Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

Massively parallel approximate Gaussian process regression

We explore how the big-three computing paradigms -- symmetric multi-processor (SMC), graphical processing units (GPUs), and cluster computing -- can together be brought to bare on large-data Gaussian processes (GP) regression problems via a careful implementation of a newly developed local approximation scheme. Our methodological contribution focuses primarily on GPU computation, as this requires the most care and also provides the largest performance boost. However, in our empirical work we study the relative merits of all three paradigms to determine how best to combine them. The paper concludes with two case studies. One is a real data fluid-dynamics computer experiment which benefits from the local nature of our approximation; the second is a synthetic data example designed to find the largest design for which (accurate) GP emulation can performed on a commensurate predictive set under an hour.Comment: 24 pages, 6 figures, 1 tabl

Gaussian Process Regression with Mismatched Models

Learning curves for Gaussian process regression are well understood when the `student' model happens to match the `teacher' (true data generation process). I derive approximations to the learning curves for the more generic case of mismatched models, and find very rich behaviour: For large input space dimensionality, where the results become exact, there are universal (student-independent) plateaux in the learning curve, with transitions in between that can exhibit arbitrarily many over-fitting maxima. In lower dimensions, plateaux also appear, and the asymptotic decay of the learning curve becomes strongly student-dependent. All predictions are confirmed by simulations.Comment: 7 pages, style file nips01e.sty include

Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries

Battery calendar aging prediction is of extreme importance for developing durable electric vehicles. This paper derives machine learning-enabled calendar aging prediction for lithium-ion batteries. Specifically, the Gaussian process regression (GPR) technique is employed to capture the underlying mapping among capacity, storage temperature, and SOC. By modifying the isotropic kernel function with an automatic relevance determination (ARD) structure, high relevant input features can be effectively extracted to improve prediction accuracy and robustness. Experimental battery calendar aging data from nine storage cases are utilized for model training, validation, and comparison, which is more meaningful and practical than using the data from a single condition. Illustrative results demonstrate that the proposed GPR model with ARD Matern32 (M32) kernel outperforms other counterparts and can achieve reliable prediction results for all storage cases. Even for the partial-data training test, multi-step prediction test and accelerated aging training test, the proposed ARD-based GPR model is still capable of excavating the useful features, therefore offering good generalization ability and accurate prediction results for calendar aging under various storage conditions. This is the first known data-driven application that utilizes the GPR with ARD kernel to perform battery calendar aging prognosis