Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table

A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs

Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to quantitative inputs and cross-validation. Here, we provide a straightforward construction of doubly orthogonal quasi-Sudoku Latin squares which can be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for both the full design and each slice. A construction of quasi-sliced orthogonal arrays based on these constructed doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn, be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for the full design and and uniformity in two-dimensional projections for each slice. These constructions are very practical to implement and yield a spectrum of design sizes and numbers of factors not currently broadly available.Comment: 15 pages, 9 figure

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

High-speed observation of sprite streamers

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Sprites are optical emissions in the mesosphere mainly at altitudes 50–90 km. They are caused by the sudden re-distribution of charge due to lightning in the troposphere which can produce electric fields in the mesosphere in excess of the local breakdown field. The resulting optical displays can be spectacular and this has led to research into the physics and chemistry involved. Imaging at faster than 5,000 frames per second has revealed streamer discharges to be an important and very dynamic part of sprites, and this paper will review high-speed observations of sprite streamers. Streamers are initiated in the 65–85 km altitude range and observed to propagate both down and up at velocities normally in the 106–5 9 107 m/s range. Sprite streamer heads are small, typically less than a few hundreds of meters, but very bright and appear in images much like stars with signals up to that expected of a magnitude -6 star. Many details of streamer formation have been modeled and successfully compared with observations. Streamers frequently split into multiple sub-streamers. The splitting is very fast. To resolve details will require framing rates higher than the maximum 32,000 fps used so far. Sprite streamers are similar to streamers observed in the laboratory and, although many features appear to obey simple scaling laws, recent work indicates that there are limits to the scaling.Research funding has been provided by the US National Science Foundation grants to the University of Alaska Fairbanks, and the US Air Force Academy, and by DARPA through a grant to the University of Florida

Accuracy of multi-point boundary crossing time analysis

Recent multi-spacecraft studies of solar wind discontinuity crossings using the timing (boundary plane triangulation) method gave boundary parameter estimates that are significantly different from those of the well-established single-spacecraft minimum variance analysis (MVA) technique. A large survey of directional discontinuities in Cluster data turned out to be particularly inconsistent in the sense that multi-point timing analyses did not identify any rotational discontinuities (RDs) whereas the MVA results of the individual spacecraft suggested that RDs form the majority of events. To make multi-spacecraft studies of discontinuity crossings more conclusive, the present report addresses the accuracy of the timing approach to boundary parameter estimation. Our error analysis is based on the reciprocal vector formalism and takes into account uncertainties both in crossing times and in the spacecraft positions. A rigorous error estimation scheme is presented for the general case of correlated crossing time errors and arbitrary spacecraft configurations. Crossing time error covariances are determined through cross correlation analyses of the residuals. The principal influence of the spacecraft array geometry on the accuracy of the timing method is illustrated using error formulas for the simplified case of mutually uncorrelated and identical errors at different spacecraft. The full error analysis procedure is demonstrated for a solar wind discontinuity as observed by the Cluster FGM instrument