  Automatic music transcription (AMT) aims to infer a latent symbolic
representation of a piece of music (piano-roll), given a corresponding observed
audio recording. Transcribing polyphonic music (when multiple notes are played
simultaneously) is a challenging problem, due to highly structured overlapping
between harmonics. We study whether the introduction of physically inspired
Gaussian process (GP) priors into audio content analysis models improves the
extraction of patterns required for AMT. Audio signals are described as a
linear combination of sources. Each source is decomposed into the product of an
amplitude-envelope, and a quasi-periodic component process. We introduce the
Mat\'ern spectral mixture (MSM) kernel for describing frequency content of
singles notes. We consider two different regression approaches. In the sigmoid
model every pitch-activation is independently non-linear transformed. In the
softmax model several activation GPs are jointly non-linearly transformed. This
introduce cross-correlation between activations. We use variational Bayes for
approximate inference. We empirically evaluate how these models work in
practice transcribing polyphonic music. We demonstrate that rather than
encourage dependency between activations, what is relevant for improving pitch
detection is to learnt priors that fit the frequency content of the sound
events to detect.
