Tree-structured Gaussian Process Approximations
Gaussian process regression can be accelerated by constructing a small pseudo-dataset to summarise 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 paper we devise an 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) minimisation. Inference and learning can then be performed efficiently using the Gaussian belief propagation algorithm. We demonstrate the validity of our approach on a set of challenging regression tasks including missing data imputation for audio and spatial datasets. 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.
Code (0)
등록된 구현이 없습니다.
Tasks
ImputationregressionTime SeriesTime Series AnalysisSimilar Papers 제목 키워드 기반
On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models
Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-…
Gaussian ProcessesPerturbative Corrections for Approximate Inference in Gaussian Latent Variable Models
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can…
Vecchia-Inducing-Points Full-Scale Approximations for Gaussian Processes
Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome the…
Gaussian ProcessesStructured Variational Inference for Coupled Gaussian Processes
Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many…
Gaussian ProcessesVariational InferenceSparse Gaussian Processes: Structured Approximations and Power-EP Revisited
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to …
Gaussian Processes