Quiz

Gaussian Process regression is an elegant and powerful method with many practical applications, not only within shape modelling. Here you can check whether you have understood the main ideas.

Question 1

In the derivation of Gaussian Process regression with noisy observation, we made the assumption that the noise is independent Gaussian noise. Do you think this assumption is essential?

Yes, because in this case the joint distribution is still a multivariate normal distribution and this is the key to deriving the closed form solutions for the mean and covariance function.

No, any other assumption about the noise would have worked as well.

Question 2

Which of the following assertions about the solution of a Gaussian Process regression are true? Multiple answers are possible.

The posterior mean is independent of the observed deformation.

The posterior covariance is independent of the observed deformation.

The posterior mean is a linear combination of the kernel functions, evaluated at the observed points.

Question 3

What can we say about the total variance in a posterior model?

It is smaller than the total variance of the prior model.

It is equal to the total variance of the prior model.

It is larger than the total variance of the prior model.

Question 4

Assume you have a Gaussian Process model with a Gaussian kernel with a large standard deviation. Assume we observe a deformation at a point x. What can we say about the variance of a deformation at a point that is close to x?

We cannot say anything, as the deformation at this point is independent of the deformation at x.

The variance decreases, as the point correlates with the observation.

The variance increases as we also have to account for the uncertainty of the observation.