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Results tagged with measure-concentration
Search options questions only
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user 78756
4
votes
1
answer
273
views
Upper tail concentration of sample covariance matrices
I'm interested in concentration of the following random matrix sum in spectral norm
$\frac{1}{m}\sum_{k=1}^m b_k^2\mathbf{a}_k\mathbf{a}_k^*$
Here $\mathbf{a}_k\in\mathbb{R}^n$ are i.i.d. standard n …
- 363
2
votes
0
answers
60
views
Mean width of intersection of two elipsoid
My question is regarding mean widths. For a set $\mathcal{T}$ define the mean width
\begin{align*}
\omega(T)=\mathbb{E}_{\mathbf{g}\sim\mathcal{N}(0,\mathbf{I})}\bigg[\underset{\mathbf{u}\in\mathcal …
- 363
1
vote
0
answers
145
views
minimum eigenvalue of Katri-Rao product of two Gaussian matrices
Let $\mathbf{A}\in\mathbb{R}^{k\times n}$ and $\mathbf{B}\in\mathbb{R}^{d\times n}$ be independent matrices with i.i.d. $\mathcal{N}(0,1)$ entries. I'm interested in lower bounding the minimum eigenva …
- 363
10
votes
4
answers
642
views
Expected value of Bernoulli quadratic forms
Let $\mathbf{Y}\in\mathbb{R}^{n\times n}$ be a symmetric matrix. Let $\mathbf{x}\in\mathbb{R}^n$ be random vectors with entries i.i.d. $\pm 1$ with equal probability. I'm interested in a lower bound o …
- 363