exercise 1.1
apparrently i copied the answer above, 1.2 the variance is a vector and the j-th element is exactly the form of above which is softmax(0)_j(1-softmax(0)_j)In formula 3.4.7,
Hi @Gavin, great question. A simple answer is:
For more details, please check 22.7. Maximum Likelihood — Dive into Deep Learning 1.0.3 documentation
@goldpiggy
The simple answer seems to be Tautology.
I have read URL you give.
But I think it didn’t solve this question.
I can’t find anything in it.
Hello. I am still not able to understand clearly how these 2 equations are related. Can you please explain, how for a particular observation i, the probability y given x is related to the entropy definition overall classes?
Thank you for your response. My question was more specifically why
is same as
l(y,y_hat)
Is this because y when 1-hot encoded has only single position with 1 and hence when we sum up the y * log(y_hat) over the entire class, we are left with the probability y_hat corresponding to true y. Please advise.
@Abinash_Sahu
l (y，y _ hat)
Cross entropy loss
Only one type of these losses we often use.
https://ml-cheatsheet.readthedocs.io/en/latest/loss_functions.html
Q1.2. Compute the variance of the distribution given by softmax(𝐨)softmax(o) and show that it matches the second derivative computed above.
Can someone point me in the right direction? I tried to use Var[𝑋]=𝐸[(𝑋−𝐸[𝑋])^2]=𝐸[𝑋^2]−𝐸[𝑋]^2 to find the variance but I ended up having the term 1/q^2… it doesn’t look like the second derivative from Q1.1.
Thanks!
It appears that there is a reference that remained unresolved:
:eqref: eq_l_cross_entropy
in 3.4.5.3
to keep unified form,should the yj in later two equations should have an upper right mark (i) ?
I cannot understand the equation in 3.4.9
I may have an explanation considering equivalence between log likehood and cross-entropy.
?
