We consider (regression) estimation of a function x u(x) from noisy observations. If the data-generating process is not well understood, simple parametric learning algorithms, for example ones from the generalized linear model (GLM) family, may be hard to apply because of the difficulty of choosing good features. In contrast, the nonparametric Gaussian process (GP) model [19] offers a flexible and powerful alternative. However, a major drawback of GP models is that the computational cost of learning is about O(n 3), and the cost of making a single prediction is O(n), where n is the number of training examples. This high computational complexity severely limits its scalability to large problems, and we believe has proved a significant barrier to the wider adoption of the GP model.

This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.

This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.

This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.