Trainable Tree Distance and an Application to Question Categorisation

Continuing a line of work initiated in Boyer et al. (2007), the generalisation of stochastic string distance to a stochastic tree distance, specically to stochastic Tai distance, is considered. An issue in modifying Zhang/Shasha tree-distance for stochastic variants is noted, a Viterbi EM costadaptation algorithm for this distance is proposed and a counter-example noted to an all-paths EM proposal. Experiments are reported in which a kNN categorisation algorithm is applied to a semantically categorised, syntactically annotated corpus. We show that a 67.7% base-line using standard unitcosts can be improved to 72.5% by cost adaptation. 1 Theory and Algorithms The classification of syntactic structures into semantic categories arises in a number of settings. A possible approach to such a classifier is to compute a category for a test item based on its distances to a set of k nearest neighbours in a precategorised example set. This paper takes such an approach and deploying variants of a tree-distance measure, a measure which has been used with some success in a variety of semantically-oriented tasks such as Question-Answering, Entailment Recognition and Semantic Role Labelling (Punyakanok et al., 2004; Kouylekov and Magnini, 2005; Emms, 2006a; Emms, 2006b; Franco-Penya, 2010). An issue which will be considered is how to adapt the atomic costs underlying the tree-distance measure. Tai (1979) first proposed a tree-distance measure. Where S and T are ordered, labelled trees, a Tai mapping is a partial, 1-to-1 mapping σ from the nodes of S to the nodes of T , which respects leftto-right order and ancestry1, such as a