Bayesian modelling of music : algorithmic advances and experimental studies of shift-invariant sparse coding
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 procedure. 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.