Context tree estimation for not necessarily finite memory processes, via BIC and MDL

I. Csiszar, Z. Talata
2005 Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.  
The concept of context tree, usually defined for finite memory processes, is extended to arbitrary stationary ergodic processes (with finite alphabet). These context trees are not necessarily complete, and may be of infinite depth. The familiar BIC and MDL principles are shown to provide strongly consistent estimators of the context tree, via optimization of a criterion for hypothetical context trees of finite depth, allowed to grow with the sample size as
doi:10.1109/isit.2005.1523438 dblp:conf/isit/CsiszarT05 fatcat:ipphfazck5hjhje3tyoel2we3y