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Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning (Hardcover)
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Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning (Hardcover)
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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.
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