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terrytao.wordpress.com | ||
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almostsuremath.com
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| | | | | According to Kolmogorov's axioms, to define a probability space we start with a set and an event space consisting of a sigma-algebra F? on ?. A probability measure on this gives the probability space (?,?F?,?), on which we can define random variables as measurable maps from to the reals or other measurable... | |
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cornellmath.wordpress.com
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| | | | | When discussing the validity of the Axiom of Choice, the most common argument for not taking it as gospel is the Banach-Tarski paradox. Yet, this never particularly bothered me. The argument against the Axiom of Choice which really hit a chord I first heard at the Olivetti Club, our graduate colloquium. It's an extension... | |
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www.randomservices.org
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| | | | | [AI summary] The text covers various topics in probability and statistics, including continuous distributions, empirical density functions, and data analysis. It discusses the uniform distribution, rejection sampling, and the construction of continuous distributions without probability density functions. The text also includes data analysis exercises involving empirical density functions for body weight, body length, and gender-specific body weight. | |
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tylerneylon.com
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| | | [AI summary] The text provides an in-depth exploration of neural networks through visualizations and mathematical insights. It discusses the creation of fractal-like images using random neural networks, the impact of different activation functions (like ReLU), the role of hyperparameters in shaping network behavior, and the mathematical principles behind weight initialization techniques such as He and Glorot. The author also explains how these visualizations are generated using Python, Grapher, and Shadertoy, and highlights the aesthetic and functional value of understanding neural network architecture. | ||
