Pure high-order word dependence mining via information geometry

The classical bag-of-word models fail to capture contextual associations between words. We propose to investigate the "high-order pure dependence" among a number of words forming a semantic entity, i.e., the high-order dependence that cannot be reduced to the random coincidence of lower-order dependence. We believe that identifying these high-order pure dependence patterns will lead to a better representation of documents. We first present two formal definitions of pure dependence: Unconditional Pure Dependence (UPD) and Conditional Pure Dependence (CPD). The decision on UPD or CPD, however, is a NP-hard problem. We hence prove a series of sufficient criteria that entail UPD and CPD, within the well-principled Information Geometry (IG) framework, leading to a more feasible UPD/CPD identification procedure. We further develop novel methods to extract word patterns with high-order pure dependence, which can then be used to extend the original unigram document models. Our methods are evaluated in the context of query expansion. Compared with the original unigram model and its extensions with term associations derived from constant n-grams and Apriori association rule mining, our IG-based methods have proved mathematically more rigorous and empirically more effective.