As Kernel Ridge Regression computes inverse (Not a pseudo inverse) of a square matrix, so whether obtained solution would always be global optimal or not?


In the case that the inverse exists, it is the same as the pseudo inverse. Unless the method crashes due to the fact that the inverse does not exist, the results will be the same.

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  • $\begingroup$ Completely agree. however, just want to know whether this solution would be globally optimal or not? If yes/no then why? $\endgroup$ – Chandan Gautam Jun 4 '18 at 18:41
  • $\begingroup$ Ridge regression optima are always global, I am not sure about kernelized Ridge, but if kernelized Ridge just transforms the features then the optimum us global. $\endgroup$ – David Masip Jun 5 '18 at 6:41
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    $\begingroup$ As the documentation says: scikit-learn.org/stable/modules/generated/… it looks like it is only ridge regression with kernelized features. Therefore the solution is indeed a global optimum, as the solution for ridge is always a global optimum (local optima in quadratic functions are global optima). $\endgroup$ – David Masip Jun 5 '18 at 8:05

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