A. Acharya, J. Ghosh, and M. Zhou, Nonparametric bayesian factor analysis for dynamic count matrices, AISTATS, 2015.

J. Aitchison and C. Ho, The multivariate Poisson-log normal distribution, Biometrika, vol.76, issue.4, pp.643-653, 1989.
DOI : 10.1093/biomet/76.4.643

T. W. Anderson, An introduction to multivariate statistical analysis, Series in Probability and Statistics, 2003.

C. Biernacki, G. Celeux, and G. Govaert, Assessing a mixture model for clustering with the integrated completed likelihood, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.22, issue.7, pp.719-744, 2000.
DOI : 10.1109/34.865189

H. Richard, P. Byrd, J. Lu, C. Nocedal, and . Zhu, A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientific Computing, vol.16, issue.5, pp.1190-1208, 1995.

Y. Cao and Y. Xie, Poisson matrix completion, 2015 IEEE International Symposium on Information Theory (ISIT), pp.1841-1845, 2015.
DOI : 10.1109/ISIT.2015.7282774
URL : http://arxiv.org/abs/1501.06243

M. Collins, S. Dasgupta, and R. Schapire, A generalization of principal components analysis to the exponential family, Advances in neural information processing systems, pp.617-624, 2001.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Statist. Soc. B, vol.39, pp.1-38, 1977.

C. Eckart and G. Young, The approximation of one matrix by another of lower rank, Psychometrika, vol.1, issue.3, pp.211-218, 1936.
DOI : 10.1007/BF02288367

P. Hall and J. Ormerod, Theory of gaussian variational approximation for a Poisson mixed model, Statistica Sinica, pp.369-389, 2011.

R. Izsák, Maximum likelihood fitting of the Poisson lognormal distribution, Environmental and Ecological Statistics, vol.74, issue.2, pp.143-156, 2008.
DOI : 10.1093/biomet/38.3-4.427

T. S. Jaakkola and M. I. Jordan, Bayesian parameter estimation via variational methods, Statistics and Computing, vol.10, issue.1, pp.25-37, 2000.
DOI : 10.1023/A:1008932416310

B. Jakuschkin, V. Fievet, L. Schwaller, T. Fort, C. Robin et al., Deciphering the Pathobiome: Intra- and Interkingdom Interactions Involving the Pathogen Erysiphe alphitoides, Microbial Ecology, vol.40, issue.194, pp.1-11, 2016.
DOI : 10.1007/978-81-322-1575-2_17
URL : https://hal.archives-ouvertes.fr/hal-01533883

D. Karlis, EM Algorithm for Mixed Poisson and Other Discrete Distributions, ASTIN Bulletin, vol.39, issue.01, pp.3-24, 2005.
DOI : 10.1080/01621459.1990.10474930

J. Lafond, Low rank matrix completion with exponential family noise. arXiv preprint, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01120132

J. Landgraf and Y. Lee, Dimensionality reduction for binary data through the projection of natural parameters, 2015.

D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization, Advances in neural information processing systems, pp.556-562, 2001.

J. Li and D. Tao, Simple exponential family PCA, AISTATS, pp.453-460, 2010.

T. Liu, E. Dobriban, and A. Singer, ePCA: High Dimensional Exponential Family PCA. ArXiv e-prints, 2016.

N. Mach, M. Berri, J. Estellé, F. Levenez, G. Lemonnier et al., Early-life establishment of the swine gut microbiome and impact on host phenotypes, Environmental Microbiology Reports, vol.17, issue.3, pp.554-569, 2015.
DOI : 10.22358/jafs/66470/2008
URL : https://hal.archives-ouvertes.fr/hal-01168456

K. V. Mardia, J. T. Kent, J. M. Bibby, and . Minka, Multivariate analysis. Academic press Automatic choice of dimensionality for PCA, NIPS, pp.598-604, 1979.

Z. Mohamed, K. A. Ghahramani, and . Heller, Bayesian exponential family PCA, Advances in neural information processing systems, pp.1089-1096, 2009.

J. Nelson, Multivariate Gamma-Poisson Models, Journal of the American Statistical Association, vol.54, issue.4, pp.828-834, 1985.
DOI : 10.1090/S0002-9947-1943-0012401-3

H. William, . Press, P. Brian, . Flannery, A. Saul et al., Numerical recipes R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 1989.

J. A. Royle and C. Wikle, Efficient statistical mapping of avian count data, Environmental and Ecological Statistics, vol.96, issue.1, pp.225-243, 2005.
DOI : 10.1007/978-1-4612-1494-6

J. Salmon, Z. Harmany, C. Deledalle, and R. Willett, Poisson Noise Reduction with Non-local PCA, Journal of Mathematical Imaging and Vision, vol.15, issue.2, pp.279-294, 2014.
DOI : 10.1198/106186006X113430
URL : https://hal.archives-ouvertes.fr/hal-00957837

. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-465, 1978.
DOI : 10.1214/aos/1176344136

S. Srivastava and L. Chen, A two-parameter generalized Poisson model to improve the analysis of RNA-seq data, Nucleic Acids Research, vol.38, issue.17, pp.170-170, 2010.
DOI : 10.1093/nar/gkq670

M. E. Tipping and C. Bishop, Probabilistic Principal Component Analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.3, pp.61611-622, 1999.
DOI : 10.1111/1467-9868.00196

M. J. Wainwright and M. I. Jordan, Graphical Models, Exponential Families, and Variational Inference, Foundations and Trends?? in Machine Learning, vol.1, issue.1???2, pp.1-305, 2008.
DOI : 10.1561/2200000001

H. Wickham, ggplot2: Elegant Graphics for Data Analysis, 2009.

D. Witten, R. Tibshirani, and T. Hastie, A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis, Biostatistics, vol.10, issue.3, p.8, 2009.
DOI : 10.1093/biostatistics/kxp008

M. Zhou, Nonparametric bayesian negative binomial factor analysis. arXiv preprint, 2016.

M. Zhou, L. Hannah, D. Dunson, and L. Carin, Beta-negative binomial process and poisson factor analysis, AISTATS, pp.1462-1471, 2012.