The majority of all commonly used machine learning methods can not be applied directly to data sets with missing values. However, most such methods only depend on the relative differences between samples instead of their particular values, and thus one useful approach is to directly estimate the pairwise distances between all samples in the data set. This is accomplished by fitting a Gaussian mixture model to the data, and using it to derive estimates for the distances. Experimental simulations confirm that the proposed method provides accurate estimates compared to alternative methods for estimating distances.

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with a Gaussian copula mixture model, since copulas, and in particular the Gaussian ones, are powerful tools for easily modelling the distribution of multivariate variables. Indeed, considering a mixing of continuous, integer and ordinal variables (thus all having a cumulative distribution function), this copula mixture model defines intracomponent dependencies similar to a Gaussian mixture, so with classical correlation meaning. Simultaneously, it preserves standard margins associated to continuous, integer and ordered features, namely the Gaussian, the Poisson and the ordered multinomial distributions. As an interesting by-product, the proposed mixture model generalizes many well-known ones and also provides tools of visualization based on the parameters. At a practical level, the Bayesian inference is retained and it is achieved with a Metropolis-within-Gibbs sampler. Experiments on simulated and real data sets finally illustrate the expected advantages of the proposed model for mixed data: flexible and meaningful parametrization combined with visualization features.

Background: Finding over-or under-represented motifs in biological sequences is now a common task in genomics. Thanks to p-value calculation for motif counts, exceptional motifs are identified and represent candidate functional motifs. The present work addresses the related question of comparing the exceptionality of one motif in two different sequences. Just comparing the motif count p-values in each sequence is indeed not sufficient to decide if this motif is significantly more exceptional in one sequence compared to the other one. A statistical test is required.

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