I have this confusion, why are gaussian processes called smoothers. I mean I know they are also used for regression. But why are they called smoothers. Any guidance will be much appreciated
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1$\begingroup$ To my eye you seem to be conflating different things, but it might just be a difference in terminology (different areas often use terms puzzling to others). Can you point to an example of a "gaussian process" itself being called a "smoother", rather than say a computation applied to the output of a gaussian process? $\endgroup$– Glen_bCommented May 26, 2013 at 2:36
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$\begingroup$ @Glen_b. I was looking at kriging which is equivalent to Gaussian process and they say it is a smoother. $\endgroup$– user34790Commented May 26, 2013 at 3:29
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3$\begingroup$ Your response is not an example, but a repetition of the original claim. Who says that, and where? Kriging is a form of smoothing, certainly. However, kriging is not a 'Gaussian process'; it's an operation that is applied to what is assumed to be a Gaussian process. $\endgroup$– Glen_bCommented May 26, 2013 at 8:25
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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 combination of past observations. Each observed output will be given a weight, which depends on its associated input, the input for which you want to make a prediction, and the covariance function. The weighted observed outputs are then simply added together.
This becomes obvious if you look at the formula for the predictive mean: grouping operations such that all computations not involving past outputs are done, you will end up with a matrix (i.e. linear function) that, when multiplied with past outputs, will give you the predicted mean at the requested set of points.
