Graduate School and Research Center in Digital Sciences

Constraining the dynamics of deep probabilistic models

Lorenzi, Marco; Filippone, Maurizio

Submitted on ArXiV, February 2018

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on the dynamics of the functions they can model. 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 characterize the posterior distribution over model and constraint parameters through stochastic variational inference techniques. As a result, the proposed approach allows for accurate and scalable uncertainty quantification of predictions and 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 monotonic regression on 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.

Arxiv Bibtex

Title:Constraining the dynamics of deep probabilistic models
Department:Data Science
Eurecom ref:5467
Copyright: © EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Submitted on ArXiV, February 2018 and is available at :
Bibtex: @inproceedings{EURECOM+5467, year = {2018}, title = {{C}onstraining the dynamics of deep probabilistic models}, author = {{L}orenzi, {M}arco and {F}ilippone, {M}aurizio}, booktitle = {{S}ubmitted on {A}r{X}i{V}, {F}ebruary 2018 }, address = {}, month = {02}, url = {} }
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