The Dual Numbers
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)
abs and relu are not Mercer Kernels
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) + […]
PAC Learning and VC Dimension
(link)
New Math Chalk Talk: The Real Numbers
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)
Some Thoughts on Numbers
Sabine Hossenfelder’s excellent lecture “Is Infinity Real?” has inspired me to talk a bit about numbers. (link)
Evaluating Probability Models
A video introduction on how to evaluate probability models using the statistical deviance. (link)
Measure Theoretic Probability Video
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)
Tailored Models are Not The Same as Simple Corrections
Let’s take a stab at our first note on a topic that pre-establishing the definitions of probability model homotopy makes much easier to write. In this note we will discuss tailored probability models. There are models deliberately fit to training data that has an outcome prevalence equal to the expected […]
Upcoming Series: Probability Model Homotopy
I am planning a new example-based series of articles using what I am calling probability model homotopy. This is a notation I am introducing to slow down and make clearer discussing how probability models perform on different populations.
Kolmogorov’s Axioms of Probability: Even Smarter Than You Have Been Told
Introduction I’d like to talk about the Kolmogorov Axioms of Probability as another example of revisionist history in mathematics (another example here). What is commonly quoted as the Kolmogorov Axioms of Probability is, in my opinion, a less insightful formulation than what is found in the 1956 English translation of […]