arXiv subjects

Marc G. Genton

Publications and source records attributed to Marc G. Genton.

At least 55 records · Page 3Linked to original sources

arXiv2022

Large-scale Environmental Data Science with ExaGeoStatR

Parallel computing in Gaussian process calculations becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications. The evaluation of the Gaussian log-likelihood function requires O(n^2) storage and O(n^3) operations where n is the number of geographical locations. Thus, computing the log-likelihood function with a large number of locations requires exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, to solve this computational complexity. In this paper, we advocate the use of ExaGeoStatR, a package for exascale Geostatistics in R that supports a parallel computation of the exact maximum likelihood function on a wide variety of parallel architectures. Parallelization in ExaGeoStatR depends on breaking down the numerical linear algebra operations in the log-likelihood function into a set of tasks and rendering them for a task-based programming model. The package can be used directly through the R environment on parallel systems. Currently, ExaGeoStatR supports several maximum likelihood computation variants such as exact, Diagonal Super Tile (DST), Tile Low-Rank (TLR) approximations, and Mixed-Precision (MP). ExaGeoStatR also provides a tool to simulate large-scale synthetic datasets. These datasets can help to assess different implementations of the maximum log-likelihood approximation methods. Here, we demonstrate ExaGeoStatR by illustrating its implementation details, analyzing its performance on various parallel architectures, and assessing its accuracy using synthetic datasets with up to 250K observations. We provide a hands-on tutorial to analyze a sea surface temperature real dataset. The performance evaluation involves comparisons with the popular packages geoR and fields for exact likelihood evaluation.

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arXiv2022

Scalable Gaussian-process regression and variable selection using Vecchia approximations

Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that are related to the response. For this setting, we propose a novel, scalable algorithm, coined VGPR, which optimizes a penalized GP log-likelihood based on the Vecchia GP approximation, an ordered conditional approximation from spatial statistics that implies a sparse Cholesky factor of the precision matrix. We traverse the regularization path from strong to weak penalization, sequentially adding candidate covariates based on the gradient of the log-likelihood and deselecting irrelevant covariates via a new quadratic constrained coordinate descent algorithm. We propose Vecchia-based mini-batch subsampling, which provides unbiased gradient estimators. The resulting procedure is scalable to millions of responses and thousands of covariates. Theoretical analysis and numerical studies demonstrate the improved scalability and accuracy relative to existing methods.

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arXiv2022

Sensitivity Analysis of Wind Energy Resources with Bayesian non-Gaussian and nonstationary Functional ANOVA

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia's planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade.

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arXiv2022

Nonseparable Space-Time Stationary Covariance Functions on Networks cross Time

The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but a generalized network (termed a graph with Euclidean edges). Additionally, data are repeatedly measured over different temporal instants. We provide new classes of nonseparable space-time stationary covariance functions where {\em space} can be a generalized network, a Euclidean tree, or a linear network, and where time can be linear or circular (seasonal). Because the construction principles are technical, we focus on illustrations that guide the reader through the construction of statistically interpretable examples. A simulation study demonstrates that we can recover the correct model when compared to misspecified models. In addition, our simulation studies show that we effectively recover simulation parameters. In our data analysis, we consider a traffic accident dataset that shows improved model performance based on covariance specifications and network-based metrics.

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arXiv2022

Multivariate Functional Outlier Detection using the FastMUOD Indices

We present definitions and properties of the fast massive unsupervised outlier detection (FastMUOD) indices, used for outlier detection (OD) in functional data. FastMUOD detects outliers by computing, for each curve, an amplitude, magnitude and shape index meant to target the corresponding types of outliers. Some methods adapting FastMUOD to outlier detection in multivariate functional data are then proposed. These include applying FastMUOD on the components of the multivariate data and using random projections. Moreover, these techniques are tested on various simulated and real multivariate functional datasets. Compared with the state of the art in multivariate functional OD, the use of random projections showed the most effective results with similar, and in some cases improved, OD performance.

