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doi:10.1016/S0004-3702(02)00192-3 
Copyright © 2002 Elsevier Science B.V. All rights reserved.
A hybrid graphical model for rhythmic parsing*1
Christopher Raphael
Received 4 October 2001.
Abstract
A method is presented for the rhythmic parsing problem: Given a sequence of observed musical note onset times, we simultaneously estimate the corresponding notated rhythm and tempo process. A graphical model is developed that represents the evolution of tempo and rhythm and relates these hidden quantities to an observable performance. The rhythm variables are discrete and the tempo and observation variables are continuous. We show how to compute the globally most likely configuration of the tempo and rhythm variables given an observation of note onset times. Experiments are presented on both MIDI data and a data set derived from an audio signal. A generalization to computing MAP estimates for arbitrary conditional Gaussian distributions is outlined.
Author Keywords: Conditional Gaussian distribution; Rhythmic parsing; MAP estimate; Dynamic programming; Music recognition; Hybrid graphical model
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*1 This is an extended version of the paper presented at the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), Seattle, WA, USA. This work is supported by NSF grants IIS-0113496 and IIS-9987898.
