Context models on sequences of covers

We consider estimation of a class of context models that can approximate partially observable Markov processes. This class is related to the context tree weighting algorithm for discrete sequence prediction (Willems et al., 1995). We present a constructive definition of a context process which extends the one proposed in (Dimitrakakis, 2010) for the estimation of variable order Markov models. The resulting class generalises the inference process from partition trees to cover trees and thus contains both variable order Markov models, mixtures of k-order Markov models, as well as other interesting types.