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francisbach.com | ||
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www.ethanepperly.com
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| | | | | [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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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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fa.bianp.net
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| | | | | The Langevin algorithm is a simple and powerful method to sample from a probability distribution. It's a key ingredient of some machine learning methods such as diffusion models and differentially private learning. In this post, I'll derive a simple convergence analysis of this method in the special case when the ... | |
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ianwrightsite.wordpress.com
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| | | Riemann's Zeta function is an infinite sublation of Hegelian integers. | ||
