arXiv subjects

Marc G. Genton

Publications and source records attributed to Marc G. Genton.

At least 19 recordsLinked to original sources

arXiv2026

Scaled Block Vecchia Approximation for High-Dimensional Gaussian Process Emulation on GPUs

Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for statistical emulation, but their poor scalability limits applicability to large datasets. We introduce the Scaled Block Vecchia (SBV) algorithm for distributed GPU-based systems. SBV integrates the Scaled Vecchia approach for anisotropic input scaling with the Block Vecchia (BV) method to reduce computational and memory complexity while leveraging GPU acceleration techniques for efficient linear algebra operations. To the best of our knowledge, this is the first distributed implementation of any Vecchia-based GP variant. Our implementation employs MPI for inter-node parallelism and the MAGMA library for GPU-accelerated batched matrix computations. We demonstrate the scalability and efficiency of the proposed algorithm through experiments on synthetic and real-world workloads, including a 50M point simulation from a respiratory disease model. SBV achieves near-linear scalability on up to 512 A100 and GH200 GPUs, handles 2.56B points, and reduces energy use relative to exact GP solvers, establishing SBV as a scalable and energy-efficient framework for emulating large-scale scientific models on GPU-based distributed systems.

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arXiv2026

MPCR: Multi-Precision Computations Package in R

In the early days of computing, severe memory constraints made it necessary to use lower floating-point precision. As hardware capabilities have advanced, modern systems, particularly in computational statistics and scientific computing, have widely adopted 64-bit precision to reduce numerical errors and support complex calculations. However, in some applications, double-precision accuracy exceeds practical requirements, prompting interest in lower-precision alternatives that decrease computational complexity while maintaining adequate accuracy. This trend has accelerated with the advent of hardware optimized for low-precision computations, such as leveraging Tensor Cores technology in recent NVIDIA GPUs. Although lower precision can introduce numerical and accuracy challenges, many applications demonstrate robustness under these conditions. Consequently, new multi-precision algorithms have been developed to balance accuracy and computational cost. To facilitate the adoption of these approaches in statistical computing, this article introduces MPCR, a new R package that supports arithmetic operations at 16-, 32-, and 64-bit precision. Written in C++ and integrated with Rcpp, MPCR delivers highly optimized multi-precision computations on both CPU and GPU, enabling seamless low-precision operations. Several examples demonstrate the benefits of MPCR across both performance and accuracy.

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arXiv2026

Fisher Scoring for Exact Matérn Covariance Estimation through Stable Smoothness Optimization

Gaussian Random Fields (GRFs) with Matérn covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness parameter is challenging to estimate using maximum likelihood estimation (MLE), which involves evaluating the likelihood based on the full covariance matrix of the GRF, due to numerical instability. Moreover, MLE remains computationally prohibitive for large spatial datasets. To address this challenge, we propose the Fisher-BackTracking (Fisher-BT) method, which integrates the Fisher scoring algorithm with a backtracking line search strategy and adopts a series approximation for the modified Bessel function. This method enables an efficient MLE estimation for spatial datasets using the ExaGeoStat high-performance computing framework. Our proposed method not only reduces the number of iterations and accelerates convergence compared to derivative-free optimization methods but also improves the numerical stability of the smoothness parameter estimation. Through simulations and real-data analysis using a soil moisture dataset covering the Mississippi River Basin, we show that the proposed Fisher-BT method achieves accuracy comparable to existing approaches while significantly outperforming derivative-free algorithms such as BOBYQA and Nelder-Mead in terms of computational efficiency and numerical stability.

