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, University of Toulouse)
Cédric Févotte is a CNRS research director with the Institut de Recherche en Informatique de Toulouse (IRIT). Previously, he has been a CNRS researcher at Laboratoire Lagrange (Nice, 2013-2016) & 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, with particular interests in matrix factorisation, representation learning, source separation and recommender systems. He is currently the principal investigator of the European Research Council (ERC) project FACTORY (New paradigms for latent factor estimation, 2016-2022, 2M€).
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2014 Poster: Low-Rank Time-Frequency Synthesis »
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2012 Poster: Clustering by Nonnegative Matrix Factorization Using Graph Random Walk »
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