Mathematical & Statistical Foundations
Review the mathematical ideas that appear repeatedly in analytics and machine learning: probability, statistics, linear algebra, optimisation, loss functions and generalisation. The topic is split into focused lessons so definitions, implementation decisions, diagnostics and common failure modes can be learned separately.
Learn the mechanism one decision at a time
Work through the lessons in order if the topic is new. If you already know the basics, open the specific leaf lesson that matches the operation, diagnostic or failure mode you need.
1Definition→
2Mechanism→
3Example→
4Diagnostic→
5Decision
Statistics and probabilityStatistics summarises data and quantifies uncertainty; probability provides a language for uncertain events and distributions. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.
02Linear algebraLinear algebra describes vectors, matrices, projections and transformations used throughout ML. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.
03OptimisationOptimisation searches for parameters or decisions that minimise loss or maximise utility subject to constraints. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.
04Loss and objective functionsA loss measures how undesirable a prediction is; an objective may combine loss with regularisation or other constraints. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.
05Generalisation, bias and varianceGeneralisation is performance on unseen data. Bias reflects systematic underfitting; variance reflects sensitivity to training data. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.