Title: On learning kernels for numerical approximation and learning.
Abstract: There is a growing interest in solving numerical approximation problems as learning problems. Popular approaches can be divided into (1) Kernel methods, and (2) methods based on variants of Artificial Neural Networks. We illustrate the importance of using adapted kernels in kernel methods and discuss strategies for learning kernels from data. We show how ANN methods can be formulated and analyzed as (1) kernel methods with warping kernels learned from data, and (2) discretized solvers for a generalization of image registration algorithms in which images are replaced by high dimensional shapes.
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