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This monograph demonstrates a new approach to the classical mode
decomposition problem through nonlinear regression models, which
achieve near-machine precision in the recovery of the modes. The
presentation includes a review of generalized additive models,
additive kernels/Gaussian processes, generalized Tikhonov
regularization, empirical mode decomposition, and Synchrosqueezing,
which are all related to and generalizable under the proposed
framework. Although kernel methods have strong theoretical
foundations, they require the prior selection of a good kernel.
While the usual approach to this kernel selection problem is
hyperparameter tuning, the objective of this monograph is to
present an alternative (programming) approach to the kernel
selection problem while using mode decomposition as a prototypical
pattern recognition problem. In this approach, kernels are
programmed for the task at hand through the programming of
interpretable regression networks in the context of additive
Gaussian processes. It is suitable for engineers, computer
scientists, mathematicians, and students in these fields working on
kernel methods, pattern recognition, and mode decomposition
problems.
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