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www.jeremykun.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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almostsuremath.com
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| | | | | The monotone class theorem is a very helpful and frequently used tool in measure theory. As measurable functions are a rather general construct, and can be difficult to describe explicitly, it is common to prove results by initially considering just a very simple class of functions. For example, we would start by looking at continuous... | |
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thenumb.at
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yang-song.net
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| | | This blog post focuses on a promising new direction for generative modeling. We can learn score functions (gradients of log probability density functions) on a large number of noise-perturbed data distributions, then generate samples with Langevin-type sampling. The resulting generative models, often called score-based generative models, has several important advantages over existing model families: GAN-level sample quality without adversarial training, flexible model architectures, exact log-likelihood ... | ||
