We have found that for 2 by 2 confusion matrices (a common summary relating the relation between categorical variables) the expected value of the xicor coefficient of correlation specializes into the re-normalized square of the determinant! One can summarize how a 0/1 variable x relates to a 0/1 variable y […]
For no good reason I decided to work out what shape minimized the tension at the attachment points of a draped cable. It turns out to be a lot droopier than one might expect. All of the details of the calculation using sympy can be found here.
I have a new math chalk talk up: The Game of Infinity Questions. This is back to establishing the “reasonableness” of Kolmogorov’s Axiom of continuity (in his actual formulation of his axiomatization of probability). Remember, his argument is “it is a bit off to have strong opinions on infinite processes, […]
We introduce the dual numbers, a number system that is simple to calculate with that allows us to perform automatic differentiation. For more on the dual number please see: https://win-vector.com/tag/dual-numbers/. (link)
I am sharing some rough notes (in R and Python) here on how while dot(a, b) fulfills “Mercer’s condition” (by definition!, and I’ll just informally call these beasts a “Mercer Kernel”), the seemingly harmless variations abs(dot(a, b)) relu(dot(a, b)) are not Mercer Kernels (relu(x) = max(0, x) = (abs(x) + […]
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I have a new math chalk talk to share: “The Real Numbers.” Here I go into some of the terrifying true nature of our common model for continuous quantities. (link)
Sabine Hossenfelder’s excellent lecture “Is Infinity Real?” has inspired me to talk a bit about numbers. (link)
A video introduction on how to evaluate probability models using the statistical deviance. (link)
I’d like to share a brief orientation video on measure theory based probability. Measure theory is a rigorous axiomatic treatment of probability that defers on interpretation (such as frequentist interpretation, Bayesian interpretation, or even Kolmogorov/Chaitin complexity). (link)