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June 2009 Testing statistical hypothesis on random trees and applications to the protein classification problem
Jorge R. Busch, Pablo A. Ferrari, Ana Georgina Flesia, Ricardo Fraiman, Sebastian P. Grynberg, Florencia Leonardi
Ann. Appl. Stat. 3(2): 542-563 (June 2009). DOI: 10.1214/08-AOAS218

Abstract

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov–Smirnov-type goodness-of-fit test proposed by Balding et al. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford–Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton–Watson related processes.

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Jorge R. Busch. Pablo A. Ferrari. Ana Georgina Flesia. Ricardo Fraiman. Sebastian P. Grynberg. Florencia Leonardi. "Testing statistical hypothesis on random trees and applications to the protein classification problem." Ann. Appl. Stat. 3 (2) 542 - 563, June 2009. https://doi.org/10.1214/08-AOAS218

Information

Published: June 2009
First available in Project Euclid: 22 June 2009

zbMATH: 1166.62079
MathSciNet: MR2750672
Digital Object Identifier: 10.1214/08-AOAS218

Keywords: Hypothesis testing , Protein classification , Random trees , variable length Markov chains

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 2 • June 2009
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