Generative statistical models of chord sequences play crucial roles in music processing. To capture syntactic similarities among certain chords (e.g. in C major key, between G and G7 and between F and Dm), we study hidden Markov models and probabilistic context-free grammar models with latent variables describing syntactic categories of chord symbols and their unsupervised learning techniques for inducing the latent grammar from data. Surprisingly, we find that these models often outperform conventional Markov models in predictive power, and the self-emergent categories often correspond to traditional harmonic functions. This implies the need for chord categories in harmony models from the informatics perspective.
Unsupervised learning of PCFG models was studied in the context of grammar induction and parsing @cite_6 . The maximum likelihood estimation using the EM algorithm and Bayesian estimation using GS were compared and the latter method was shown to give higher accuracies in some cases. It was argued that even though for both learning schemes fully unsupervised grammar induction using simple PCFG models is difficult, Bayesian learning seems to induce more meaningful grammar owing to its ability to prefer sparse grammars.
@cite_6
2164151151
This paper presents two Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of probabilistic context free grammars (PCFGs) from terminal strings, providing an alternative to maximum-likelihood estimation using the Inside-Outside algorithm. We illustrate these methods by estimating a sparse grammar describing the morphology of the Bantu language Sesotho, demonstrating that with suitable priors Bayesian techniques can infer linguistic structure in situations where maximum likelihood methods such as the Inside-Outside algorithm only produce a trivial grammar.