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www.ethanepperly.com | ||
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fa.bianp.net
There's a fascinating link between minimization of quadratic functions and polynomials. A link that goes deep and allows to phrase optimization problems in the language of polynomials and vice versa. Using this connection, we can tap into centuries of research in the theory of polynomials and shed new light on ... |
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djalil.chafai.net
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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nhigham.com
For an $latex n\times n$ matrix $latex \notag A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix} \qquad (1) $ with nonsingular $latex (1,1)$ block $LATEX A_{11}$ the Schur complement is $LATEX A_{22} - A_{21}A_{11}^{-1}A_{12}$. It is denoted by $LATEX A/A_{11}$. The block with respect to which the Schur complement is taken need... |
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liorsinai.github.io
A denoising diffusion probabilistic model for generating numbers based on the MNIST dataset. The underlying machine learning model is a U-Net model, which is... |
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