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arXiv2022

Sub-dimensional Mardia measures of multivariate skewness and kurtosis

The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets.

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arXiv2022

Sparse Functional Boxplots for Multivariate Curves

This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate functional data. The sparse functional boxplot, based on the functional boxplot, displays sparseness proportions within the 50\% central region. The intensity sparse functional boxplot indicates the relative intensity of fitted sparse point patterns in the central region. The two-stage functional boxplot, which derives from the functional boxplot to detect outliers, is furthermore extended to its sparse form. We also contribute to sparse data fitting improvement and sparse multivariate functional data depth. In a simulation study, we evaluate the goodness of data fitting, several depth proposals for sparse multivariate functional data, and compare the results of outlier detection between the sparse functional boxplot and its two-stage version. The practical applications of the sparse functional boxplot and intensity sparse functional boxplot are illustrated with two public health datasets. Supplementary materials and codes are available for readers to apply our visualization tools and replicate the analysis.

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arXiv2022

Spatio-Temporal Cross-Covariance Functions under the Lagrangian Framework with Multiple Advections

When analyzing the spatio-temporal dependence in most environmental and earth sciences variables such as pollutant concentrations at different levels of the atmosphere, a special property is observed: the covariances and cross-covariances are stronger in certain directions. This property is attributed to the presence of natural forces, such as wind, which cause the transport and dispersion of these variables. This spatio-temporal dynamics prompted the use of the Lagrangian reference frame alongside any Gaussian spatio-temporal geostatistical model. Under this modeling framework, a whole new class was birthed and was known as the class of spatio-temporal covariance functions under the Lagrangian framework, with several developments already established in the univariate setting, in both stationary and nonstationary formulations, but less so in the multivariate case. Despite the many advances in this modeling approach, efforts have yet to be directed to probing the case for the use of multiple advections, especially when several variables are involved. Accounting for multiple advections would make the Lagrangian framework a more viable approach in modeling realistic multivariate transport scenarios. In this work, we establish a class of Lagrangian spatio-temporal cross-covariance functions with multiple advections, study its properties, and demonstrate its use on a bivariate pollutant dataset of particulate matter in Saudi Arabia.

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arXiv2022

Are You All Normal? It Depends!

The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in multivariate normality tests for i.i.d. data, with emphasis on the skewness and kurtosis approaches. We show through simulation studies that some of these tests cannot be used directly for testing normality of spatial data. We further review briefly the few existing univariate tests under dependence (time or space), and then propose a new multivariate normality test for spatial data by accounting for the spatial dependence. The new test utilizes the union-intersection principle to decompose the null hypothesis into intersections of univariate normality hypotheses for projection data, and it rejects the multivariate normality if any individual hypothesis is rejected. The individual hypotheses for univariate normality are conducted using a Jarque-Bera type test statistic that accounts for the spatial dependence in the data. We also show in simulation studies that the new test has a good control of the type I error and a high empirical power, especially for large sample sizes. We further illustrate our test on bivariate wind data over the Arabian Peninsula.

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arXiv2022

Functional Time Series Analysis Based on Records

In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA is to assume that data are continuous functions and that each continuous function is considered as a single observation. Thus, FDA deals with large-scale and complex data. However, visualization and exploratory data analysis, which is very important in practice, can be challenging due to the complexity of the continuous functions. Here we propose some nonparametric tools for functional data observed over time (functional time series). For that, we propose to use the concept of record. We study the properties of the trajectory of the number of record curves under different scenarios. Also, we propose a unit root test based on the number of records. The trajectory of the number of records over time and the unit root test can be used as visualization and exploratory data analysis. We illustrate the advantages of our proposal through a Monte Carlo simulation study. We also illustrate our method on two different datasets: Annual mortality rates in France and daily wind speed curves at Yanbu, Saudi Arabia. Overall, we can identify the type of functional time series being studied based on the number of record curves observed.

