Constraining the Dynamics of Deep Probabilistic Models
This work addresses the need for flexible constraint integration in probabilistic modeling, offering a methodological framework that is incremental but enhances expressiveness and scalability for domain-specific tasks.
The authors tackled the problem of incorporating soft constraints on function dynamics in deep probabilistic models, achieving accurate and scalable uncertainty quantification with competitive results in applications like parameter inference in ODE models and monotonic regression of count data.
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.