Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes

Manuel Haussmann, Sebastian Gerwinn, Andreas Look, Barbara Rakitsch, Melih Kandemir

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Abstract

Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification of the large set of free parameters. This paper presents a recipe to improve the prediction accuracy of such models in three steps: i) accounting for epistemic uncertainty by assuming probabilistic weights, ii) incorporation of partial knowledge on the state dynamics, and iii) training the resultant hybrid model by an objective derived from a PAC-Bayesian generalization bound. We observe in our experiments that this recipe effectively translates partial and noisy prior knowledge into an improved model fit.
Original languageEnglish
Title of host publicationInternational Conference on Artificial Intelligence and Statistics : AISTATS
Volume130
Publication date2021
Publication statusPublished - 2021
Externally publishedYes
Event24th International Conference on Artificial Intelligence and Statistics - Virtual
Duration: 13. Apr 202115. Apr 2021

Conference

Conference24th International Conference on Artificial Intelligence and Statistics
LocationVirtual
Period13/04/202115/04/2021
SeriesProceedings of Machine Learning Research
Volume130
ISSN2640-3498

Keywords

  • cs.LG
  • stat.ML

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