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arXiv2025

Quantile-based causal inference for spatio-temporal processes: Assessing the impacts of wildfires on US air quality

Wildfires pose an increasingly severe threat to air quality, yet quantifying their causal impact remains challenging due to unmeasured meteorological and geographic confounders. Moreover, wildfire impacts on air quality may exhibit heterogeneous effects across pollution levels, which conventional mean-based causal methods fail to capture. To address these challenges, we develop a Quantile-based Latent Spatial Confounder Model (QLSCM) that substitutes conditional expectations with conditional quantiles, enabling causal analysis across the entire outcome distribution. We establish the causal interpretation of QLSCM theoretically, prove the identifiability of causal effects, and demonstrate estimator consistency under mild conditions. Simulations confirm the bias correction capability and the advantage of quantile-based inference over mean-based approaches. Applying our method to contiguous US wildfire and air quality data, we uncover important heterogeneous effects: fire radiative power exerts significant positive causal effects on aerosol optical depth at high quantiles in Western states like California and Oregon, while insignificant at lower quantiles. This indicates that wildfire impacts on air quality primarily manifest during extreme pollution events. Regional analyses reveal that Western and Northwestern regions experience the strongest causal effects during such extremes. These findings provide critical insights for environmental policy by identifying where and when mitigation efforts would be most effective.

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arXiv2025

Uniform-over-dimension location tests for multivariate and high-dimensional data

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say, $n$). On the other hand, multivariate asymptotic testing methods are valid for fixed dimension only and their implementations typically require the sample size to be large compared to the dimension to yield desirable results. In practical scenarios, it is usually not possible to determine whether the dimension of the data conform to the conditions required for the validity of the high-dimensional asymptotic methods for hypothesis testing, or whether the sample size is large enough compared to the dimension of the data. In this work, we first describe the notion of uniform-over-$p$ convergences and subsequently, develop a uniform-over-dimension central limit theorem. An asymptotic test for the two-sample equality of locations is developed, which now holds uniformly over the dimension of the observations. Using simulated and real data, it is demonstrated that the proposed test exhibits better performance compared to several popular tests in the literature for high-dimensional data as well as the usual scaled two-sample tests for multivariate data, including the Hotelling's $T^2$ test for multivariate Gaussian data.

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arXiv2025

High-Performance Statistical Computing (HPSC): Challenges, Opportunities, and Future Directions

We recognize the emergence of a statistical computing community focused on working with large computing platforms and producing software and applications that exemplify high-performance statistical computing (HPSC). The statistical computing (SC) community develops software that is widely used across disciplines. However, it remains largely absent from the high-performance computing (HPC) landscape, particularly on platforms such as those featured on the Top500 or Green500 lists. Many disciplines already participate in HPC, mostly centered around simulation science, although data-focused efforts under the artificial intelligence (AI) label are gaining popularity. Bridging this gap requires both community adaptation and technical innovation to align statistical methods with modern HPC technologies. We can accelerate progress in fast and scalable statistical applications by building strong connections between the SC and HPC communities. We present a brief history of SC, a vision for how its strengths can contribute to statistical science in the HPC environment (such as HPSC), the challenges that remain, and the opportunities currently available, culminating in a possible roadmap toward a thriving HPSC community.

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arXiv2025

Scalable Asynchronous Federated Modeling for Spatial Data

Spatial data are central to applications such as environmental monitoring and urban planning, but are often distributed across devices where privacy and communication constraints limit direct sharing. Federated modeling offers a practical solution that preserves data privacy while enabling global modeling across distributed data sources. For instance, environmental sensor networks are privacy- and bandwidth-constrained, motivating federated spatial modeling that shares only privacy-preserving summaries to produce timely, high-resolution pollution maps without centralizing raw data. However, existing federated modeling approaches either ignore spatial dependence or rely on synchronous updates that suffer from stragglers in heterogeneous environments. This work proposes an asynchronous federated modeling framework for spatial data based on low-rank Gaussian process approximations. The method employs block-wise optimization and introduces strategies for gradient correction, adaptive aggregation, and stabilized updates. We establish linear convergence with explicit dependence on staleness, a result of standalone theoretical significance. Moreover, numerical experiments demonstrate that the asynchronous algorithm achieves synchronous performance under balanced resource allocation and significantly outperforms it in heterogeneous settings, showcasing superior robustness and scalability.

