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> The Poisson lognormal model and variants[^1] can be used for a variety of multivariate problems when count data are at play. This package implements efficient variational algorithms to fit such models, accompanied with a set of functions for visualization and diagnostic. See [all the dedicated vignettes](https://pln-team.github.io/PLNmodels/articles/) for a comprehensive introduction.
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> The Poisson lognormal model and variants[@chiquet2021] can be used for a variety of multivariate problems when count data are at play. This package implements efficient variational algorithms to fit such models, accompanied with a set of functions for visualization and diagnostic. See [all the dedicated vignettes](https://pln-team.github.io/PLNmodels/articles/) for a comprehensive introduction.
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**PLNmodels** covers the following models, all built around the multivariate Poisson-lognormal distribution and sharing a common formula-based interface (covariates, offsets, weights) and a choice of optimization backends (a fast built-in Newton solver, NLOPT, and an experimental torch backend):
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-**PLN**[^2]: unpenalized multivariate Poisson regression, with several covariance structures (full, diagonal, spherical, fixed, or a genetic/heritability structure).
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-**PLNPCA**[^3]: probabilistic Poisson PCA — a rank-constrained covariance for dimension reduction and visualization.
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-**PLNLDA**: Poisson lognormal discriminant analysis[^4] for the supervised classification of count data.
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-**PLNnetwork**[^5]: sparse inverse-covariance (network) inference via a graphical-lasso-like penalty[^6].
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-**PLNmixture**: model-based clustering[^7] of count data via a mixture of PLN models.
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-**ZIPLN**[^8]: a zero-inflated extension of PLN for data with excess zeros, with the same family of covariance structures and an optional sparse (`ZIPLNnetwork`[^9]) variant.
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[^1]: J. Chiquet, M. Mariadassou and S. Robin: The Poisson-lognormal model as a versatile framework for the joint analysis of species abundances, Frontiers in Ecology and Evolution, 2021. [doi:10.3389/fevo.2021.588292](https://www.frontiersin.org/articles/10.3389/fevo.2021.588292/full)
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[^2]: Aitchison, J. and Ho, C. H. The multivariate Poisson-log normal distribution. Biometrika, 76(4), 1989, 643–653.
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[^3]: J. Chiquet, M. Mariadassou and S. Robin: Variational inference for probabilistic Poisson PCA, the Annals of Applied Statistics, 12: 2674–2698, 2018. [doi:10.1214/18-AOAS1177](http://dx.doi.org/10.1214/18%2DAOAS1177)
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[^4]: Fisher, R. A. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 1936; Rao, C. R. The utilization of multiple measurements in problems of biological classification. JRSS B, 10(2), 1948.
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[^5]: J. Chiquet, M. Mariadassou and S. Robin: Variational inference for sparse network reconstruction from count data, Proceedings of the 36th International Conference on Machine Learning (ICML), 2019. [link](http://proceedings.mlr.press/v97/chiquet19a.html)
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[^6]: Friedman, J., Hastie, T. and Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 2008.
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[^7]: Fraley, C. and Raftery, A. E. MCLUST: Software for model-based cluster analysis. Journal of Classification, 16(2), 1999.
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[^8]: Batardière, B., Chiquet, J., Gindraud, F. and Mariadassou, M. Zero-inflation in the multivariate Poisson lognormal family. Statistics and Computing, 35, 2025. [doi:10.1007/s11222-025-10729-0](https://doi.org/10.1007/s11222-025-10729-0)
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[^9]: Tous, J., Chiquet, J., Deacon, A. E., Fontrodona-Eslava, A., Fraser, D. F. and Magurran, A. E. A JSDM with zero-inflation to improve inference of association networks from count community data with structural zeros. bioRxiv preprint, 2025. [doi:10.1101/2025.07.24.666553](https://doi.org/10.1101/2025.07.24.666553)
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-**PLN**[@AiH89]: unpenalized multivariate Poisson regression, with several covariance structures (full, diagonal, spherical, fixed, or a genetic/heritability structure).
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-**PLNPCA**[@PLNPCA]: probabilistic Poisson PCA — a rank-constrained covariance for dimension reduction and visualization.
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-**PLNLDA**: Poisson lognormal discriminant analysis [@fisher1936] for the supervised classification of count data.
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-**PLNnetwork**[@PLNnetwork]: sparse inverse-covariance (network) inference via a graphical-lasso-like penalty [@FHT08].
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-**PLNmixture**: model-based clustering [@fraley1999] of count data via a mixture of PLN models.
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-**ZIPLN**[@ZIPLN]: a zero-inflated extension of PLN for data with excess zeros, with the same family of covariance structures and an optional sparse (`ZIPLNnetwork`) variant [@ZIPLNnetwork].
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## Installation
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## Illustration
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We illustrate the main models on the `barents` data set[^10]: the abundance of 30 fish species observed in 89 sites in the Barents sea, along with depth, temperature and geographic coordinates for each site.
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[^10]: Fossheim, M., Nilssen, E. M. and Aschan, M. Fish assemblages in the Barents Sea. Marine Biology Research, 2(4), 2006. [doi:10.1080/17451000600815698](https://doi.org/10.1080/17451000600815698)
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We illustrate the main models on the `barents` data set [@fossheim2006]: the abundance of 30 fish species observed in 89 sites in the Barents sea, along with depth, temperature and geographic coordinates for each site.
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