In this paper we describe a maximum likelihood likelihood approach for dictionary learning in the multiplicative exponential noise model. This model is prevalent in audio signal processing where it underlies a generative composite model of the power spectrogram. Maximum joint likelihood estimation of the dictionary and expansion coefficients leads to a nonnegative matrix factorization problem where the Itakura-Saito divergence is used. The optimality of this approach is in question because the number of parameters (which include the expansion coefficients) grows with the number of observations. In this paper we describe a variational procedure for optimization of the marginal likelihood, i.e., the likelihood of the dictionary where the activation coefficients have been integrated out (given a specific prior). We compare the output of both maximum joint likelihood estimation (i.e., standard Itakura-Saito NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical datasets. The MMLE approach is shown to embed automatic model order selection, akin to automatic relevance determination.
Onur Dikmen (University of Helsinki)
Cédric Févotte (CNRS)
Cédric Févotte is a CNRS senior researcher at Institut de Recherche en Informatique de Toulouse (IRIT). Previously, he has been a CNRS researcher at Laboratoire Lagrange (Nice, 2013-2016) & at Télécom ParisTech (2007-2013), a research engineer at Mist-Technologies (the startup that became Audionamix, 2006-2007) and a postdoc at University of Cambridge (2003-2006). He holds MEng and PhD degrees in EECS from École Centrale de Nantes. His research interests concern statistical signal processing and machine learning, for inverse problems and source separation. He is a member of the IEEE Machine Learning for Signal Processing technical committee and an associate editor for the IEEE Transactions on Signal Processing. In 2014, he was the co-recipient of an IEEE Signal Processing Society Best Paper Award for his work on audio source separation using multichannel nonnegative matrix factorisation. He is the principal investigator of the ERC project FACTORY (New paradigms for latent factor estimation, 2016-2021).
More from the Same Authors
2016 Poster: Optimal spectral transportation with application to music transcription »
Rémi Flamary · Cédric Févotte · Nicolas Courty · Valentin Emiya
2014 Poster: Low-Rank Time-Frequency Synthesis »
Cédric Févotte · Matthieu Kowalski
2012 Poster: Clustering by Nonnegative Matrix Factorization Using Graph Random Walk »
Zhirong Yang · Tele Hao · Onur Dikmen · Xi Chen · Erkki Oja