1,038 research outputs found
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
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