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A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is high. Gaussian process models with additive correlation functions are scalable to dimensionality, but they are very restrictive as they only work for additive functions. In this work, we consider a projection pursuit model, in which the nonparametric part is driven by an additive Gaussian process regression. The dimension of the additive function is chosen to be higher than the original input dimension. We show that this dimension expansion can help approximate more complex functions. A gradient descent algorithm is proposed to maximize the likelihood function. Simulation studies show that the proposed method outperforms the traditional Gaussian process models.

The area of transfer learning comprises supervised machine learning methods that cope with the issue when the training and testing data have different input feature spaces or distributions. In this work, we propose a novel transfer learning algorithm called Renewing Iterative Self-labeling Domain Adaptation (Re-ISDA). This work is motivated by a cervical spine motion prediction problem, with the goal of predicting the cervical spine motion of different subjects using the measurements of "exterior features". The joint distribution of the exterior features for each subject may vary with one's distinct BMI, sex and other characteristics; the sample size of this problem is limited due to the high experimental cost. The proposed method is well suited for transfer learning problems with limited training samples. The learning problem is formulated as a dynamic programming model and the latter is then solved by an efficient greedy algorithm. Numerical studies show that the proposed method outperforms prevailing transfer learning methods. The proposed method also achieves high prediction accuracy for the cervical spine motion problem.