All Questions
7 questions with no upvoted or accepted answers
3
votes
0
answers
229
views
Expectation of angle between two vectors in the image of a gaussian random matrix
Let $m$ and $n$ be large positive integers (going to infinity), and let $W$ be a random matrix of size $n \times m$ with iid entries from $N(0,1/m)$. Let $x,y \in \mathbb R^m$ be deterministic vectors,...
- 6,853
2
votes
0
answers
68
views
Approximate any point of the interval $[-1/2,1/2]$ by the sum of $n$ iid uniform random variables from $[-1,1]$
Let $x \in [-1/2,1/2]$ and $X_1,\ldots,X_n$ be drawn iid from the uniform distribution on $[-1,1]$.
Question. Given $\varepsilon \ge 0$ an integer $k \in [1,n]$, what is a good lower-bound on the ...
- 6,853
1
vote
0
answers
64
views
Dependence rank: what is the size of the largest subcollection of random variables which is statistically independent?
Let $X_1,\ldots,X_p$ be random variables on the same space. Define their dependence rank, denoted $rank(X_1,\ldots,X_p)$ as the largest nonnegative integer $k$ such that there is a subcollection of $k$...
- 6,853
1
vote
0
answers
334
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Strong data-processing inequality ? Upper bound on a certain modified total-variation metric
Let $\mathcal X=(\mathcal X,d)$ be a Polish space equipped with the Borel sigma-algebra. Let $p\ge 1$ and $P_1,P_2$ be probability distributions on $\mathcal X$ such that $\max_{k=1,2}\int d(x,x_0)^...
- 6,853
1
vote
0
answers
245
views
Random walk conditioned on sum and last step
Can anyone help with the following (slightly weird) random walk question? I have a random walk starting at $X_0 = 1 = S_0$ where the steps $X_i$ are independent uniform random variates in $[-1,1]$. ...
- 747
0
votes
0
answers
195
views
Upper-bound for bracketing number in terms of VC-dimension
Let $P$ be a probability distribution on a measurable space $\mathcal X$ (e.g;, some euclidean $\mathbb R^m$) and let $F$ be a class of funciton $f:\mathcal X \to \mathbb R$. Given, $f_1,f_2 \in F$, ...
- 6,853
0
votes
0
answers
330
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Lower-bound smallest eigenvalue of covariance matrix of $y = f(Ax)$, for $x$ uniform on unit-sphere
Let $A=(a_1,\ldots,a_)$ be a fixed $k \times d$ matrix (with $d$ large), and $x$ be a random vector uniformly distributed on the unit-sphere in $\mathbb R^d$. Let $f:\mathbb R \to \mathbb R$ be a ...
- 6,853