Learning from data

Part of the Machine Learning course.

Start with a dataset and work toward a fitted model. These lessons explain what a prediction estimates, how we learn it from examples, and how we measure its error.

The prerequisites are conditional distributions, expectation, and variance.

Contents

1. Dots with a hidden rule — Identify inputs and outputs, define the conditional mean, and state the noise assumptions.
2. The best guess is the average — Calculate prediction error and derive why the mean minimizes squared loss.
3. Average your neighbors — Estimate a local average and see why neighbors become scarce in many dimensions.
4. Assume a shape, then fit it — Choose a model family and fit its parameters to the data.
5. Grade it on dots it hasn’t seen — Separate training, validation, and test data.
6. Where the error comes from — Distinguish expected error, squared bias, prediction variance, and output noise.
7. One dataset, from fitting to a final test — Fit three models, compare validation errors, and evaluate the chosen model once.
8. Worked notation problems — Translate a formal question and work through its calculation.
9. Cheat sheet — Look up notation, formulas, and their conditions.
10. Mixed practice — Choose the operation a question needs, with optional hints and saved review.