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Abstract:
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In this talk, we will focus on learning nonconvex hierarchical interactions in high-dimensional statistical models. We first use the affine sparsity constraints to provide a precise characterization of both strong and weak hierarchical interactions. However, these affine sparsity constraints do not lead to a closed feasible region. To address this issue, we derive the explicit closure of the affine sparsity constraint for learning nonconvex hierarchical interactions. We prove that the global solution can be found by solving a sequence of folded concave penalized estimation and the desired strong or weak hierarchy holds with probability one. Furthermore, we study the local convergence theory for learning hierarchical interactions using the folded concave penalized estimation. Numerical studies are used to demonstrate the power of our proposed methods.
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