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arXiv2022

Scalable computation of predictive probabilities in probit models with Gaussian process priors

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the binary responses. A widely-implemented solution is to express the probability parameter via a probit mapping of a Gaussian process indexed by predictors. However, unlike for continuous settings, there is a lack of closed-form results for predictive distributions in binary models with Gaussian process priors. Markov chain Monte Carlo methods and approximation strategies provide common solutions to this problem, but state-of-the-art algorithms are either computationally intractable or inaccurate in moderate-to-high dimensions. In this article, we aim to cover this gap by deriving closed-form expressions for the predictive probabilities in probit Gaussian processes that rely either on cumulative distribution functions of multivariate Gaussians or on functionals of multivariate truncated normals. To evaluate these quantities we develop novel scalable solutions based on tile-low-rank Monte Carlo methods for computing multivariate Gaussian probabilities, and on mean-field variational approximations of multivariate truncated normals. Closed-form expressions for the marginal likelihood and for the posterior distribution of the Gaussian process are also discussed. As shown in simulated and real-world empirical studies, the proposed methods scale to dimensions where state-of-the-art solutions are impractical.

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arXiv2021

Forecasting High-Frequency Spatio-Temporal Wind Power with Dimensionally Reduced Echo State Networks

Fast and accurate hourly forecasts of wind speed and power are crucial in quantifying and planning the energy budget in the electric grid. Modeling wind at a high resolution brings forth considerable challenges given its turbulent and highly nonlinear dynamics. In developing countries, where wind farms over a large domain are currently under construction or consideration, this is even more challenging given the necessity of modeling wind over space as well. In this work, we propose a machine learning approach to model the nonlinear hourly wind dynamics in Saudi Arabia with a domain-specific choice of knots to reduce the spatial dimensionality. Our results show that for locations highlighted as wind abundant by a previous work, our approach results in an 11% improvement in the two-hour-ahead forecasted power against operational standards in the wind energy sector, yielding a saving of nearly one million US dollars over a year under current market prices in Saudi Arabia.

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arXiv2021

Efficiency Assessment of Approximated Spatial Predictions for Large Datasets

Due to the well-known computational showstopper of the exact Maximum Likelihood Estimation (MLE) for large geospatial observations, a variety of approximation methods have been proposed in the literature, which usually require tuning certain inputs. For example, the recently developed Tile Low-Rank approximation (TLR) method involves many tuning parameters, including numerical accuracy. To properly choose the tuning parameters, it is crucial to adopt a meaningful criterion for the assessment of the prediction efficiency with different inputs, which the most commonly-used Mean Square Prediction Error (MSPE) criterion and the Kullback-Leibler Divergence criterion cannot fully describe. In this paper, we present three other criteria, the Mean Loss of Efficiency (MLOE), Mean Misspecification of the Mean Square Error (MMOM), and Root mean square MOM (RMOM), and show numerically that, in comparison with the common MSPE criterion and the Kullback-Leibler Divergence criterion, our criteria are more informative, and thus more adequate to assess the loss of the prediction efficiency by using the approximated or misspecified covariance models. Hence, our suggested criteria are more useful for the determination of tuning parameters for sophisticated approximation methods of spatial model fitting. To illustrate this, we investigate the trade-off between the execution time, estimation accuracy, and prediction efficiency for the TLR method with extensive simulation studies and suggest proper settings of the TLR tuning parameters. We then apply the TLR method to a large spatial dataset of soil moisture in the area of the Mississippi River basin, and compare the TLR with the Gaussian predictive process and the composite likelihood method, showing that our suggested criteria can successfully be used to choose the tuning parameters that can keep the estimation or the prediction accuracy in applications.

