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A Comparative Study of Gamma Markov Chains for Temporal Non-Negative Factorization

Abstract : Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Pois- son or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined station- ary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.
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https://hal.archives-ouvertes.fr/hal-02883800
Contributor : Cédric Févotte Connect in order to contact the contributor
Submitted on : Monday, March 1, 2021 - 1:06:34 PM
Last modification on : Friday, October 15, 2021 - 1:41:28 PM

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Louis Filstroff, Olivier Gouvert, Cédric Févotte, Olivier Cappé. A Comparative Study of Gamma Markov Chains for Temporal Non-Negative Factorization. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2021, ⟨10.1109/TSP.2021.3060000⟩. ⟨hal-02883800v3⟩

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