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gregorygundersen.com | ||
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almostsuremath.com
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| | | | | The Rademacher distribution is probably the simplest nontrivial probability distribution that you can imagine. This is a discrete distribution taking only the two possible values $latex {\{1,-1\}}&fg=000000$, each occurring with equal probability. A random variable X has the Rademacher distribution if $latex \displaystyle {\mathbb P}(X=1)={\mathbb P}(X=-1)=1/2. &fg=000000$ A Randemacher sequence is an IID sequence of... | |
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www.kuniga.me
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| | | | | NP-Incompleteness: | |
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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.jeremykun.com
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| | | When addressing the question of what it means for an algorithm to learn, one can imagine many different models, and there are quite a few. This invariably raises the question of which models are "the same" and which are "different," along with a precise description of how we're comparing models. We've seen one learning model so far, called Probably Approximately Correct (PAC), which espouses the following answer to the learning question: | ||
