Differentiable Likelihoods for Fast Inversion of 'Likelihood-free' Dynamical Systems

This repository contains the python code that was used for the paper

[1] Kersting, H., Krämer, N., Schiegg, M., Daniel, C., Tiemann, M., and Hennig, P. Differentiable likelihoods for fast inversion of ‘likelihood-free’ dynamical systems. In: Proceedings of the 37th International Conference on Machine Learning, Online, PMLR 119, 2020.**

and some related methods.

Contents

Linear state space models, Kalman filter, probabilistic solvers for ODEs, Markov Chain Monte Carlo simulation and more. The focus is on those methods that were introduced/used in the aforementioned paper.

Installation

In the root directory, run

pip install .

Requirements

numpy, scipy, matplotlib, dataclasses

Example

Below is a code snippet that applies a probabilistic ODE solver to an initial value problem based on a linear ODE.

from difflikelihoods import statespace
from difflikelihoods import odesolver
from difflikelihoods import ode
ibm = statespace.IBM(q=2, dim=1)
lin_ode = ode.LinearODE(t0=0.1, tmax=2.0, params=2.1, initval=0.9)
solver = odesolver.ODESolver(ibm, filtertype="kalman")
tsteps, means, stdevs = solver.solve(lin_ode, stepsize=0.01)

More examples are contained in the examples directory.

Experiments

The experiments from the paper are in the experiments folder and sorted as FigureN.ipynb. For example, the notebook for Figure 3 can be found in ./experiments/Figure3.ipynb. If you want to apply this algorithm to your own problems, those notebooks might be good starting points/tutorials.

Cite as

Please cite this work as

@article{kersting2020differentiable,
  title={Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems},
  author={Kersting, Hans and Kr{\"a}mer, Nicholas and Schiegg, Martin and Daniel, Christian and Tiemann, Michael and Hennig, Philipp},
  journal={Proceedings of the 37th International Conference on Machine Learning, Online, PMLR 119},
  year={2020}
}