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arXiv2025

Robust Maximum $L_q$-Likelihood Covariance Estimation for Replicated Spatial Data

Parameter estimation with the maximum $L_q$-likelihood estimator (ML$q$E) is an alternative to the maximum likelihood estimator (MLE) that considers the $q$-th power of the likelihood values for some $q<1$. In this method, extreme values are down-weighted because of their lower likelihood values, which yields robust estimates. In this work, we study the properties of the ML$q$E for spatial data with replicates. We investigate the asymptotic properties of the ML$q$E for Gaussian random fields with a Matérn covariance function, and carry out simulation studies to investigate the numerical performance of the ML$q$E. We show that it can provide more robust and stable estimation results when some of the replicates in the spatial data contain outliers. In addition, we develop a mechanism to find the optimal choice of the hyper-parameter $q$ for the ML$q$E. The robustness of our approach is further verified on a United States precipitation dataset. Compared with other robust methods for spatial data, our proposal is more intuitive and easier to understand, yet it performs well when dealing with datasets containing outliers.

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arXiv2025

RCOMPSs: A Scalable Runtime System for R Code Execution on Manycore Systems

R has become a cornerstone of scientific and statistical computing due to its extensive package ecosystem, expressive syntax, and strong support for reproducible analysis. However, as data sizes and computational demands grow, native R parallelism support remains limited. This paper presents RCOMPSs, a scalable runtime system that enables efficient parallel execution of R applications on multicore and manycore systems. RCOMPSs adopts a dynamic, task-based programming model, allowing users to write code in a sequential style, while the runtime automatically handles asynchronous task execution, dependency tracking, and scheduling across available resources. We present RCOMPSs using three representative data analysis algorithms, i.e., K-nearest neighbors (KNN) classification, K-means clustering, and linear regression and evaluate their performance on two modern HPC systems: KAUST Shaheen-III and Barcelona Supercomputing Center (BSC) MareNostrum 5. Experimental results reveal that RCOMPSs demonstrates both strong and weak scalability on up to 128 cores per node and across 32 nodes. For KNN and K-means, parallel efficiency remains above 70% in most settings, while linear regression maintains acceptable performance under shared and distributed memory configurations despite its deeper task dependencies. Overall, RCOMPSs significantly enhances the parallel capabilities of R with minimal, automated, and runtime-aware user intervention, making it a practical solution for large-scale data analytics in high-performance environments.

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arXiv2025

GPU-Accelerated Modified Bessel Function of the Second Kind for Gaussian Processes

Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing robust GPU-hosted implementations of special functions, such as the modified Bessel function, is crucial for performance. Existing implementations of the modified Bessel function of the second kind rely on CPUs and have limited coverage of the full range of values needed in some applications. In this work, we present a robust implementation of the modified Bessel function of the second kind on GPUs, eliminating the dependence on the CPU host. We cover a range of values commonly used in real applications, providing high accuracy compared to common libraries like the GNU Scientific Library (GSL) when referenced to Mathematica as the authority. Our GPU-accelerated approach also demonstrates a 2.68X performance improvement using a single A100 GPU compared to the GSL on 40-core Intel Cascade Lake CPUs. Our implementation is integrated into ExaGeoStat, the HPC framework for Gaussian process modeling, where the modified Bessel function of the second kind is required by the Matern covariance function in generating covariance matrices. We accelerate the matrix generation process in ExaGeoStat by up to 12.62X with four A100 GPUs while maintaining almost the same accuracy for modeling and prediction operations using synthetic and real datasets.

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arXiv2025

Decentralized Inference for Spatial Data Using Low-Rank Models

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by vulnerabilities such as single-point failures and communication bottlenecks. This paper presents a decentralized framework tailored for parameter inference in spatial low-rank models to address these challenges. A key obstacle arises from the spatial dependence among observations, which prevents the log-likelihood from being expressed as a summation-a critical requirement for decentralized optimization approaches. To overcome this challenge, we propose a novel objective function leveraging the evidence lower bound, which facilitates the use of decentralized optimization techniques. Our approach employs a block descent method integrated with multi-consensus and dynamic consensus averaging for effective parameter optimization. We prove the convexity of the new objective function in the vicinity of the true parameters, ensuring the convergence of the proposed method. Additionally, we present the first theoretical results establishing the consistency and asymptotic normality of the estimator within the context of spatial low-rank models. Extensive simulations and real-world data experiments corroborate these theoretical findings, showcasing the robustness and scalability of the framework.

