LEADER 03061nam 2200445 450 001 996475763503316 005 20221126183411.0 010 $a9789811903984$b(electronic bk.) 010 $z9789811903977 035 $a(MiAaPQ)EBC6975910 035 $a(Au-PeEL)EBL6975910 035 $a(CKB)21957563100041 035 $a(OCoLC)1314619055 035 $a(PPN)269155023 035 $a(EXLCZ)9921957563100041 100 $a20221126d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKernel Methods for Machine Learning with Math and RaKernel methods for machine learning with math and R $e100 exercises for building logic /$fJoe Suzuki 210 1$aGateway East, Singapore :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (203 pages) 311 08$aPrint version: Suzuki, Joe Kernel Methods for Machine Learning with Math and R Singapore : Springer,c2022 9789811903977 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- How to Overcome Your Kernel Weakness -- What Makes KMMR Unique? -- Acknowledgments -- Contents -- 1 Positive Definite Kernels -- 1.1 Positive Definiteness of a Matrix -- 1.2 Kernels -- 1.3 Positive Definite Kernels -- 1.4 Probability -- 1.5 Bochner's Theorem -- 1.6 Kernels for Strings, Trees, and Graphs -- Appendix -- Exercises 1 sim 15 -- 2 Hilbert Spaces -- 2.1 Metric Spaces and Their Completeness -- 2.2 Linear Spaces and Inner Product Spaces -- 2.3 Hilbert Spaces -- 2.4 Projection Theorem -- 2.5 Linear Operators -- 2.6 Compact Operators -- Appendix: Proofs of Propositions -- Exercises -- 3 Reproducing Kernel Hilbert Space -- 3.1 RKHSs -- 3.2 Sobolev Space -- 3.3 Mercer's Theorem -- Appendix -- Exercises -- 4 Kernel Computations -- 4.1 Kernel Ridge Regression -- 4.2 Kernel Principle Component Analysis -- 4.3 Kernel SVM -- 4.4 Spline Curves -- 4.5 Random Fourier Features -- 4.6 Nyström Approximation -- 4.7 Incomplete Cholesky Decomposition -- Appendix -- Exercises 46sim64 -- 5 The MMD and HSIC -- 5.1 Random Variables in RKHSs -- 5.2 The MMD and Two-Sample Problem -- 5.3 The HSIC and Independence Test -- 5.4 Characteristic and Universal Kernels -- 5.5 Introduction to Empirical Processes -- Appendix -- 6 Gaussian Processes and Functional Data Analyses -- 6.1 Regression -- 6.2 Classification -- 6.3 Gaussian Processes with Inducing Variables -- 6.4 Karhunen-Lóeve Expansion -- 6.5 Functional Data Analysis -- Appendix -- Exercises 83sim100 -- Appendix Bibliography. 606 $aR (Computer program language) 606 $aKernel functions 615 0$aR (Computer program language) 615 0$aKernel functions. 676 $a006.31 700 $aSuzuki$b Joe$0846228 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996475763503316 996 $aKernel Methods for Machine Learning with Math and RaKernel methods for machine learning with math and R$92965121 997 $aUNISA