Blog

I write about concepts I’m working to understand, mostly machine learning, statistics, and algorithms.

The Fourier Transform

How mathematics hears which notes are hidden in a chord.

May 15, 2026

PCA: the shape hidden in your data

The geometry behind principal component analysis: how the covariance matrix encodes the shape of your data, and why eigenvectors are the natural axes to read it from.

May 8, 2026

The Kruskal-Wallis test, derived from first principles

statistics

hypothesis testing

Deriving the Kruskal-Wallis test from scratch, using a pain management trial to show where ANOVA falls short.

Apr 26, 2026

The EM-algorithm

probabilistic ML

algorithms

variational inference

A deep dive into the Expectation-Maximisation algorithm: The method behind clustering, missing data, and probabilistic models.

Apr 14, 2026

Variational Inference & the ELBO

variational inference

probabilistic ML

A step-by-step derivation of the Evidence Lower Bound (ELBO), from intractable posteriors to the reconstruction-regularisation decomposition used in VAEs.

Apr 2, 2026