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lucatrevisan.wordpress.com | ||
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nickhar.wordpress.com
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| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
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www.ethanepperly.com
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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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mathematicaloddsandends.wordpress.com
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| | | The function $latex f(x) = x \log x$ occurs in various places across math/statistics/machine learning (e.g. in the definition of entropy), and I thought I'd put a list of properties of the function here that I've found useful. Here is a plot of the function: $latex f$ is defined on $latex (0, \infty)$. The only... | ||
