#StackBounty: #cross-validation #ridge-regression #vc-dimension Rademacher Bound, An Alternative to Cross Validation for Ridge?

Bounty: 100

Below is a theorem from the book “Foundations of Machine Learning”.

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It specifies the generalization bounds for Kernel Ridge Regression by making use of the Rademacher Complexity on linear models. $R(h)$ is the generalization error, and $hat{R}(h)$ is the empirical error. Now pretty much everything is either known to us, picked by us, or can be calculated by us. $m$ is the number of training samples.

Instead of finding the right penalty $Lambda$ via cross validation, can we simply pick the $Lambda$ that minimizes the right hand side of the inequality? What should be the $delta$ value to be set in order to achieve best predictive result? How to choose $r$ as tight as possible?

Is this an alternative to Cross Validation for Kernel Ridge (or just Ridge) Regression?

Get this bounty!!!

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