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MSE Proof convexity using definition

Hi everyone,

Could you please elaborate the intermediate steps for this computation?
Also, where can I find a good crash course about norms ?

Thank you,

LHS.jpg

It's recommended to write out the equation using the loss \(\mathcal{L}\) defined before.

If you need a refresher on Linear Algebra (which is a course requirement), see e.g. chapter 2 of https://mml-book.github.io/
For a crash course on norms, refer to the single page section 3.1 of that same (free) book.

Reviewing the material, I have the same question. Sadly the references given didn't help me at all. I think I can prove convexity using triangle inequality, but computing the LHS seems to be a quite long calculation, unless I am missing a trick that would make it less brute force ...

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