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Chiwoo Park

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5 papers

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JMLR Journal 2022 Journal Article

Jump Gaussian Process Model for Estimating Piecewise Continuous Regression Functions

Chiwoo Park

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In many scientific and engineering applications of regression analysis, the underlying regression functions are often piecewise continuous in that data follow different continuous regression models for different input regions with discontinuities across regions. However, many conventional GP regression approaches are not designed for piecewise regression analysis. There are piecewise GP models to use explicit domain partitioning and pose independent GP models over partitioned regions. They are not flexible enough to model real datasets where data domains are divided by complex and curvy jump boundaries. We propose a new GP modeling approach to estimate an unknown piecewise continuous regression function. The new GP model seeks a local GP estimate of an unknown regression function at each test location, using local data neighboring the test location. Considering the possibilities of the local data being from different regions, the proposed approach partitions the local data into pieces by a local data partitioning function. It uses only the local data likely from the same region as the test location for the regression estimate. Since we do not know which local data points come from the relevant region, we propose a data-driven approach to split and subset local data by a local partitioning function. We discuss several modeling choices of the local data partitioning function, including a locally linear function and a locally polynomial function. We also investigate an optimization problem to jointly optimize the partitioning function and other covariance parameters using a likelihood maximization criterion. Several advantages of using the proposed approach over the conventional GP and piecewise GP modeling approaches are shown by various simulated experiments and real data studies. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2018 Journal Article

Patchwork Kriging for Large-scale Gaussian Process Regression

Chiwoo Park
Daniel Apley

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patching together the local GP models nearly seamlessly to ensure that the local GP models for two neighboring regions produce nearly the same response prediction and prediction error variance on the boundary between the two regions. This largely mitigates the well-known discontinuity problem that degrades the prediction accuracy of existing local partitioned GP methods over regional boundaries. Our main innovation is to represent the continuity conditions as additional pseudo-observations that the differences between neighboring GP responses are identically zero at an appropriately chosen set of boundary input locations. To predict the response at any input location, we simply augment the actual response observations with the pseudo-observations and apply standard GP prediction methods to the augmented data. In contrast to heuristic continuity adjustments, this has an advantage of working within a formal GP framework, so that the GP-based predictive uncertainty quantification remains valid. Our approach also inherits a sparse block-like structure for the sample covariance matrix, which results in computationally efficient closed-form expressions for the predictive mean and variance. In addition, we provide a new spatial partitioning scheme based on a recursive space partitioning along local principal component directions, which makes the proposed approach applicable for regression domains having more than two dimensions. Using three spatial datasets and three higher dimensional datasets, we investigate the numerical performance of the approach and compare it to several state-of-the-art approaches. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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JMLR Journal 2016 Journal Article

Efficient Computation of Gaussian Process Regression for Large Spatial Data Sets by Patching Local Gaussian Processes

Chiwoo Park
Jianhua Z. Huang

This paper develops an efficient computational method for solving a Gaussian process (GP) regression for large spatial data sets using a collection of suitably defined local GP regressions. The conventional local GP approach first partitions a domain into multiple non-overlapping local regions, and then fits an independent GP regression for each local region using the training data belonging to the region. Two key issues with the local GP are (1) the prediction around the boundary of a local region is not as accurate as the prediction at interior of the local region, and (2) two local GP regressions for two neighboring local regions produce different predictions at the boundary of the two regions, creating undesirable discontinuity in the prediction. We address these issues by constraining the predictions of local GP regressions sharing a common boundary to satisfy the same boundary constraints, which in turn are estimated by the data. The boundary constrained local GP regressions are solved by a finite element method. Our approach shows competitive performance when compared with several state- of-the-art methods using two synthetic data sets and three real data sets. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JMLR Journal 2012 Journal Article

GPLP: A Local and Parallel Computation Toolbox for Gaussian Process Regression

Chiwoo Park
Jianhua Z. Huang
Yu Ding

This paper presents the Getting-started style documentation for the local and parallel computation toolbox for Gaussian process regression (GPLP), an open source software package written in Matlab (but also compatible with Octave). The working environment and the usage of the software package will be presented in this paper. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2012. ( edit, beta )

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JMLR Journal 2011 Journal Article

Domain Decomposition Approach for Fast Gaussian Process Regression of Large Spatial Data Sets

Chiwoo Park
Jianhua Z. Huang
Yu Ding

Gaussian process regression is a flexible and powerful tool for machine learning, but the high computational complexity hinders its broader applications. In this paper, we propose a new approach for fast computation of Gaussian process regression with a focus on large spatial data sets. The approach decomposes the domain of a regression function into small subdomains and infers a local piece of the regression function for each subdomain. We explicitly address the mismatch problem of the local pieces on the boundaries of neighboring subdomains by imposing continuity constraints. The new approach has comparable or better computation complexity as other competing methods, but it is easier to be parallelized for faster computation. Moreover, the method can be adaptive to non-stationary features because of its local nature and, in particular, its use of different hyperparameters of the covariance function for different local regions. We illustrate application of the method and demonstrate its advantages over existing methods using two synthetic data sets and two real spatial data sets. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

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