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    $\begingroup$ I know of several definitions of "Gaussian processes," so it's not apparent what your question is really asking about. But as you consider how to clarify it, ask yourself this: exactly how would you parametrize the Gaussian process you have in mind? If you cannot do it in a natural way with a finite number of real parameters, then it should be considered nonparametric. $\endgroup$ Commented Dec 27, 2012 at 16:15
  • $\begingroup$ @whuber. AFAIK, the main parameters of gaussian processes are the mean and the covariance functions. But as we keep on adding data points, they keep on increasing. So it keeps on increasing. Is that why gaussian processes are termed as non parametric? $\endgroup$ Commented Dec 27, 2012 at 17:04
  • $\begingroup$ @whuber If I have millions of training data points, then my GP f ~ N(m,k) will be a million dimensional multivariate gaussian distribution. Isn't that too big? I mean as new training data comes it gets bigger and bigger. Doesn't it give rise to computational issue? $\endgroup$ Commented Dec 27, 2012 at 17:06
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    $\begingroup$ "Parametric" versus "non-parametric" are terms that do not apply to particular processes: they apply to the entire family of processes that could be fit to data. Although I still do not know what family you have in mind, it sounds like although the number of parameters may be finite in any circumstance, there is no limit to the number of parameters that may appear among members of the family: ergo, the problem is non-parametric. $\endgroup$ Commented Dec 27, 2012 at 17:35