Covariance Functions (Kernels): Properties and Selection
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Gaussian Processes for Machine Learning, Carl Edward Rasmussen and Christopher K. I. Williams, 2006 (The MIT Press) - The authoritative textbook on Gaussian Processes, providing a thorough explanation of covariance functions, their properties, common types, and construction rules. Essential for a comprehensive understanding.
Machine Learning: A Probabilistic Perspective, Kevin P. Murphy, 2012 (The MIT Press) - A broad and deep textbook covering probabilistic machine learning. Offers a foundational perspective on kernels within the broader context of machine learning, including Gaussian Processes and support vector machines.
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, Bernhard Schölkopf, Alexander J. Smola, 2002 (The MIT Press) - This book is a foundational text for kernel methods in machine learning, offering detailed discussions on Mercer's theorem, positive definite kernels, and their applications beyond Gaussian Processes.