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Variational inference for probabilistic Poisson PCA

Abstract : Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to understand the co-variations between these species. The Gaussian setting provides a canonical way to model such dependencies, but does not apply in general. We consider here the multivariate exponential family framework for which we introduce a generic model with multivariate Gaussian latent variables. We show that approximate maximum likelihood inference can be achieved via a variational algorithm for which gradient descent easily applies. We show that this setting enables us to account for covariates and offsets. We then focus on the case of the Poisson-lognormal model in the context of community ecology.
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https://hal.archives-ouvertes.fr/hal-01608912
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Submitted on : Tuesday, October 3, 2017 - 2:05:19 AM
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Julien Chiquet, Mahendra Mariadassou, Stephane Robin. Variational inference for probabilistic Poisson PCA. [University works] auto-saisine. 2017. ⟨hal-01608912⟩

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