/explore
|
You are here 
|
www.ethanepperly.com | ||
| | | | |
extremal010101.wordpress.com
|
|
| | | | | Suppose we want to understand under what conditions on $latex B$ we have $latex \begin{aligned} \mathbb{E} B(f(X), g(Y))\leq B(\mathbb{E}f(X), \mathbb{E} g(Y)) \end{aligned}$holds for all test functions, say real valued $latex f,g$, where $latex X, Y$ are some random variables (not necessarily all possible random variables!). If $latex X=Y$, i.e., $latex X$ and $latex Y$ are... | |
| | | | |
jaketae.github.io
|
|
| | | | | Note: This blog post was completed as part of Yale's CPSC 482: Current Topics in Applied Machine Learning. | |
| | | | |
djalil.chafai.net
|
|
| | | | | This post is devoted to a concentration inequality of Lipschitz functions for a class of projected probability distributions on the unit sphere of $\mathbb{R}^n$, $n\geq2$, \[ \mathbb{S}^{n-1}=\Bigl\{x\in\mathbb{R}^n:|x|:=\sqrt{x_1^2+\cdots+x_n^2}=1\Bigr\}. \] We take this opportunity to recall various aspects of concentration for Gaussians. Concentration. Let... | |
| | | | |
qchu.wordpress.com
|
|
| | | (Part I of this post ishere) Let $latex p(n)$ denote the partition function, which describes the number of ways to write $latex n$ as a sum of positive integers, ignoring order. In 1918 Hardy and Ramanujan proved that $latex p(n)$ is given asymptotically by $latex \displaystyle p(n) \approx \frac{1}{4n \sqrt{3}} \exp \left( \pi \sqrt{ \frac{2n}{3}... | ||
