Multilevel Modeling with Structured Penalties for Classification from Imaging Genetics Data

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 \(\ell _1\)-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 \(\ell _2\)-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 [13, 15]. It exhibits good performances in AD diagnosis; and at the same time, reveals relationships between genes, brain regions and the disease status.