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arXiv2021

High Performance Multivariate Geospatial Statistics on Manycore Systems

Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the cokriging technique. The latter requires the evaluation of the expensive Gaussian log-likelihood function, which has impeded the adoption of multivariate geospatial models for large multivariate spatial datasets. However, this large-scale cokriging challenge provides a fertile ground for supercomputing implementations for the geospatial statistics community as it is paramount to scale computational capability to match the growth in environmental data coming from the widespread use of different data collection technologies. In this paper, we develop and deploy large-scale multivariate spatial modeling and inference on parallel hardware architectures. To tackle the increasing complexity in matrix operations and the massive concurrency in parallel systems, we leverage low-rank matrix approximation techniques with task-based programming models and schedule the asynchronous computational tasks using a dynamic runtime system. The proposed framework provides both the dense and the approximated computations of the Gaussian log-likelihood function. It demonstrates accuracy robustness and performance scalability on a variety of computer systems. Using both synthetic and real datasets, the low-rank matrix approximation shows better performance compared to exact computation, while preserving the application requirements in both parameter estimation and prediction accuracy. We also propose a novel algorithm to assess the prediction accuracy after the online parameter estimation. The algorithm quantifies prediction performance and provides a benchmark for measuring the efficiency and accuracy of several approximation techniques in multivariate spatial modeling.

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arXiv2021

Assessing the Reliability of Wind Power Operations under a Changing Climate with a Non-Gaussian Bias Correction

Facing increasing societal and economic pressure, many countries have established strategies to develop renewable energy portfolios, whose penetration in the market can alleviate the dependence on fossil fuels. In the case of wind, there is a fundamental question related to the resilience, and hence profitability of future wind farms to a changing climate, given that current wind turbines have lifespans of up to thirty years. In this work, we develop a new non-Gaussian method data to simulations and to estimate future wind, predicated on a trans-Gaussian transformation and a cluster-wise minimization of the Kullback-Leibler divergence. Future winds abundance will be determined for Saudi Arabia, a country with a recently established plan to develop a portfolio of up to 16 GW of wind energy. Further, we estimate the change in profits over future decades using additional high-resolution simulations, an improved method for vertical wind extrapolation, and power curves from a collection of popular wind turbines. We find an overall increase in the daily profit of $272,000 for the wind energy market for the optimal locations for wind farming in the country.

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arXiv2021

Vector Autoregressive Models with Spatially Structured Coefficients for Time Series on a Spatial Grid

We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data that may be collected at hundreds of locations and capturing the spatial non-stationarity. In essence, our model is a vector autoregressive model that utilizes the spatial structure to achieve parsimony of autoregressive matrices at two levels. The first level ensures the sparsity of the autoregressive matrices using a lagged-neighborhood scheme. The second level performs a spatial clustering of the non-zero autoregressive coefficients such that nearby locations share similar coefficients. This model is interpretable and can be used to identify geographical subregions, within each of which, the time series share similar dynamical behavior with homogeneous autoregressive coefficients. The model parameters are obtained using the penalized maximum likelihood with an adaptive fused Lasso penalty. The estimation procedure is easy to implement and can be tailored to the need of a modeler. We illustrate the performance of the proposed estimation algorithm in a simulation study. We apply our model to a wind speed time series dataset generated from a climate model over Saudi Arabia to illustrate its usefulness. Limitations and possible extensions of our method are also discussed.

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arXiv2021

Conditional Normal Extreme-Value Copulas

We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is modeled using one unobserved factor. Conditional on this factor, the distribution of these variables is given by the Gaussian copula. This structure allows one to build flexible and parsimonious models for data with complex dependence structures, such as data with spatial dependence or factor structure. We study the extreme-value limits of these models and show some interesting special cases of the proposed class of copulas. We develop estimation methods for the proposed models and conduct a simulation study to assess the performance of these algorithms. Finally, we apply these copula models to analyze data on monthly wind maxima and stock return minima.

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arXiv2021

Tractable Bayes of Skew-Elliptical Link Models for Correlated Binary Data

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior. The new methodology is illustrated by application to COVID-19 pandemic data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides better fit to our highly imbalanced dataset.

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