Exponential inequalities for empirical unbounded context trees

2007/10/31 by Antonio Galves, Galves, Antonio, Florencia Leonardi +1
Biochemistry, Genetics and Molecular Biology · #60G99 #62M09 #FOS: Mathematics #Gene Regulatory Network Analysis #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0710.5900

openalex publication_date 2007/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field.

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