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

Multilevel Modeling with Structured Penalties for Classification from Imaging Genetics data