Hello,
Could you perhaps explain to me how we find out that answer d is wrong? I do not really understand how we are supposed to find out whether this function is convex or not.
Thank you :)
c) Here, the objective is effectively (1 + 2+ 3 + 4 + ... + 30) ||w||^2. A stochastic gradient should be equal to this in expectation. If you always select only one term to differentiate, you systematically under-estimate the true gradient.
d) Try to find a counter-example here, two inputs A and B such that \(\alpha f(A) + (1-\alpha) f(B)\) < f(\alpha A + (1-\alpha)B)).
c) Here, the objective is effectively (1 + 2+ 3 + 4 + ... + 30) ||w||^2. A stochastic gradient should be equal to this in expectation. If you always select only one term to differentiate, you systematically under-estimate the true gradient.
d) Try to find a counter-example here, two inputs A and B such that \(\alpha f(A) + (1-\alpha) f(B)\) < f(\alpha A + (1-\alpha)B)).
Exam 2017 Q 19
Hello,
Could you perhaps explain to me how we find out that answer d is wrong? I do not really understand how we are supposed to find out whether this function is convex or not.
Thank you :)
2
c) Here, the objective is effectively (1 + 2+ 3 + 4 + ... + 30) ||w||^2. A stochastic gradient should be equal to this in expectation. If you always select only one term to differentiate, you systematically under-estimate the true gradient.
d) Try to find a counter-example here, two inputs A and B such that \(\alpha f(A) + (1-\alpha) f(B)\) < f(\alpha A + (1-\alpha)B)).
I would be interested in the answer too. And also, why the answer c) is wrong. Thanks!
1
Here's the question:
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c) Here, the objective is effectively (1 + 2+ 3 + 4 + ... + 30) ||w||^2. A stochastic gradient should be equal to this in expectation. If you always select only one term to differentiate, you systematically under-estimate the true gradient.
d) Try to find a counter-example here, two inputs A and B such that \(\alpha f(A) + (1-\alpha) f(B)\) < f(\alpha A + (1-\alpha)B)).
Can you give a counter example please ? :)
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