Semester 1 · Core
Probability & Statistics for ML
https://epochschool.com/subjects/probability-statistics-for-ml
The language of uncertainty behind every model: probability, random variables and distributions, limit theorems, estimation, hypothesis tests, and designing experiments that answer causal questions.
Every result is derived, then checked by simulation.
- Prerequisites
- Recommended: Helpful background. You can start without it if you are willing to fill the gaps.
What you’ll be able to do
- LO1Compute probabilities with counting, conditioning, independence and Bayes' theorem.
- LO2Model data with discrete and continuous random variables and compute expectations, variances and conditional expectations.
- LO3Describe data and relationships with summary statistics, covariance and correlation.
- LO4Explain the law of large numbers and the central limit theorem, and use sampling distributions.
- LO5Estimate parameters by maximum likelihood and quantify uncertainty with confidence intervals and the bootstrap.
- LO6Run and interpret z, t and chi-squared tests, and design randomised experiments with adequate power.
Chapters
- 01Counting and the rules of probability
- 02Conditional probability and Bayes' theorem
- 03Discrete random variables
- 04Continuous random variables
- 05Describing data and relationships
- 06Sampling and the limit theorems
- 07Estimation and confidence intervals
- 08Hypothesis testing
- 09Experiments, A/B tests and causal thinking
Graded labs
- L1
Probability by simulation
After chapter 2 · about 7 hours · Simulated birthdays, screening-camp patients and cricket-card packets · Generated for this course; no third-party data · Runs on a CPU
- L2
Distributions from scratch
After chapter 4 · about 7 hours · Samples drawn from the learner's own inverse-CDF samplers · Generated for this course; no third-party data · Runs on a CPU
- L3
The CLT and the bootstrap
After chapter 7 · about 7 hours · Synthetic UPI transaction amounts · Generated for this course; no third-party data · Runs on a CPU
- L4
Hypothesis tests from scratch
After chapter 8 · about 7 hours · Diabetes · BSD-3-Clause (scikit-learn) · Runs on a CPU
- L5
Designing and analysing an A/B test
After chapter 9 · about 7 hours · Synthetic checkout experiment log · Generated for this course; no third-party data · Runs on a CPU
Before you start
Recommended
Helpful background. You can start without it if you are willing to fill the gaps.
Where it leads
Neural Networks & Deep Learning
Optimisation & Training at Scale
Sequence Models & Transformers
Responsible AI, Ethics & Governance
NLP & Language Model Foundations
Image Formation and Classical Computer Vision
Deep Generative Models
Probabilistic ML & Bayesian Methods
Reinforcement Learning Foundations
Capstone Project
How it’s taught
You read short sections written for the page. Each ends with a check, and in-browser exercises let you practise. Graded labs run on your own cloud lab machine, CPU-friendly.
No videos. No live classes. No AI tutor.