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francisbach.com | ||
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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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djalil.chafai.net
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| | | | | This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for... | |
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djalil.chafai.net
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| | | | | 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... | |
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www.capicua.com
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| | | Machine Learning has gained traction over the last few years, cybersecurity being one of them. Let's learn how to use it to boost your system's protection! | ||
