Gaussian tree constraints applied to acoustic linguistic functional data

Abstract

Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.

The correlation space of Gaussian latent tree models and model selection without fitting

“…Some of the methods described in this paper are particularly useful as part of an exploratory analysis for defining the relevant model search space, whereas others are ideal as a final step to check the conclusions of a model search. The complete semialgebraic structure of the correlation space has not been utilized elsewhere for assessing tree-compatibility of data, though the positivity constraint has been used previously, see Shiers et al (2014). Incorporating a prior such as the inverse-Wishart and sampling from the posterior distribution allows for probabilistic conclusions about the model.…”

“…Consider now the linguistic data set from Shiers et al (2014). This comprises phonetic functional spectrogram data from five Romance languages: French, Italian, Portuguese, and two forms of Spanish, namely American and Iberian.…”

“…Here the evolutionary dependencies between spoken numbers is studied with each extant language treated as a leaf vertex. The high dimensional spectrogram data is projected from 8100 dimensions to 15 dimensions using a variation of canonical variate analysis, the full details of which can be found in Shiers et al (2014). Each of the 15 canonical components projects the mean word data to obtain 15 new data sets referred to as canonical scores.…”

“…For illustration we focus on the candidate tree for the second component, which is displayed in Fig 1 . It is known from the analysis and expert interpretation in Shiers et al (2014) that this component is likely to relate to variation in vowel sounds, nasality, and the lip rounding of language speakers. By isolating these phonetic features and identifying an accompany tree that fits the data we can gain insights which may have otherwise been obscured.…”

Latent tree models

“…Moreover, with the burst of new genomic data, such as gene expression, phylogenetic models for continuous traits are again becoming important; see [43] and references therein. Latent tree models in this evolutionary context are also popular in linguistics [68,76], where a tree represents evolution of languages with modern languages represented by the leaves. The data here typically consists of the acoustic structure of spoken words and are continuous although there are also approaches using syntatic (discrete) data; see, for example, [41,78].…”