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Gaussian processes refer to stochastic processes whose realization consists of normally distributed random variables, with the additional property that any finite collection of these random variables have a multivariate normal distribution. The machinery of Gaussian processes can be employed in regression and classification problems.

4 votes

Why are gaussian processes called smoothers

It's been a long time since this question has been asked, but in case anybody still needs to know the answer: yes, GPs are (linear) smoothers. This means that any prediction a GP makes is a linear co …
Markus Mottl's user avatar
2 votes
Accepted

Stationary covariance function three times continuously differentiable with finit support?

I unfortunately don't know of a covariance function with compact support that is continuously differentiable an odd (= 3) number of times, but the GPML book describes some piecewise polynomial CFs tha …
Markus Mottl's user avatar
5 votes
Accepted

Are predictions from Bayesian Gaussian Process Regression normally distributed?

GPR does not make any statistical assumptions about the predictors. They don't even have to be numbers! All you need is a prior mean function and a covariance function, which can also be defined fo …
Markus Mottl's user avatar
4 votes
Accepted

Is Gaussian Process Regression a linear model?

I think the technically correct term to use here is that GP regression is a linear smoother, i.e. its predictions are a linearly weighted combination of past observed outputs. This does not make the …
Markus Mottl's user avatar
3 votes

Marginal Likelihood of a Gaussian Process Model, Duplicate entries in kernel matrix

Your covariance function apparently does not allow for noise. Maybe your problem does not even exhibit noise, which would mean that the same two inputs would always yield the exact same outputs. In …
Markus Mottl's user avatar
3 votes

MCMC and approximate inference for Gaussian processes

In practice you might actually run into an extreme case of this problem: if you need to learn a function that you know is noiseless (i.e. no noise term added to the diagonal of the covariance matrix) …
Markus Mottl's user avatar