What is the evidence for a Gaussian process?

What is the evidence for a Gaussian process?

For Gaussian processes our evidence is the training data. Now that we’ve seen some evidence let’s use Bayes’ rule to update our belief about the function to get the posterior Gaussian process AKA our updated belief about the function we’re trying to fit.

How are Gaussian processes used in Bayesian inference?

Since Gaussian processes let us describe probability distributions over functions we can use Bayes’ rule to update our distribution of functions by observing training data. To reinforce this intuition I’ll run through an example of Bayesian inference with Gaussian processes which is exactly analogous to the example in the previous section.

Can a Gaussian distribution be specified by its mean?

Any Gaussian distribution is completely specified by its first and second central moments (mean and covariance), and GP’s are no exception. We can specify a GP completely in terms of its mean function μ: X → R and covariance function k: X × X → R.

How is Gaussian process regression used in machine learning?

A common application of Gaussian processes in machine learning is Gaussian process regression. The idea is that we wish to estimate an unknown function given noisy observations y1, …, yN of the function at a finite number of points x1, …xN.

How is a Gaussian process used in regression?

Gaussian process regression (GPR) is an even finer approach than this. Rather than claiming relates to some specific models (e.g. ), a Gaussian process can represent obliquely, but rigorously, by letting the data ‘speak’ more clearly for themselves.

How is a Gaussian process different from supervisedlearning?

Gaussian process regression (GPR) is an even finer approach than this. Rather than claiming relates to some specific models (e.g. ), a Gaussian process can represent obliquely, but rigorously, by letting the data ‘speak’ more clearly for themselves. GPR is still a form of supervisedlearning, but the training data are harnessed in a subtler way.

How is a Gaussian process related to Bayes rule?

A Gaussian process is a probability distribution over possible functions. Since Gaussian processes let us describe probability distributions over functions we can use Bayes’ rule to update our distribution of functions by observing training data.