Analyzing Word Frequencies in Large Text Corpora Using Inter-arrival Times and Bootstrapping

Comparing frequency counts over texts or corpora is an important task in many applications and scientific disciplines. Given a text corpus, we want to test a hypothesis, such as “word X is frequent”, “word X has become more frequent over time”, or “word X is more frequent in male than in female speech”. For this purpose we need a null model of word frequencies. The commonly used bag-of-words model, which corresponds to a Bernoulli process with fixed parameter, does not account for any structure present in natural languages. Using this model for word frequencies results in large numbers of words being reported as unexpectedly frequent. We address how to take into account the inherent occurrence patterns of words in significance testing of word frequencies. Based on studies of words in two large corpora, we propose two methods for modeling word frequencies that both take into account the occurrence patterns of words and go beyond the bag-of-words assumption. The first method models word frequencies based on the spatial distribution of individual words in the language. The second method is based on bootstrapping and takes into account only word frequency at the text level. The proposed methods are compared to the current gold standard in a series of experiments on both corpora. We find that words obey different spatial patterns in the language, ranging from bursty to non-bursty/uniform, independent of their frequency, showing that the traditional approach leads to many false positives.