Uncertainty Quantification

p1-25 January 21 15:10-16:10

Model error covariances estimation in the mapping particle filter using an online expectation-maximization algorithm

Tadeo Cocucci (FaMAF, UNCordoba, Argentina), Magdalena Lucini (University of Reading, UK), Peter Jan van Leeuwen (University of Reading, UK) and Manuel Pulido (University of Reading, UK)


The estimation of hyperparameters, such as model error and observational covariances, of hidden Markov models in sequential Monte Carlo techniques poses a big challenge. The posterior density associated to hyperparameters collapses when using the standard augmented state techniques. The expectation-maximization algorithm is a suitable method that permits to maximize the complete observation likelihood using observations distributed in time. However, the direct application of the expectation-maximization algorithm is prohibitive even for low dimensional spaces. This is because the complete likelihood calculation requires the application of a particle smoother for the whole sequence in each iteration of the algorithm. Based on the pioneer work of Neal and Hinton (1998), we develop an incremental expectation-maximization algorithm which changes the density for only the current state of the system. Under this approximation the algorithm only requires a sequential Monte Carlo filter and avoids the use of a smoother. The implementation combines the online expectation-maximization algorithm with the recently developed mapping particle filter to estimate model error covariances in the hidden Markov model. The evaluation is conducted in Lorenz-63 and Lorenz-96 experiments. An excellent convergence of the hyperparameters is obtained after 10-50 cycles. The only tuning parameter is the learning rate of the hyperparameters which is evaluated in twin experiments. A highly efficient algorithm is obtained since its application does not require a backward recursion except between the previous and the actual state variables.

Contact information

Prof. Manuel Pulido University of Reading