A node-wise multinomial Potts model with sparse group Lasso and structural distance weights predicts mutation fitness better than EVmutation across 12 protein families, with new convergence rate guarantees.
Sharp minimax optimality of LASSO and SLOPE under double sparsity assumption
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abstract
This paper introduces a rigorous approach to establish the sharp minimax optimalities of both LASSO and SLOPE within the framework of double sparse structures, notably without relying on RIP-type conditions. Crucially, our findings illuminate that the achievement of these optimalities is fundamentally anchored in a sparse group normalization condition, complemented by several novel sparse group restricted eigenvalue (RE)-type conditions introduced in this study. We further provide a comprehensive comparative analysis of these eigenvalue conditions. Furthermore, we demonstrate that these conditions hold with high probability across a wide range of random matrices. Our exploration extends to encompass the random design, where we prove the random design properties and optimal sample complexity under both weak moment distribution and sub-Gaussian distribution.
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Modeling and prediction of mutation fitness on protein functionality with structural information using high-dimensional Potts model
A node-wise multinomial Potts model with sparse group Lasso and structural distance weights predicts mutation fitness better than EVmutation across 12 protein families, with new convergence rate guarantees.