This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.

This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.

Learn to build and fly your own authentic traditional chinese kites with this user-friendly crafts book. Kites and China are practically synonymous, since these childhood toys were originally invented there before becoming popular around the world. For over 2000 years, kites have been a common sight in China, from the imperial court to the common people, and over that time period the craftsmanship of the kite has been perfected-and includes a diversity and richness of styles. In Chinese Kites, you'll learn not only the history and varied forms of the Chinese kite, but also how to produce, step-by-step, a beautiful Chinese kite of your own! Learn how to: Create the kite's framework Paint colorful designs Master the techniques of putting the painted cover on the framework Fly your creation! With Chinese Kites, you will be able to experience firsthand the joy of seeing a kite you made soaring across the sky.