Probability

Part of the Machine Learning course.

Contents

1. Chance is a fraction — Count outcomes, then calculate probabilities with unequal weights and new information.
2. Attach a number, get a distribution — Define a random variable and distinguish probability mass from density.
3. The running total, and its slope — Use a cumulative distribution to calculate interval probabilities.
4. The average, and the swing — Calculate expectation and variance, including sums of dependent variables.
5. The usual suspects — Work with Bernoulli, binomial, uniform, and normal distributions.
6. Two at once — Read joint tables, condition on information, and average across cases.
7. Worked notation problems — Translate a formal question and work through its calculation.
8. Cheat sheet — Look up notation, formulas, and their conditions.
9. Mixed practice — Choose the operation a question needs, with optional hints and saved review.

Next

Learning from data applies these ideas to prediction. A conditional distribution describes possible outputs at a given input. Its mean gives the best prediction under squared loss, and its variance describes the expected squared error that remains when predicting that mean.