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.
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.
The Kruskal-Wallis test, derived from first principles
Deriving the Kruskal-Wallis test from scratch, using a pain management trial to show where ANOVA falls short.
The EM-algorithm
A deep dive into the Expectation-Maximisation algorithm: The method behind clustering, missing data, and probabilistic models.
Variational Inference & the ELBO
A step-by-step derivation of the Evidence Lower Bound (ELBO), from intractable posteriors to the reconstruction-regularisation decomposition used in VAEs.
A* Pathfinding Algorithm
A* finds the shortest path between two points by balancing actual travel cost and a heuristic estimate of remaining distance.
KL Divergence
How to measure the difference between two probability distributions, and why it sits at the heart of modern LLM alignment.