A particle filtering based kernel HMM predictor

A novel kernel algorithm is proposed for nonlinear prediction whereby the signal is modelled as a state of a hidden Markov model (HMM). The transition function of the HMM is approximated using kernels, whose weights are also part of the state of the system and are learnt in an unsupervised fashion by a sample importance resampling (SIR) particle filter. The SIR proposal density is designed so as to maintain a diverse population of particles, thus avoiding particle degeneracy arising from inaccuracies of early model estimates. The kernel HMM algorithm is further equipped with a sparsification criterion based on approximate linear dependence and its performance is evaluated against the KNLMS and KRLS algorithms for the prediction of synthetic signals and real world point-of-gaze data.