Analyzing Nonstationary Spatial Data Using Piecewise Gaussian Processes

By Hyoung‐Moon Kim, Bani K. Mallick, Christopher C. Holmes. 2005

246 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0dc151ce012a278aa1d985742e9f5a53f0919822

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Citations in the corpus

Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design (2019, background): “One avenue of research has explored partitioning the input space (and hence the training data) via, e.g., trees [19] or Voronoi cells [20], and ﬁ tting an independent GP to each partition.”
Near-optimal sensor placements in Gaussian processes (2005, unknown): “In the partitioning approach, the space is partitioned into a disjoint collection of cells, each of which is modeled by a stationary Gaussian process (Gramacy, 2005; Kim et al., 2005).”
Anomaly Detection and Removal Using Non-Stationary Gaussian Processes (2015, background): “PROBLEM DESCRIPTION We will assume that a domain can be partitioned such that within regions (tiles) the process is stationary [4].”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, background): “Kim et al. (2005) propose a random partition model where the study region is partitioned using Voronoi tessellation so that within subregions the covariance structure is assumed stationary, and observations are considered independent across subregions.”
A Scalable Hierarchical Gaussian Process Classifier (2019, methodology): “Earlier MoGPEs resort to the intensive MCMC sampling for inference [25]–[28], [60].”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, background): “, the Voronoi tessellations [107] and trees [109], [110], and trains independent local GP experts, resulting in O(nm(2)0), where m0 = n/M is the training size for each expert.”
Bayesian Treed Gaussian Process Models With an Application to Computer Modeling (2007, background): “All of these shortcomings can be addressed by partitioning the input space into regions, and ﬁtting separate stationary GP models within each region (e.g., Kim et al., 2005).”
A non‐stationary covariance‐based Kriging method for metamodelling in engineering design (2007, background): “Similar phenomena have been observed in geostatistics and environmental problems, where the geology of spatial locations greatly influences the correlation between responses [13, 14].”
Considering covariates in the covariance structure of spatial processes (2011, unknown): “Kim et al. (2005) propose a different approach, to decompose the spatial domain into disjoint regions within which the process is assumed to be stationary.”
Parameter space exploration with Gaussian process trees (2004, methodology): “This approach bears some similarity to the models of Kim et al. (2002), who ﬁt separate GPs in each element of a Voronoi tessellation.”
Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies (2008, unknown): “In the partitioning approach, the space is partitioned into a disjoint collection of cells, each of which is modeled by a stationary Gaussian process (Gramacy, 2005; Kim et al., 2005).”