The Statistical Approximation Hypothesis: A Cognitive Linguistic explanation for the effectiveness of function word frequency

The reason for the effectiveness of function word frequency in stylometry is still a mystery. Although some notable attempts have been made in the past to shed some light on this, like Kestemont (2014) or McMenamin (2002), these explanations are still rather unsatisfactory. For example, although one could argue that the frequency of a function word like the is part of the style of an author, it is still unclear why this is the case. In addition, any stylometric method based on frequency of single words is similarly implausible scientifically because the basic unit of language processing is not the word but something larger and more similar to a phrase (Sinclair 2004; Christiansen & Chater 2016; Langacker 1987).
In this paper I introduce a Theory of Linguistic Individuality based on Cognitive Linguistics that can explain the effectiveness of function word frequencies with the Statistical Approximation Hypothesis: the frequency of function words is a statistical approximation to the distribution of a person’s unique repository of basic linguistic units. This repository is idiosyncratic because of the processes of entrenchment (Schmid 2015) and chunking (Gobet et al. 2001). Despite their simplicity, methods compatible with this Theory, such as n-gram tracing (Grieve et al. 2019), outperform Delta as well as more sophisticated machine learning methods in tests on the English refcor corpus (Jannidis et al. 2015) and the c50 corpus (Houvardas & Stamatatos 2006). This finding is interpreted as indirect evidence in favour of the proposed hypothesis.

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