Computer Science Colloquium

Hidden Markov Models of Musical Structure

Panos Mavromatis
Assistant Professor of Music and Performing Arts Professions
Steinhardt School, New York University

Friday, January 25, 2008 11:30 A.M.
Room 1302 Warren Weaver Hall
251 Mercer Street
New York, NY 10012-1110

Directions: http://cs.nyu.edu/csweb/Location/directions.html
Colloquium Information: http://cs.nyu.edu/csweb/Calendar/colloquium/index.html

Host

Ernest Davis, davise@cs.nyu.edu, (212) 998-3123

Synopsis

This talk explores the application of Hidden Markov Models (HMMs) to the extraction of structural rules from a musical corpus. These rules capture syntactic constraints among musical variables and/or related non-musical variables, such as word stress of sung text. The technique allows a systematic exploration of the unconscious internalized musical knowledge possessed by experts, which is usually not amenable to other types of analysis.

Identifying the best HMM for a musical corpus breaks down into two sub-problems: (i) identifying the model topology (how states and transitions are connected) and (ii) for a given topology, identifying the model parameters (transition and output probabilities). Subproblem (ii) is adequately addressed by the Baum-Welch (BW) algorithm. Here we emphasize subproblem (i), as it is essential for the grammatical interpretation of the HMM. We show how a systematic search on the space of model topologies can be carried out using state-merging, state-splitting, or a combination of the two. This search is governed by a cost function based on the Minimum Description Length principle. This function is designed to reward goodness-of-fit while penalizing model complexity to safeguard against overfitting. We present several applications of the technique using real and artificial corpora that exemplify different types of syntactic patterns.

Bio

Panos Mavromatis (BA, MA Mathematics, Cambridge University; MA Physics, Boston University; PhD Music Theory, Eastman School of Music) is a professor of Music Theory at NYU Steinhardt's Department of Music and Performing Arts, where he directs the music theory program. His work focuses on the computational modeling of music theory and cognition. His research interests include machine learning applications to music, and more recently, intelligent tutoring systems for the development of musical skill.

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