Multi-scale Switching Linear Dynamical Systems

Abstract

Switching linear dynamic systems can monitor systems that operate in different regimes. In this article we introduce a class of multi-scale switching linear dynamical systems that are particularly suited if such regimes form a hierarchy. The setup consists of a specific switching linear dynamical system for every level of coarseness. Jeffrey's rule of conditioning is used to coordinate the models at the different levels. When the models are appropriately constrained, inference at finer levels can be performed independently for every subtree. This makes it possible to determine the required degree of detail on-line. The refinements of very improbable regimes need not be explored. The computational complexity of exact inference in both the standard and the multi-class switching linear dynamical system is exponential in the number of observations. We describe an appropriate approximate inference algorithm based on expectation propagation and relate it to a variant of the Bethe free energy.