  A typical audio signal processing pipeline includes multiple disjoint
analysis stages, including calculation of a time-frequency representation
followed by spectrogram-based feature analysis. We show how time-frequency
analysis and nonnegative matrix factorisation can be jointly formulated as a
spectral mixture Gaussian process model with nonstationary priors over the
amplitude variance parameters. Further, we formulate this nonlinear model's
state space representation, making it amenable to infinite-horizon Gaussian
process regression with approximate inference via expectation propagation,
which scales linearly in the number of time steps and quadratically in the
state dimensionality. By doing so, we are able to process audio signals with
hundreds of thousands of data points. We demonstrate, on various tasks with
empirical data, how this inference scheme outperforms more standard techniques
that rely on extended Kalman filtering.
