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Feb
3
comment If $\sum x_n$ converges absolutely . I'll have to show that $\sum \frac{x_n }{1+ x_n} $ converges .
They may not be exactly the same as your question, but the approaches are applicable to this problem and your statement is proved in more or less the same fashion.
Feb
3
comment If $\sum x_n$ converges absolutely . I'll have to show that $\sum \frac{x_n }{1+ x_n} $ converges .
1] math.stackexchange.com/questions/708831/… 2] math.stackexchange.com/questions/1264577/… 3] math.stackexchange.com/questions/395292/… 4] math.stackexchange.com/questions/411280/…
Feb
2
comment Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$
@JellyBelly math.stackexchange.com/questions/504663/…
Jan
27
comment Derivative of trace of matrix product
cal.cs.illinois.edu/~johannes/research/matrix%20calculus.pdf
Jan
20
comment Solving SVM classifier with two weight vectors
@user2204324 Updated based on your recent edits.
Jan
20
comment Solving SVM classifier with two weight vectors
@user2204324 just updated the constraints as well.
Jan
13
comment Prove that $\int_{2}^{\infty} \frac{dx}{x^{1-\epsilon}\cdot \ln(x)^{\beta}}$ diverges for every $\beta$.
Put $\ln x = y$. Should make your analysis easier.
Jan
13
comment Mutual Information Always Non-negative
@becko The same arguments hold, you just have to replace the summations by integrals.
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
@AlexR. I have added the gradient to the original post.
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
Whosoever downvoted the question, please at the very least give an explanation for your downvote. Otherwise, you are just being ridiculous.
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
@AlexR. Ok, I am looking to give an analytical expression for arg max in terms of $c,m, n$. Secondly, if you look at the optimization problem, my x is constrained in [0, 1]. However, if we differentiate and set to 0, we are doing unconstrained optimization. So, the natural question here is why must the roots of the quadratic lie in [0, 1] always for all $c,m,n$?
Nov
21
comment Prove that Pb(x) = x / $||$x$||$ if $||$x$||$ $\gt$ 1 or x if $||$x$||$ $\leq$ 1.
Hint: Think of 2D space. Draw the norm ball, which is essentially a circle at the center in 2D. Take any point x in the plane. If you draw a line from the center to that point x, then this line will intersect with the exterior of the norm ball, what is that point?
Oct
28
comment How to prove that if $\lambda_{\max}(A)\leq t\quad\iff\quad A\preceq tI$?
Hint: Prove the first implication $A \preceq tI \Rightarrow \lambda_{\max}(A) \leq t$. What does it mean for $tI - A$ to be positive semidefinite? (start from the definition)
Oct
26
comment Orthogonality of stochastic matrix
@AlgebraicPavel Thanks for the pointer! Theorem 4.1 looks very very useful!!
Oct
18
comment Understanding Markov's inequality
Are you sure the first inequality would be true, if $\textrm{Range}(g) = [-\infty, 0]$?
Oct
7
comment $(u_1,\ldots,u_k,v_1,\ldots,v_l)$ is linearly ind. iff $\operatorname{span}(u_1,\ldots,u_k) \cap (\operatorname{span}(v_1,\ldots,v_l) = \{0\} $
math.stackexchange.com/questions/392636/…
Sep
30
comment find $\det(\det(A)B[\det(B)A^{-1}])$
@shuuichi_nitori Because A and B are square matrices of order 3.
Sep
30
comment find $\det(\det(A)B[\det(B)A^{-1}])$
@shuuichi_nitori I had added some more explanation to the answer.
Sep
15
comment Let $Y\sim\text{uniform}(0,1)$ and define $X=\min\{Y,1-Y\}$. What is the PDF of $X$?
Should not be surprising. If you look at your derivation, you will realize that either Y < 1/2 or > 1/2 and thus min will always lie in [0, 1/2] and it will be uniform.
Jun
3
comment Why do we use gradient descent in the backpropagation algorithm?
@moose I will have to think about your suggestion carefully. That would require me to elaborate on the answer a little more than I would like to do, but let me see.