Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
This work addresses a bottleneck in ODE inverse problems for researchers in computational science and machine learning, offering a more efficient alternative to existing likelihood-free approaches.
The paper tackled the problem of slow inference in likelihood-free dynamical systems by constructing a differentiable likelihood approximation using Gaussian ODE filtering, resulting in new solvers that outperform standard methods on three benchmark systems.
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.