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The $k$-support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the $k$-support norm to matrices, and we observe that it is a special case of the matrix cluster norm. Using this formulation we derive an efficient algorithm to compute the proximity operator of both norms. This improves upon the standard algorithm for the $k$-support norm and allows us to apply proximal gradient methods to the cluster norm. We also describe how to solve regularization problems which employ center
A zero initial velocity of the axion field is assumed in the conventional misalignment mechanism. We propose an alternative scenario where the initial velocity is nonzero, which may arise from an explicit breaking of the PQ symmetry in the early Univ
Recently, the perfect phylogeny model with persistent characters has attracted great attention in the literature. It is based on the assumption that complex traits or characters can only be gained once and lost once in the course of evolution. Here,
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual $ell_1$-n
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important ca
Let ${mathcal S}_m$ be the set of all $mtimes m$ density matrices (Hermitian positively semi-definite matrices of unit trace). Consider a problem of estimation of an unknown density matrix $rhoin {mathcal S}_m$ based on outcomes of $n$ measurements o