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djalil.chafai.net | ||
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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... |
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www.ethanepperly.com
[AI summary] The user has provided a comprehensive set of mathematical derivations and inequalities related to probability and statistics, focusing on bounding the probability that the sample mean deviates from its expected value. The key points include: (1) Using the Chernoff bound to derive a tail inequality for bounded random variables, (2) Applying the Hoeffding's inequality to show that the probability of the sample mean deviating by more than t is exponentially small in n, (3) Deriving the final result that the probability is bounded by 2exp(-2nt^2/(b-a)^2), and (4) Mentioning the connection to the Hoeffding inequality. The user also included some unrelated text about an ORCID iD and an email profile, which seems to be an error or unrelated information... |
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francisbach.com
[AI summary] This mathematical post explores the geometry of positive semi-definite matrices using the von Neumann entropy and related Bregman divergences to derive concentration inequalities for random matrices. |
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margint.blog
One discussion I find myself in more often recently is people asking me whether something is "really AI" or not. Often, what people seem to mean with that is whether someone is already using deep learning, or still "just" machine learning. I mentioned this to a friend in the industry and he just rolled his... |
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