Monte Carlo Methods for Tempo Tracking and Rhythm Quantization
  We present a probabilistic generative model for timing deviations in
expressive music performance. The structure of the proposed model is equivalent
to a switching state space model. The switch variables correspond to discrete
note locations as in a musical score. The continuous hidden variables denote
the tempo. We formulate two well known music recognition problems, namely tempo
tracking and automatic transcription (rhythm quantization) as filtering and
maximum a posteriori (MAP) state estimation tasks. Exact computation of
posterior features such as the MAP state is intractable in this model class, so
we introduce Monte Carlo methods for integration and optimization. We compare
Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated
annealing and iterative improvement) and sequential Monte Carlo methods
(particle filters). Our simulation results suggest better results with
sequential methods. The methods can be applied in both online and batch
scenarios such as tempo tracking and transcription and are thus potentially
useful in a number of music applications such as adaptive automatic
accompaniment, score typesetting and music information retrieval.
