Bayesian modelling of music: algorithmic advances and experimental studies of shift-invariant sparse coding
University of London, Department of Electronic Engineering,
In order to perform many signal processing tasks such as classification,
pattern recognition and coding, it is helpful to specify a signal model in
terms of meaningful signal structures. In general, designing such a model
is complicated and for many signals it is not feasible to specify the appropriate
structure. Adaptive models overcome this problem by learning
structures from a set of signals. Such adaptive models need to be general
enough, so that they can represent relevant structures. However, more
general models often require additional constraints to guide the learning
In this thesis a sparse coding model is used to model time-series. Relevant
features can often occur at arbitrary locations and the model has to be
able to reflect this uncertainty, which is achieved using a shift-invariant
sparse coding formulation. In order to learn model parameters, we use
Bayesian statistical methods, however, analytic solutions to this learning
problem are not available and approximations have to be introduced. In
this thesis we study three approximations, one based on an analytical
integral approximation and two based on Monte Carlo approximations.
But even with these approximations, a solution to the learning problem
is computationally too expensive for the applications under investigation.
Therefore, we introduce further approximations by subset selection.
Music signals are highly structured time-series and offer an ideal testbed
for the studied model. We show the emergence of note- and score-like features
from a polyphonic piano recording and compare the results to those
obtained with a different model suggested in the literature. Furthermore,
we show that the model finds structures that can be assigned to an individual
source in a mixture. This is shown with an example of a mixture
containing guitar and vocal parts for which blind source separation can
be performed based on the shift-invariant sparse coding model.
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