Hello, I have a question regarding Problem 1. It is a simple question but I don't see how the Cauchy Schwarz inequality is applied. I don't understand why there is >=, I would have written <=. I think my error come from the minus sign but I don't understand where the minus sign come from.
Thank you in advance
This implies a lower and upper bound on \(w^T \delta\): \(-||w||_2 ||\delta||_2 \leq w^T \delta \leq ||w||_2 ||\delta||_2 \)
The lower bound is what we used for this exercise (assuming \(w\) is already multiplied by the label \(y_i\)). I think it indeed just boils down to carefully thinking about the direction of the inequality and where the minus sign should go.
lab 10
Hello, I have a question regarding Problem 1. It is a simple question but I don't see how the Cauchy Schwarz inequality is applied. I don't understand why there is >=, I would have written <=. I think my error come from the minus sign but I don't understand where the minus sign come from.
Thank you in advance
Hi,
The Cauchy-Schwarz inequality is usually given as follows (e.g., https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality):
\(|w^T \delta| \leq ||w||_2 ||\delta||_2 \)
This implies a lower and upper bound on \(w^T \delta\):
\(-||w||_2 ||\delta||_2 \leq w^T \delta \leq ||w||_2 ||\delta||_2 \)
The lower bound is what we used for this exercise (assuming \(w\) is already multiplied by the label \(y_i\)). I think it indeed just boils down to carefully thinking about the direction of the inequality and where the minus sign should go.
I hope that helps!
2
Yes it helps. Thank you!
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