2018/02/15 by Marco Lorenzi, Lorenzi, Marco, Maurizio Filippone +1 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1802.05680
openalex publication_date 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives of a given order are subject to inequality or equality constraints. We then characterize the posterior distribution over model and constraint parameters through stochastic variational inference. As a result, the proposed approach allows for accurate and scalable uncertainty quantification on the predictions and on all parameters. We demonstrate the application of equality constraints in the challenging problem of parameter inference in ordinary differential equation models, while we showcase the application of inequality constraints on the problem of monotonic regression of count data. The proposed approach is extensively tested in several experimental settings, leading to highly competitive results in challenging modeling applications, while offering high expressiveness, flexibility and scalability.