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francisbach.com | ||
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stephenmalina.com
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| | | | | Matrix Potpourri # As part of reviewing Linear Algebra for my Machine Learning class, I've noticed there's a bunch of matrix terminology that I didn't encounter during my proof-based self-study of LA from Linear Algebra Done Right. This post is mostly intended to consolidate my own understanding and to act as a reference to future me, but if it also helps others in a similar position, that's even better! | |
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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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nhigham.com
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| | | | | A $latex p$th root of an $latex n\times n$ matrix $LATEX A$ is a matrix $LATEX X$ such that $latex X^p = A$, and it can be written $latex X = A^{1/p}$. For a rational number $latex r = j/k$ (where $latex j$ and $latex k$ are integers), defining $latex A^r$ is more difficult: is... | |
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jonathankinlay.com
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| | | The capability of machine learning techniques like Random Forests and Nearest Neighbor Classification to forecast market direction needs to be checked. | ||
