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.
 This paper defines a generative probabilistic model of parse trees, which we call PCFG-LA. This model is an extension of PCFG in which non-terminal symbols are augmented with latent variables. Fine-grained CFG rules are automatically induced from a parsed corpus by training a PCFG-LA model using an EM-algorithm. Because exact parsing with a PCFG-LA is NP-hard, several approximations are described and empirically compared. In experiments using the Penn WSJ corpus, our automatically trained model gave a performance of 86.6 (F1, sentences ≤ 40 words), which is comparable to that of an unlexicalized PCFG parser created using extensive manual feature selection. The kinds of tree representations used in a treebank corpus can have a dramatic effect on performance of a parser based on the PCFG estimated from that corpus, causing the estimated likelihood of a tree to differ substantially from its frequency in the training corpus. This paper points out that the Penn II treebank representations are of the kind predicted to have such an effect, and describes a simple node relabeling transformation that improves a treebank PCFG-based parser's average precision and recall by around 8 , or approximately half of the performance difference between a simple PCFG model and the best broad-coverage parsers available today. This performance variation comes about because any PCFG, and hence the corpus of trees from which the PCFG is induced, embodies independence assumptions about the distribution of words and phrases. The particular independence assumptions implicit in a tree representation can be studied theoretically and investigated empirically by means of a tree transformation detransformation process.