Robust Estimation of Context Trees (Simulations)

We consider m independent samples (strings) where each sample come from one of two possible Variable Memory Markov Chain with context tree T or T', respectively. Each sample is generated from tree T with probability p or tree T' with probability (1-p), 1/2 < p <1, that is, we consider the mixture model p T + (1-p) T', 1/2 < p <1. We propose a robust procedure to estimate T. Our procedure is based on a robust function applied to the rate entropy between two trees. We show that the proposed procedure is robust and we show four scenarios simulation.