Penalized regression methods such as the lasso and the elastic net have proven useful in high-dimensional setting such as genome-wide association studies where a large number of predictors are analyzed simultaneously and sparsity is common. Sparse non-hierarchical interaction models are of special interest in these settings since gene-gene and gene-environment interactions may well give rise to these non-hierarchical interactions.
In the talk we discuss the interaction situations that arise in genetic studies, and present a penalization approach to accommodate these special, structured situations. We compare the performance to results obtained from alternative penalization approaches such as two-step inclusion procedures, overlap group lasso, or deliberately misspecifying the model. Finally, we apply the proposed method to a large-scale genetic dataset of type-2 related diabetes.
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