Fast Approximate Multioutput Gaussian Processes

Gaussian processes regression models are an appealing machine learning method as they learn expressive nonlinear from exemplar data with minimal parameter tuning and estimate both the mean covariance of unseen points. However, cubic computational complexity growth number samples has been a long standing challenge. Training requires inversion $N \times N$N×N kernel at every iteration, whereas needs computation $m N$m×N kernel, where $N$N $m$m training test points, respectively. This work demonstrates how approximating using eigenvalues functions leads to approximate process significant reduction in complexity. now computing only n$N×n eigenfunction matrix $n n$n×n inverse, $n$n is selected eigenvalues. Furthermore, n$m×n matrix. Finally, special case, hyperparameter optimization completely independent samples. The proposed can regress over multiple outputs, correlations between them, their derivatives any order. reduction, capabilities, multioutput correlation learning, comparison state art demonstrated simulation examples. Finally we show approach be utilized model real human data.