Quiz

We have seen that Gaussian Processes are not only a nice theoretical concept, but lead to practical computer implementations in terms of the multivariate normal distribution, thanks to the marginalisation property. In this quiz we further explore this property as well as the connection between the Gaussian Process and the multivariate normal distribution.

Question 1

Why is marginalisation special in the case of normal distributions? What is the problem when computing the marginal with arbitrary distributions?

Marginalisation means integrating out all the values of the random variables we are not interested in. This integration is infeasible for most distributions.

The concept of a marginal distribution is not defined for other distributions.

Marginalising means that we need to condition on the variables. Conditional distributions are easiest to compute for normal distributions.

Question 2

If you marginalise out variables of a multivariate normal distribution, how are their values reflected in the marginal distribution?

These values enter as known observations.

They are effectively ignored.

The marginal distribution is the sum of the random variables that we marginalise out.

Question 3

Why is it better to model continuous variations of shapes instead of discrete ones?

For efficiency reasons. We never know if we even have to discretise.

The earlier we discretise, the more imprecise our computations will be.

A good discretisation is always determined by the application and cannot be chosen by the model.

Question 4

We saw that the marginalisation property makes Gaussian Processes practical. However, if we choose too many points for discretisation, we still run into a problem. Where do you think the bottleneck is?

Storing the mean vector.

The process of marginalisation.

Storing the covariance matrix.