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I am reading the book "Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (Adaptive Computation and Machine Learning)". I finished the first chapter and didn't notice any approach taken by the authors, but I assume according to the material in the first chapter it is a frequentist approach. So my question is from the people who has read the book or know about it. Am I right about this assumption?

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Yes.

The first chapter talks mostly about support vector machines and hyperplane classifiers(among other things). So, yes, they have discussed a frequentist approach. They do discuss bayesian methods in chapter 16 and give a good explanation for the connection between regularized loss minimization and bayesian methods.

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