Comparing models of symbolic music using probabilistic grammars and probabilistic programming

We conduct a systematic comparison of several probabilistic models of symbolic music, including zeroth and first order Markov models over pitches and intervals, a hidden Markov model over pitches, and a probabilistic context free grammar with two parameterisations, all implemented uniformly using a probabilistic programming language (PRISM). This allows us to take advantage of variational Bayesian methods for learning parameters and assessing the goodness of fit of the models in a principled way. When applied to a corpus of Bach chorales and the Essen folk song collection, we show that, depending on various parameters, the probabilistic grammars sometimes but not always out-perform the simple Markov models. On looking for evidence of over- fitting of complex models to small datasets, we find that even the smallest dataset is sufficient to support the richest parameterisation of the probabilistic grammars. However, examining how the models perform on smaller subsets of pieces, we find that the simpler Markov models do indeed out-perform the best grammar-based model at the small end of the scale.