2014/11/27 by Sandro Gallo, Gallo, Sandro, Florencia Leonardi +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gene expression and cancer classification #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1411.7650
openalex publication_date 2014/11/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider the problem of estimating the context tree of a stationary\nergodic process with finite alphabet without imposing additional conditions on\nthe process. As a starting point we introduce a Hamming metric in the space of\nirreducible context trees and we use the properties of the weak topology in the\nspace of ergodic stationary processes to prove that if the Hamming metric is\nunbounded, there exist no consistent estimators for the context tree. Even in\nthe bounded case we show that there exist no two-sided confidence bounds.\nHowever we prove that one-sided inference is possible in this general setting\nand we construct a consistent estimator that is a lower bound for the context\ntree of the process with an explicit formula for the coverage probability. We\ndevelop an efficient algorithm to compute the lower bound and we apply the\nmethod to test a linguistic hypothesis about the context tree of codified\nwritten texts in European Portuguese.\n