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007 | cr cnu|||unuuu | ||
008 | 200416s2020 si ob 001 0 eng d | ||
040 |
_a WSPC _b eng _c WSPC |
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010 | _z 2020001727 | ||
020 |
_a9789811216572 _q(ebook) |
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020 |
_a9811216576 _q(ebook) |
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020 |
_z9811216568 _q(hbk.) |
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020 |
_z9789811216565 _q(hbk.) |
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_aQA184.2 _b.G35 2020 |
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_aCOM _x014000 _2bisacsh |
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082 | 0 | 4 |
_a512/.5 _223 |
100 | 1 |
_aGallier, Jean H. _94003 |
|
245 | 1 | 0 |
_aLinear algebra and optimization with applications to machine learning. _nVolume II, _pFundamentals of optimization theory with applications to machine learning _h[electronic resource] / _cby Jean Gallier, Jocelyn Quaintance. |
260 |
_aSingapore ; _aHackensack, NJ : _bWorld Scientific, _c[2020] |
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300 | _a1 online resource (xvii, 877 p.) | ||
504 | _aIncludes bibliographical references and index. | ||
538 | _aMode of access: World Wide Web. | ||
538 | _aSystem requirements: Adobe Acrobat Reader. | ||
520 | _a"Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included"--Publisher's website. | ||
650 | 0 |
_aAlgebras, Linear. _94004 |
|
650 | 0 |
_aMachine learning _xMathematics. _94005 |
|
655 | 0 |
_aElectronic books. _93294 |
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700 | 1 |
_aQuaintance, Jocelyn. _94006 |
|
856 | 4 | 0 |
_uhttps://www.worldscientific.com/worldscibooks/10.1142/11722#t=toc _zAccess to full text is restricted to subscribers. |
880 | 0 |
_6505-00 _aPreface -- Introduction -- Preliminaries for optimization theory. Opology. Differential calculus. Extrema of real-valued functions. Newton's method and its generalizations. Quadratic optimization problems. Schur complements and applications -- Linear optimization. Convex sets, cones, H-polyhedra. Linear programs. The simplex algorithm. Linear programming and duality -- Nonlinear optimization. Basics of hilbert spaces. General results of optimization theory. Introduction to nonlinear optimization. Subgradients and subdifferentials of convex functions. Dual ascent methods ; ADMM -- Applications to machine learning. Positive definite kernels. Soft margin support vector machines. Ridge regression, lasso, elastic net. Ν-sv regression -- Appendix a : total orthogonal families in hilbert spaces -- Appendix b : matlab programs -- Bibliography -- Index. |
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942 | _cEBK | ||
999 |
_c72579 _d72579 |