Music modeling with random fields

Abstract

Recent interest in the area of music information retrieval is exploding. However, very few of the existing music retrieval techniques take advantage of recent developments in statistical modeling. In this report we discuss an application of Random Fields to the problem of statistical modeling of polyphonic music. With such models in hand, the challenges of developing effective searching, browsing, and organization techniques for the growing bodies of music collections may be successfully met. 1 Polyphonic music can be thought of as a two-dimensional stochastic process. Unlike text, the musical vocabulary is relatively small, containing at most several hundred discrete note symbols. What makes music so fascinating and expressive is the very rich structure inherent in musical pieces. Whereas text samples can be reasonably modeled using simple unigram or bi-gram language models, polyphonic music is characterized by numerous periodic symmetries, repetitions, and overlapping shortand long-term interactions that are beyond the capabilities of simple Markov chains. Random Fields are a generalization of Markov chains to multidimensional spatial processes. They are incredibly flexible, allowing us to model arbitrary interactions between elements of data. Recently random fields have found applications in large-vocabulary tasks, such as language modeling and information extraction. One of the most influential works in the area is the 1997 publication of Della Pietra et al. [2], which outlined the algorithms used in parts of this paper. Berger et al. [1] were the first to suggest the use of maximum entropy models for natural language processing. While our work was inspired by applications of random fields to language processing, it bears more similarity to the use of the framework by the researchers in computer vision. In most natural language applications authors start with a reasonable set of features (which are usually single words, or hand-crafted expressions), and the main challenge is to optimize the weights corresponding to these features. This works well in natural language, where words bear significant semantic content. In our case, induction of the random field is the crucial step. We will use the techniques suggested by [2] to automatically induce new high-level, salient features, such as chords and melodic progressions.