Predictive Distribution with Gaussian process regression

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i want to create GPR models to keep us from avoiding over-fitting problems and to provide a predictive distribution of tourism demand. Although sparse GPRs are very flexible regression models, they are still limited by the form of the covariance function. For example it is difficult to model non-stationary processes with a sparse GPR model because it is hard to construct sensible non-stationary covariance functions.

And i know, Although the sparse GPR is not specifically designed to model non-stationarity, the extra flexibility associated with moving active inputs around can actually achieve this to a certain extent. The experiment shows the sparse GPR model fits to some data with an input dependent noise variance. The sparse GPR achieves a much better fit to the data than the standard GP by moving almost all the active input points outside the region of data.

I hope there is someone who can understand and experts in this field, so that the above problems can be resolved.

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