Sequential Monte Carlo with kernel embedded mappings: The mapping particle filter

PULIDO, MANUEL; VAN LEEUWEN, PETER JAN

JOURNAL OF COMPUTATIONAL PHYSICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2019

0021-9991

In this work, a novel sequential Monte Carlo filter is introduced which aims at an efficient sampling of the state space.  Particles are pushed forward  from the prediction to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between the posterior and the sequence of intermediate densities. The sequence of mappings represents a gradient flow based on the principles of local optimal transport. A key ingredient of the mappings is that they are embedded in a reproducing kernel Hilbert space, which allows for a practical and efficient Monte Carlo algorithm. The kernel embedding provides a direct means to calculate the gradient of the Kullback-Leibler divergence leading to quick convergence using well-known gradient-based stochastic optimization algorithms. Evaluation of the method is conducted in the chaotic Lorenz-63 system,  the Lorenz-96 system, which is a coarse prototype of atmospheric dynamics, and an epidemic model that describes cholera dynamics. No resampling is required in the mapping particle filter even for long recursive sequences.The number of effective particles remains close to the total number of particles in all the sequence. Hence, the mapping particle filter does not suffer from sample impoverishment.