Julien Chiquet

<p>The stochastic block model is a popular probabilistic model for random graphs. It is commonly used to cluster network data by aggregating nodes that share similar connectivity patterns into blocks. When fitting a stochastic block model to a partially observed network, it is important to consider the underlying process that generates the missing values, otherwise the inference may be biased. This paper presents missSBM, an R package that fits stochastic block models when the network is partially observed, i.e., the adjacency matrix contains not only 1s or 0s encoding the presence or absence of edges, but also NAs encoding the missing information between pairs of nodes. This package implements a set of algorithms to adjust the binary stochastic block model, possibly in the presence of external covariates, by performing variational inference suitable for several observation processes. Our implementation automatically explores different block numbers to select the most relevant model according to the integrated classification likelihood criterion. The integrated classification likelihood criterion can also help determine which observation process best fits a given dataset. Finally, missSBM can be used to perform imputation of missing entries in the adjacency matrix. We illustrate the package on a network dataset consisting of interactions between political blogs sampled during the 2007 French presidential election.</p>

Joint Species Distribution Models (JSDM) provide a general multivariate framework to study the joint abundances of all species from a community. JSDM account for both structuring factors (environmental characteristics or gradients, such as habitat type or nutrient availability) and potential interactions between the species (competition, mutualism, parasitism, etc.), which is instrumental in disentangling meaningful ecological interactions from mere statistical associations. Modeling the dependency between the species is challenging because of the count-valued nature of abundance data and most JSDM rely on Gaussian latent layer to encode the dependencies between species in a covariance matrix. The multivariate Poisson-lognormal (PLN) model is one such model, which can be viewed as a multivariate mixed Poisson regression model. Inferring such models raises both statistical and computational issues, many of which were solved in recent contributions using variational techniques and convex optimization tools. The PLN model turns out to be a versatile framework, within which a variety of analyses can be performed, including multivariate sample comparison, clustering of sites or samples, dimension reduction (ordination) for visualization purposes, or inferring interaction networks. This paper presents the general PLN framework and illustrates its use on a series a typical experimental datasets. All the models and methods are implemented in the R package PLNmodels, available from cran.r-project.org.