  In this paper, we propose a framework for automatic classification of
patients from multimodal genetic and brain imaging data by optimally combining
them. Additive models with unadapted penalties (such as the classical group
lasso penalty or $L_1$-multiple kernel learning) treat all modalities in the
same manner and can result in undesirable elimination of specific modalities
when their contributions are unbalanced. To overcome this limitation, we
introduce a multilevel model that combines imaging and genetics and that
considers joint effects between these two modalities for diagnosis prediction.
Furthermore, we propose a framework allowing to combine several penalties
taking into account the structure of the different types of data, such as a
group lasso penalty over the genetic modality and a $L_2$-penalty on imaging
modalities. Finally , we propose a fast optimization algorithm, based on a
proximal gradient method. The model has been evaluated on genetic (single
nucleotide polymorphisms-SNP) and imaging (anatomical MRI measures) data from
the ADNI database, and compared to additive models. It exhibits good
performances in AD diagnosis; and at the same time, reveals relationships
between genes, brain regions and the disease status.
