Tree Structured Gaussian Process Approximations.
9Gaussian process regression can be accelerated by constructing a small pseudo-dataset to summarize the observed data. This idea sits at the heart of many approximation schemes, but such an approach requires the number of pseudo-datapoints to be scaled with the range of the input space if the accuracy of the approximation is to be maintained. This presents problems in time-series settings or in spatial datasets where large numbers of pseudo-datapoints are required since computation typically scales quadratically with the pseudo-dataset size. In this talk I will describe a new approximation whose complexity grows linearly with the number of pseudo-datapoints. This is achieved by imposing a tree or chain structure on the pseudo-datapoints and calibrating the approximation using a Kullback-Leibler (KL) minimization. Inference and learning can then be performed efficiently using the Gaussian belief propagation algorithm. We trace out the speed-accuracy trade-off for the new method and show that the frontier dominates those obtained from a large number of existing approximation techniques. (Joint work with Thang Bui)