“Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is one country.”
-David Hilbert
Latest posts
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Computational constrained optimization 1: Lagrange multipliers - January 31, 2022
In my post on the principle of maximum entropy I showed how choosing good priors in Bayesian modeling can be expressed as a constrained optimization problem, using (relative) entropy as the objective function. This post introduces the general technique of Lagrange multipliers, as well as the concept of a partition function which simplifies calculations when the optimization objective involves entropy.
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The principle of maximum entropy - January 27, 2022
What is the correct way to select a prior in Bayesian modeling? This is a deep question which leads naturally to the principle of maximum entropy, a fundamental tool in statistics, machine learning, and beyond.
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The subtleties of computing quantiles - June 21, 2020
Computing quantiles is a good way to summarize the distribution of a numerical dataset. But confusingly there are nearly a dozen different definitions of quantile that can all claim to be correct, and in all cases it is difficult to actually compute quantiles for very large datasets. I will explain why there are so many definitions, and compare a couple of different strategies for doing computations at scale.
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Working with Python Project Directories - March 05, 2020
This short post contains some tips and tricks for dealing with complicated Python project directories in an organized way.