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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.
We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of emph{partia
By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably approximately corre
We propose a meta-learning approach that learns from multiple tasks in a transductive setting, by leveraging the unlabeled query set in addition to the support set to generate a more powerful model for each task. To develop our framework, we revisit
While the decision-theoretic optimality of the Bayesian formalism under correct model specification is well-known (Berger 2013), the Bayesian case becomes less clear under model misspecification (Grunwald 2017; Ramamoorthi 2015; Fushiki 2005). To for
Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in real-world p