Everything else is ready: study the parts, the key terms and the quiz below.
The Multivariate Normal
Extend the Gaussian to several features, and read its contours.
In this lesson5 parts
- 01Put recorded pairs on two axes
- 02Derive the centre and covariance from the clients
- 03Build the fitted joint density
- 04Test the approximation against recorded rows
- 05Reproduce and challenge the joint model
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- multivariate normal
- A normal probability model for a vector of jointly varying numeric features.
- mean vector
- One average coordinate for each feature.
- sample covariance
- Average centred cross-product, using one less than the sample count.
- covariance matrix
- All feature variances on the diagonal and pairwise covariances off it.
- Pearson correlation
- Covariance divided by the product of the two standard deviations.
- density contour
- Locations with equal fitted probability density.
- Mahalanobis distance
- Distance from the fitted centre after accounting for covariance.
- probability ellipse (narration)
- The region inside a squared Mahalanobis radius that holds a stated share of the model's probability.
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is Long tails, log transforms and the multivariate normal.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.
Builds on
This lesson stands on its own. These go deeper into what it uses.
- Maths 3.7