We propose a novel combination of generative models and a probabilistic graphical model. After encoding image samples by autoencoders, the distribution of data is modeled by Random and Tensorized Sum-Product Networks ensuring exact and efficient inference at test time. We evaluate different autoencoder architectures in combination with Random and Tensorized Sum-Product Networks on mammography images using patch-wise processing and observe superior performance over utilizing the models standalone and state-of-the-art in anomaly detection for medical data.

TU Darmstadt Probabilistic deep learning currently receives an increased interest, as consistent treatment of uncertainty is one of the most important goals in machine learning and AI. Most current approaches, however, have severe limitations concerning inference. Sum-Product networks (SPNs), although having excellent properties in that regard, have so far not been explored as serious deep learning models, likely due to their special structural requirements. In this paper, we make a drastic simplification and use a random structure which is trained in a "classical deep learning manner" such as automatic differentiation, SGD, and GPU support. The resulting models, called RAT-SPNs, yield comparable prediction results to deep neural networks, but maintain well-calibrated uncertainty estimates which makes them highly robust against missing data. Furthermore, they successfully capture uncertainty over their inputs in a convincing manner, yielding robust outlier and peculiarity detection.