Section: New Software and Platforms
Participants : Florence Forbes, Stéphane Girard, Gildas Mazo, Alexis Arnaud.
Joint work with: Charles Bouveyron (Univ. Paris 5) and Stéthane Dépréaux (LJK).
Mistis is involved in the development of several R packages available on the CRAN archive. They are dedicated to the construction of copulas and to the classification and clustering of data.
PBC (product of bivariate copulas). http://cran.r-project.org/web/packages/PBC/ This R package provides tools for building copulas with the PBC model, a class of multivariate copulas based on Products of Bivariate Copulas. Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, much fewer has been done when the dimension is higher. To this aim an interesting class of copulas based on products of transformed copulas has been proposed. However the use of this class for practical high dimensional problems remains challenging. Constraints on the parameters and the product form render inference, and in particular the likelihood computation, difficult. In this R package, we propose a new class of high dimensional copulas based on a product of transformed bivariate copulas. No constraints on the parameters refrain the applicability of the proposed class which is well suited for applications in high dimension. Furthermore the analytic forms of the copulas within this class allow to associate a natural graphical structure (see illustration below) which helps to visualize the dependencies and to compute the likelihood efficiently even in high dimension.
FDG (one-Factor copulas with Durante Generators). http://cran.r-project.org/web/packages/FDGcopulas/ This R package provides tools for building high-dimensional copulas with the FDG model, a class of multivariate copulas based on one-factor copulas. FDG copulas are a class of copulas featuring an interesting balance between flexibility and tractability. This package provides tools to construct, calculate the pairwise dependence coefficients of, simulate from, and fit FDG copulas. The acronym FDG stands for 'one-Factor with Durante Generators', as an FDG copula is a one-factor copula - that is, the variables are independent given a latent factor - whose linking copulas belong to the Durante class of bivariate copulas (also referred to as exchangeable Marshall-Olkin or semilinear copulas).
HDclassif (classification and clustering methods for high dimensional data). http://cran.r-project.org/web/packages/HDclassif/ The HDclassif package is devoted to the clustering and the discriminant analysis of high-dimensional data. The classification methods proposed in the package result from a new parametrization of the Gaussian mixture model which combines the idea of dimension reduction and model constraints on the covariance matrices. The supervised classification method using this parametrization has been called High Dimensional Discriminant Analysis (HDDA). In a similar manner, the associated clustering method has been called High Dimensional Data Clustering (HDDC) and uses the Expectation-Maximization (EM) algorithm for inference. In order to correctly fit the data, both methods estimate the specific subspace and the intrinsic dimension of the groups. Due to the constraints on the covariance matrices, the number of parameters to estimate is significantly lower than other model-based methods and this allows the methods to be stable and efficient in high-dimensional spaces. Experiments on artificial and real datasets show that HDDC and HDDA perform better than existing classical methods on high-dimensional datasets, even with small datasets.
robustDA (robust mixture discriminant analysis). http://cran.r-project.org/web/packages/robustDA/ Robust mixture discriminant analysis allows to build a robust supervised classifier from learning data with label noise. The idea of the proposed method is to confront an unsupervised modeling of the data with the supervised information carried by the labels of the learning data in order to detect inconsistencies. The method is able afterward to build a robust classifier taking into account the detected inconsistencies into the labels. An application to object recognition under weak supervision is presented below.
MSST (Mixtures of multiple scaled Student distributions). The package is not yet available on the CRAN but should be early 2015. It implements more efficiently the models and inference procedures described in  and will be used on large data sets of brain MRI in the context of Alexis Arnaud PhD thesis. This is joint work with S. Dépréaux who helped with writing subroutines in C++.