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jonathanweisberg.org | ||
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nelari.us
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| | | | | In inverse transform sampling, the inverse cumulative distribution function is used to generate random numbers in a given distribution. But why does this work? And how can you use it to generate random numbers in a given distribution by drawing random numbers from any arbitrary distribution? | |
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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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www.ethanepperly.com
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dennybritz.com
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| | | All the code is also available as an Jupyter notebook on Github. | ||
