Background

Platt is implemented using the PLNmodels package. PLN models are a multivariate mixed generalized linear model with a Poisson distribution, allowing them to overcome the computational challenges posed by count data. They provide a convenient framework to perform multivariate statistical regression to describe how environmental effects or perturbations alter the relative abundances of each species. The PLN network model for multivariate count data can be viewed as a PLN model with a constraint on the coefficients of $\Omega$. Correlations between pairs of species are captured by the variance matrix $\Sigma$, whereas partial correlations are encoded by its inverse: the precision matrix $\Omega$. In this setting, cell types $j$ and $k$ are associated as soon as $\Sigma_k \neq 0$ but are in direct interaction if and only if $\Omega_{jk} \neq 0$​

References

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.

2. 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.

3. J. Chiquet, M. Mariadassou and S. Robin: Variational inference for probabilistic Poisson PCA, the Annals of Applied Statistics, 12: 2674–2698, 2018.