Rao-Blackwellised Particle Filtering via Data Augmentation

SMC is often referred to as particle filtering (PF) in the context of computing filtering distributions for statistical inference and learning. It is known that the performance of PF often deteriorates in high-dimensional state spaces. In the past, we have shown that if a model admits partial analytical tractability, it is possible to combine PF with exact algorithms (Kalman filters, HMM filters, junction tree algorithm) to obtain efficient high dimensional filters (Doucet, de Freitas, Murphy and Russell 2000, Doucet, Godsill and Andrieu 2000). In particular, we exploited a marginalisation technique known as Rao-Blackwellisation (RB). Here, we attack a more complex model that does not admit immediate analytical tractability. This probabilistic model consists of Gaussian latent variables and binary observations.We show that by augmenting the model with artificial variables, it becomes possible to apply Rao-Blackwellisation and optimal sampling strategies. We focus on the problem of sequential binary classification (that is, when the data arrives one-at-a-time) using generic classifiers that consist of linear combinations of basis functions, whose coefficients evolve according to a Gaussian smoothness prior (Kitagawa and Gersch 1996). We have previously addressed this problem in the context of sequential fault detection in marine diesel engines (H0jen-S0rensen, de Freitas and Fog 2000). This application is of great importance as early detection of incipient faults can improve safety and efficiency, as well as, help to reduce downtime andplant maintenance in many industrial and transportation environments.