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fabricebaudoin.blog | ||
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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statisticaloddsandends.wordpress.com
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| | | | | Let's say we have a convex, differentiable function $latex f: \mathbb{R}^p \rightarrow \mathbb{R}$ and that we want to minimize it. In this previous post, we saw that a gradient descent step at time $latex t$ (from point $latex \beta^t$) could be viewed as the minimizer of a quadratic approximation of $latex f$ at $latex \beta^t$:... | |
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mathbabe.org
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| | | | | A continuation ofthis, where I take notes on my workshop atHCSSiM. The real numbers are uncountable Today we used Cantor's diagonal argument to prove that the real numbers aren't countable. Namely, we assumed they were, and that we had a bijection $latex f: \mathbb{N} \rightarrow \mathbb{R}$ and then proved it didn't contain the real number... | |
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terrytao.wordpress.com
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| | | A key theme in real analysis is that of studying general functions $latex {f: X \rightarrow {\bf R}}&fg=000000$ or $latex {f: X \rightarrow {\bf C}}&fg=000000$ by first approximating them b | ||
