Administrative Information
| Title | Linear Regression |
| Duration | 60 |
| Module | A |
| Lesson Type | Lecture |
| Focus | Practical - AI Modelling |
| Topic | Linear Regression |
Keywords
linear regression, maximum likelihood, maximum a posteriori, basis functions,
Learning Goals
- To acquire demonstrable knowledge of what linear regression is
- To acquire demonstrable knowledge of the various approaches to linear regression: maximum likelihood estimation (MLE), maximum a-posteriori estimation (MAP), Bayesian
- To acquire demonstrable knowledge of analytical closed form for fitting a linear regression model
- To acquire demonstrable knowledge of non-linearizing linear models
Expected Preparation
Learning Events to be Completed Before
Obligatory for Students
- A review of basic linear algebra and solving linear systems numerically.
Optional for Students
None.
References and background for students
- Bishop, Christopher M. (2006). Pattern recognition and machine learning, Chapter 3.
Recommended for Teachers
- Familiarize themselves with the demonstration material.
Lesson materials
Instructions for Teachers
Cover the topics in the lesson outline and demonstrate the concepts using the interactive notebooks (fitting a model "manually", demonstrating the effects of the hyperparameters). Give a brief overview of the code.
Outline/time schedule
| Duration (min) | Description | Concepts |
|---|---|---|
| 5 | Introduction to linear regression | hyperplane, normal, bias |
| 5 | Defining a linear regression model | additive noise, Gaussian distribution |
| 15 | Maximum likelihood estimation | squared error, linear solvers |
| 10 | Nonlinear (polynomial) regression | polynomial regression, transformation of samples |
| 10 | Maximum a posteriori estimation | hyperparameter, prior, regularization, numerical stability |
| 5 | Bayesian linear regression | posterior, uncertainty, predictive mean and variance |
| 10 | Demonstration |
Acknowledgements
The Human-Centered AI Masters programme was Co-Financed by the Connecting Europe Facility of the European Union Under Grant №CEF-TC-2020-1 Digital Skills 2020-EU-IA-0068.