All Questions
11 questions with no upvoted or accepted answers
7
votes
0
answers
759
views
Product of two random Gaussian matrices - orthant probability
Let $X \in \mathbb{R}^{m \times n}$ and $Y \in \mathbb{R}^{n \times k} $ be two independent Gaussian random matrices, i.e., with entries independently sampled from $\mathcal{N}(0,1)$ (a normal ...
- 968
5
votes
1
answer
1k
views
Explicit constant for Carbery–Wright inequality
The Carbery–Wright inequality is a seminal result about the anti-concentration of polynomials of Gaussian random variables.
See e.g. Meka, Nguyen, and Vu - Anti-concentration for polynomials of ...
- 111
5
votes
0
answers
711
views
Concentration inequality for max component of a multivariate Gaussian in the general case
I am looking to bound the variance of the maximum component of a vector distributed multivariate Gaussian in the general case where the Gaussian distribution has arbitrary mean and full covariance ...
- 283
4
votes
0
answers
162
views
Concentration Inequality for Score Functions of Exponential Familty
Let $p$ be the density of a continuous one-parameter exponential family distribution on $\mathbb{R}$. We assume that
$$p(x) = c(x)\cdot \exp\bigl [ x \cdot \theta - b(\theta ) \bigr ], $$
where $\...
- 1,127
3
votes
0
answers
334
views
Tail bound on trace norm / nuclear norm / Schatten-1 norm of Rademacher matrix
Let $0 < r \leq d$ integers. Let $X$, $Y$ be $d \times r$ matrices of independent Rademacher variables, that is, $X,Y \in \mathbb{R}^{d \times r}$ with entries $\pm1$ with probability $1/2$. I am ...
- 223
3
votes
0
answers
186
views
Anti-concentration for sum of t-wise independent uniform variables
Let $X_{1},\ldots,X_{n}$ be i.i.d. random variables, each variable is uniform over the set of integers $\{ 0,\ldots,D-1 \}$. Let $S = \sum_{i=1}^{n}X_{i}$.
By ``small ball probability'', we have that ...
- 225
2
votes
0
answers
83
views
Concentration inequalities for sets
Assume that we have a random set $B$ which is constructed by selecting elements from $U = \{ X_1, \dots, X_n \}$ where $X_i$ are independent samples from Gaussians with means $\mu_i$ and variances $\...
- 143
1
vote
0
answers
68
views
(Anti-)concentration of gap between largest and second largest component of multivariate random gaussian vector
Let $n$ be a large positive integer and let $Y=(Y_1,\ldots,Y_n)$ be a zero-centered random $n$-dmensional real vector with covariance matrix $\Sigma$, an $n$-by-$n$ positive definite matrix with ...
- 6,853
1
vote
0
answers
376
views
Anti-concentration bounds for folded normal and inverse of gaussian variables
Are there any easy to use bounds on sums of the following kind :
$$
\sum_{i = 1}^{i = N} |a_i| \geq P \\
a_i \sim \mathcal{N}(0, 1) \\
$$
and also for sums of the form :
$$
\sum_{i = 1}^{i = M} \...
- 111
0
votes
0
answers
116
views
Concentration bounds for sum of weighted sampling without replacement
Let $X$ be a collection of $2l$ non-negative numbers $X_1,X_2,\ldots,X_{2l}$. We draw $l$ weighted (proportional to values) samples without replacement from $X$. Let $S$ denote this set of $l$ samples....
- 11
0
votes
0
answers
86
views
Expected diameter of a random point set
General problem: For a point set $S\subset X$ in a metric space $(X,d)$, let $\text{diam}(S)=\max_{x,y\in S}d(x,y)$. Given a distribution $P$ on $X$ and $m$ i.i.d. points $x_1,\ldots,x_m\sim P$, what ...
- 19