Administrative information

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

Lecture: Inference and Prediction

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.

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.

The materials of this learning event are available under CC BY-NC-SA 4.0

The HCAIM consortium consists of three excellence centres, three SMEs and four Universities

Title	Linear Regression
Duration	60
Module	A
Lesson Type	Lecture
Focus	Practical - AI Modelling
Topic	Linear Regression