Blog

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

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.

Andreas Bogossian

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.

Andreas Bogossian

Apr 14, 2026

Variational Inference & the ELBO

variational inference

probabilistic ML

deep learning

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

Andreas Bogossian

Apr 2, 2026

A* Pathfinding Algorithm

algorithms

graph theory

A* finds the shortest path between two points by balancing actual travel cost and a heuristic estimate of remaining distance.

Andreas Bogossian

Mar 19, 2026

KL Divergence

information theory

probabilistic ML

llms

KL divergence measures how much one probability distribution differs from another. KL-divergence is a foundational tool in information theory and the backbone of modern LLM…

Andreas Bogossian

Mar 17, 2026

Categories

The Kruskal-Wallis test, derived from first principles

The EM-algorithm

Variational Inference & the ELBO

A* Pathfinding Algorithm

KL Divergence