Big data in omics and imaging association analysis / [electronic resource] :

• 作者： Xiong, Momiao, author.
• 出版： Boca Raton : CRC Press, Taylor & Francis Group
• 叢書名： Chapman & Hall/CRC mathematical and computational biology series
• 主題： Biometry--Data processing. , Imaging systems in biology--Statistical methods. , Big data--Statistical methods. , Electronic books.
• ISBN： 1498725805 (electronic bk.) 、 9781498725804
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Sparsity-Inducing Norms, Dual Norms, And Fenchel Conjugate -- "Entrywise" Norms -- L2,1 Norm -- Lp, q Norm -- Frobenius Norm -- l1/l2 Norm -- Overlapping Groups -- Dual Norm -- Norm Dual to the Group Norm -- Fenchel Conjugate -- Fenchel Duality -- Subdifferential -- Definition of Subgradient -- Subgradients of Differentiable Functions -- Calculus of Subgradients -- Nonnegative Scaling -- Addition -- Affine Transformation of Variables -- Pointwise Maximum -- Pointwise Supremum -- Expectation -- Chain Rule -- Subdifferential of the Norm -- Optimality Conditions: Unconstrained -- Application to Sparse Regularized Convex Optimization Problems -- Proximal Methods -- Introduction -- Basics of Proximate Methods -- Definition of Proximal Operator -- Properties of the Proximal Operator -- Separable Sum -- Moreau-Yosida Regularization -- Gradient Algorithms for the Calculation of the Proximal Operator -- Proximal Algorithms -- Proximal Point Algorithm -- Proximal Gradient Method -- Accelerated Proximal Gradient Method -- Alternating Direction Method of Multipliers -- Linearized ADMM -- Computing the Proximal Operator -- Generic Function -- Norms -- Matrix Calculus -- Derivative of a Function with Respect to a Vector -- Derivative of a Function with Respect to a Matrix -- Derivative of a Matrix with Respect to a Scalar -- Derivative of a Matrix with Respect to a Matrix or a Vector -- Rank-One.
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