Kernel embedding of maps for Bayesian inference: The variational mapping particle filter

PULIDO M.; VAN LEEUWEN, PETER JAN

Vienna

Conferencia; European Geophysical Conference; 2018

European Geophysical Union

Data assimilation for high-dimensional highly nonlinear systems is becoming crucial for several geosciencesapplications. In this work, a novel particle filter is introduced which aims to an efficient sampling of the posteriorpdf in high-dimensional state spaces considering a limited number of particles. Particles are mapped from theproposal to the posterior density using the principles of optimal transport. The Kullback-Leibler divergencebetween the posterior density and the proposal divergence is minimised using variational principles, leading to aniterative gradient-descent like algorithm. A key ingredient of the mapping is that the transformations are embeddedin a reproducing kernel Hilbert space which constrains the dimensions of the space for the optimal transport to thenumber of particles. Gradient information of the Kullback-Leibler divergence allows a quick convergence usingwell known gradient-based optimization algorithms from machine learning, adadelta and adam, which do notrequire cost function calculations.Evaluation of the method and comparison with a SIR filter is conducted as a proof-of-concept in the Lorenz-63system, where the exact solution is known. No resampling is required even for long recursive implementations.The number of effective particles remains close to the total number of particles in all the recursions. Hence,the mapping particle filter does not suffer from sample impoverishment, even in highly nonlinear settings.Finally, results from experiments on a high-dimensional turbulent geophysical system will be presented, and theperformance of the new method compared to other existing method will be discussed.