Context tree selection and linguistic rhythm retrieval from written texts

The starting point of this article is the question “How to retrieve fingerprints of rhythm in written texts?” We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.

💡 Research Summary

The paper tackles the problem of extracting rhythmic “fingerprints” from written texts, focusing on the two major dialects of Modern Portuguese: Brazilian Portuguese (BP) and European Portuguese (EP). Although the two varieties share virtually the same lexicon and produce sentences that look identical on the surface, linguistic theory predicts that they differ in the way stress and unstress patterns are organized—i.e., in their rhythm. The authors translate this linguistic question into a statistical model‑selection problem within the class of variable‑length Markov chains (VLMCs), also known as context‑tree models.

Data preparation. A corpus of over 1,200 sentences for each dialect was collected. Each sentence was automatically parsed into a sequence of three rhythmic symbols—stressed (S), unstressed (U), and neutral (N)—derived from prosodic rules that can be applied to orthographic text. This coding yields a discrete symbolic series that can be treated as a realization of a stochastic process.

Statistical framework. VLMCs allow the conditional distribution of the next symbol to depend on a context whose length varies with the past. All admissible contexts can be represented as nodes of a rooted tree (the context tree). Selecting the appropriate tree amounts to choosing which past patterns are truly predictive of the next rhythmic symbol. Traditionally, the Bayesian Information Criterion (BIC) is used:

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