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jmanton.wordpress.com | ||
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mkatkov.wordpress.com
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| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
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dominiczypen.wordpress.com
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| | | | | Let $latex \omega$ denote the first infinite cardinal - that is, the set of non-negative integers. Let $latex p_0 = 2$ be the smallest prime number, and let $latex (p_n)_{n\in\omega}$ enumerate all prime numbers in ascending order. Let $latex \mathcal{U}$ be a free ultrafilter on $latex \omega$. We consider the field $latex F = \big(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z}\big)/{\mathcal... | |
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extremal010101.wordpress.com
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| | | | | With Alexandros Eskenazis we posted a paper on arxiv "Learning low-degree functions from a logarithmic number of random queries" exponentially improving randomized query complexity for low degree functions. Perhaps a very basic question one asks in learning theory is as follows: there is an unknown function $latex f : \{-1,1\}^{n} \to \mathbb{R}$, and we are... | |
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educationechochamber.wordpress.com
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| | | Reblogged on WordPress.com | ||
