This paper presents a statistical method called Infinite Latent Harmonic Allocation (iLHA) for detecting multiple fundamentalfrequenciesin polyphonicaudiosignals. Conventional methods face a crucial problem known as model selection becausetheyassume thatthe observedspectra are superpositions of a certain fixed number of bases (sound sources and/or finer parts). iLHA avoids this problem by assuming that the observed spectra are superpositions of a stochastically-distributed unbounded (theoretically infinite) number of bases. Such uncertainty can be treated in a principled way by leveraging the state-of-the-art paradigm of machine-learning called Bayesian nonparametrics. To represent a set of time-sliced spectral strips, we formulated nested infinite Gaussian mixture models (GMMs) based on hierarchical and generalized Dirichlet processes. Each strip is allowed to contain an unbounded number of sound sources (GMMs), each of which is allowed to contain an unbounded number of harmonic partials (Gaussians). To train the nested infinite GMMs efficiently, we used a modern inference technique called collapsed variational Bayes (CVB). Our experiments using audio recordingsof real piano and guitar performances showed that fully automated iLHA based on noninformativepriorsperformedas well as optimally tuned conventional methods.
['Kazuyoshi Yoshii', 'Masataka Goto']
INFINITE LATENT HARMONIC ALLOCATION: A NONPARAMETRIC BAYESIAN APPROACH TO MULTIPITCH ANALYSIS