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# An Inequality with Applications to Structured Sparsity and Multitask Dictionary Learning

*Proceedings of The 27th Conference on Learning Theory*, PMLR 35:440-460, 2014.

#### Abstract

From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary learning or matrix factorization. A key role is played by the largest eigenvalue of the data covariance matrix.