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Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
Hans Kersting · Nicholas Krämer · Martin Schiegg · Christian Daniel · Michael Schober · Philipp Hennig

Tue Jul 14 10:00 AM -- 10:45 AM & Tue Jul 14 11:00 PM -- 11:45 PM (PDT) @

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.

Author Information

Hans Kersting (University of Tuebingen)
Nicholas Krämer (University of Tübingen)
Martin Schiegg (Bosch Center for Artificial Intelligence)
Christian Daniel (Bosch Center for Artificial Intelligence)
Michael Schober (Bosch Center for Artificial Intelligence)
Philipp Hennig (University of Tuebingen)

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