hat are close in the stand attribute space, but distant in the predictor space) in large training sets, which might partly explain the slight improvement of CI% when training set size decreases. With the Bayesian inference approach, on the contrary, a substantial drop in CI% in smaller training set sizes would be expected based on the results in [@varvia].

![Lowest, average, and the highest CI% as a function of training set size for GPR estimates.[]{data-label="fig:citrain"}](ci_nt.png){width="70mm"}

Discussion {#sec:disc}
----------

Conceptually, GPR is a non-parametric machine learning method that has similarities with kNN. Thus, many approaches proposed for improvement of kNN estimates within ABA could be also utilized to further improve GPR estimates. GPR seems to be insensitive to multicollinearity and quite large numbers of predictors can been used simultaneously [@alsgpr]. In this paper, fairly traditional ABA metrics were used, adding additional predictors, such as $\alpha$-shape [@alphashape] or composite metrics [@zhao2009], could potentially improve prediction performance. Additionally, dimension reduction, for example by using principal component analysis (PCA) [@junttila2015], would probably improve performance when using small training sets. Besides PCA, the deep belief network pretraining proposed in [@hinton2008] could be beneficial.

The prediction step of GPR is not computationally much more costly than using kNN. The most computationally expensive part is the GPR model training, which requires computing the matrix inverse of a large matrix (see the equations and ). However, the matrix inverse can be precomputed for a given set of training data. After this, computing the prediction and the prediction interval only requires calculating matrix products. In the LOO case ($n_t=492$), computing the GPR prediction and intervals for a plot/cell took on average 345 ms in Matlab on a AMD Ryzen 1700X (3.4 GHz) processor, this is more expensive than kNN (1.5 ms), but still feasible for practice. For com