Blog

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

PCA: the shape hidden in your data
linear algebra
machine learning
geometry

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.

Andreas Bogossian
May 8, 2026

Illustration of rank-based comparison of groups using the Kruskal-Wallis test

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

Visualisation of the EM-algorithm fitting two Gaussian distributions to unlabelled data

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

Diagram showing the relationship between the ELBO and the log-evidence in variational inference

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

Animated visualisation of the A* pathfinding algorithm navigating a grid

A* Pathfinding Algorithm
algorithms
search
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
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