  Recent advances in analysis of subband amplitude envelopes of natural sounds
have resulted in convincing synthesis, showing subband amplitudes to be a
crucial component of perception. Probabilistic latent variable analysis is
particularly revealing, but existing approaches don't incorporate prior
knowledge about the physical behaviour of amplitude envelopes, such as
exponential decay and feedback. We use latent force modelling, a probabilistic
learning paradigm that incorporates physical knowledge into Gaussian process
regression, to model correlation across spectral subband envelopes. We augment
the standard latent force model approach by explicitly modelling correlations
over multiple time steps. Incorporating this prior knowledge strengthens the
interpretation of the latent functions as the source that generated the signal.
We examine this interpretation via an experiment which shows that sounds
generated by sampling from our probabilistic model are perceived to be more
realistic than those generated by similar models based on nonnegative matrix
factorisation, even in cases where our model is outperformed from a
reconstruction error perspective.
