Phenotypic prediction based on metabolomic data : lasso vs Bolasso, primary data vs wavelet transformation

International audienceUnderstanding the relations between various 'omics data (such as metabolomics or genomics data) and phenotypes of interest is one of the current major challenges in biology. This question can be addressed by trying to learn a way to predict the phenotype value from the omic from joint observations of the omic and of the phenotype. In this paper, we focus on the prediction of a phenotype related to the quality of the meat from metabolomic data. As metabolomic data are high dimensional data and as, conjointly, the number of observations is often restricted, model selection methods are a way both to obtain a relevant solution to the prediction problem but also to select the most important metabolomes related to the phenotype under study. During the past years, model selection has know a growing interest in the statistical community: the first - and also probably the most known - selection method has been introducted by \citep{Tibshirani:1996} under the name of LASSO. Several variants of this original approach has then been proposed such as, recently, a bootstraped LASSO, named BOLASSO, introduced in (Bach, 2009). The proposal of this paper is to combine a wavelet representation of the metabolome spectra (see (Mallat, 1999) and (Antonini, 1992) for a complete introduction to wavelets) with the BOLASSO approach. We compare this methodology to more classical methods using either the original spectra as predictors (instead of the wavelet representation) or the original LASSO to select the model. The following section deals with the methodological description of the approach whereas the next one details the experiments and results