Bayesian Identification of Cognates and Correspondences

Prague, June 2007. c ©2007 Association for Computational Linguistics Bayesian Identi ation of Cognates and Corresponden es T. Mark Ellison Linguisti s, University of Western Australia, and Analith Ltd mark markellison.net Abstra t This paper presents a Bayesian approa h to omparing languages: identifying ognates and the regular orresponden es that ompose them. A simple model of language is extended to in lude these notions in an a ount of parent languages. An expression is developed for the posterior probability of hild language forms given a parent language. Bayes' Theorem o ers a s hema for evaluating hoi es of ognates and orresponden es to explain semanti ally mat hed data. An implementation optimising this value with gradient des ent is shown to distinguish ognates from nonognates in data from Polish and Russian. Modern histori al linguisti s addresses questions like the following. How did language originate? What were histori ally-re orded languages like? How related are languages? What were the an estors of modern languages like? Re ently, omputation has be ome a key tool in addressing su h questions. Kirby (2002) gives an overview of urrent urrent work on how language evolved, mu h of it based on omputational models and simulations. Ellison (1992) presents a linguisti ally motivated method for lassifying onsonants as onsonants or vowels. An unexpe ted result for the dead language Gothi provides added weight to one of two ompeting phonologi al interpretations of the orthography of this dead language. Other re ent work has applied omputational methods for phylogeneti s to measuring linguisti distan es, and/or onstru ting taxonomi trees from distan es between languages and diale ts (Dyen et al., 1992; Ringe et al., 2002; Gray and Atkinson, 2003; M Mahon and M Mahon, 2003; Nakleh et al., 2005; Ellison and Kirby, 2006). A entral fo us of histori al linguisti s is the re onstru tion of parent languages from the eviden e of their des endents. In histori al linguisti s proper, this is done by the omparative method (Je ers and Lehiste, 1989; Ho k, 1991) in whi h shared arbitrary stru ture is assumed to re e t ommon origin. At the phonologi al level, re onstru tion identi es ognates and orresponden es, and then onstru ts sound hanges whi h explain them. This paper presents a Bayesian approa h to assessing ognates and orresponden es. Best sets of ognates and orresponden es an then be identi ed by gradient as ent on this evaluation measure. While the work is motivated by the eventual goal of o ering software solutions to histori al linguisti s, it also hopes to show that Bayes' theorem applied to an expli it, simple model of language an lead to a prin ipled and tra table method for identifying ognates. The stru ture of the paper is as follows. The next se tion details the notions of histori al linguisti s needed for this paper. Se tion 2 formally de nes a model of language and parent language. The subsequent se tion situates the work amongst similar work in the literature,