Estimating topological entropy via a symbolic data compression technique.

We estimate topological entropy via symbolic dynamics using a data compression technique called the context-tree weighting method. Unlike other symbolic dynamical approaches, which often have to choose ad hoc parameters such as the depth of a tree, the context-tree weighting method is almost parameter-free and infers the transition structure of the system as well as transition probabilities. Our examples, including a Markov model, the logistic map, and the Hénon map, demonstrate that the convergence is fast: one obtains the theoretically correct topological entropy with a relatively short symbolic sequence.

Context-tree modeling of observed symbolic dynamics.

Modern techniques invented for data compression provide efficient automated algorithms for the modeling of the observed symbolic dynamics. We demonstrate the relationship between coding and modeling, motivating the well-known minimum description length (MDL) principle, and give concrete demonstrations of the "context-tree weighting" and "context-tree maximizing" algorithms. The predictive modeling technique obviates many of the technical difficulties traditionally associated with the correct MDL analyses.