I am also confused by this Q15, and have read the previous posts to this questions as well as the document that was mentioned there (MATH-SHU 236 High Dimensional Geometry) but not understood the mathematical details, so I wanted to check my intuition:
So in the document and your responses you only gave the reasoning of how the radii scale for the L1 and L2 norm. Is this also true for the Linf norm?
Ie. can we say for all comparisons between Li and Lj-norms, that the corresponding L_i ball is only contained in L_j ball if,
for ||x-^x||_i <= epsilon
then for
||x-^x||_j <= sqrt(d) * epsilon ?
Thanks!
Also a quick notational question:
lpnorm.JPG
What does that additional - non-subscript infinity sign mean in the sets? Is this a typo?!
Exam 2020 Q 15
Hello,
I am also confused by this Q15, and have read the previous posts to this questions as well as the document that was mentioned there (MATH-SHU 236 High Dimensional Geometry) but not understood the mathematical details, so I wanted to check my intuition:
So in the document and your responses you only gave the reasoning of how the radii scale for the L1 and L2 norm. Is this also true for the Linf norm?
Ie. can we say for all comparisons between Li and Lj-norms, that the corresponding L_i ball is only contained in L_j ball if,
for ||x-^x||_i <= epsilon
then for
||x-^x||_j <= sqrt(d) * epsilon ?
Thanks!
Also a quick notational question:
lpnorm.JPG
What does that additional - non-subscript infinity sign mean in the sets? Is this a typo?!
lpnorm.JPG
1
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