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arXiv2025

Block Vecchia Approximation for Scalable and Efficient Gaussian Process Computations

Gaussian Processes (GPs) are vital for modeling and predicting irregularly-spaced, large geospatial datasets. However, their computations often pose significant challenges in large-scale applications. One popular method to approximate GPs is the Vecchia approximation, which approximates the full likelihood via a series of conditional probabilities. The classical Vecchia approximation uses univariate conditional distributions, which leads to redundant evaluations and memory burdens. To address this challenge, our study introduces block Vecchia, which evaluates each multivariate conditional distribution of a block of observations, with blocks formed using the K-means algorithm. The proposed GPU framework for the block Vecchia uses varying batched linear algebra operations to compute multivariate conditional distributions concurrently, notably diminishing the frequent likelihood evaluations. Diving into the factor affecting the accuracy of the block Vecchia, the neighbor selection criterion is investigated, where we found that the random ordering markedly enhances the approximated quality as the block count becomes large. To verify the scalability and efficiency of the algorithm, we conduct a series of numerical studies and simulations, demonstrating their practical utility and effectiveness compared to the exact GP. Moreover, we tackle large-scale real datasets using the block Vecchia method, i.e., high-resolution 3D profile wind speed with a million points.

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arXiv2024

Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model.

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arXiv2024

A Generalized Unified Skew-Normal Process with Neural Bayes Inference

In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate that the GSUN is a valid spatial process by showing its vanishing correlation in large distances and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over the conventional CNN-based architectures regarding stability and accuracy by means of a simulation study and application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey g-and-h processes, through the probability integral transform (PIT).

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arXiv2024

Online stochastic generators using Slepian bases for regional bivariate wind speed ensembles from ERA5

Reanalysis data, such as ERA5, provide a comprehensive and detailed representation of the Earth's system by assimilating observations into climate models. While crucial for climate research, they pose significant challenges in terms of generation, storage, and management. For 3-hourly bivariate wind speed ensembles from ERA5, which face these challenges, this paper proposes an online stochastic generator (OSG) applicable to any global region, offering fast stochastic approximations while storing only model parameters. A key innovation is the incorporation of the online updating, which allows data to sequentially enter the model in blocks of time and contribute to parameter updates. This approach reduces storage demands during modeling by eliminating the need to store and analyze the entire dataset, and enables near real-time emulations that complement the generation of reanalysis data. The Slepian concentration technique supports the efficiency of the proposed OSG by representing the data in a lower-dimensional space spanned by data-independent Slepian bases optimally concentrated within the specified region. We demonstrate the flexibility and efficiency of the OSG through two case studies requiring long and short blocks, specified for the Arabian-Peninsula region (ARP). For both cases, the OSG performs well across several statistical metrics and is comparable to the SG trained on the full dataset.

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arXiv2024

Large-Scale Low-Rank Gaussian Process Prediction with Support Points

Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions is derived and the impacts of the selected knots and estimated covariance are studied. We suggest the use of support points as knots, which best represent data locations. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified.

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arXiv2024

Boosting Earth System Model Outputs And Saving PetaBytes in their Storage Using Exascale Climate Emulators

We present the design and scalable implementation of an exascale climate emulator for addressing the escalating computational and storage requirements of high-resolution Earth System Model simulations. We utilize the spherical harmonic transform to stochastically model spatio-temporal variations in climate data. This provides tunable spatio-temporal resolution and significantly improves the fidelity and granularity of climate emulation, achieving an ultra-high spatial resolution of 0.034 (approximately 3.5 km) in space. Our emulator, trained on 318 billion hourly temperature data points from a 35-year and 31 billion daily data points from an 83-year global simulation ensemble, generates statistically consistent climate emulations. We extend linear solver software to mixed-precision arithmetic GPUs, applying different precisions within a single solver to adapt to different correlation strengths. The PaRSEC runtime system supports efficient parallel matrix operations by optimizing the dynamic balance between computation, communication, and memory requirements. Our BLAS3-rich code is optimized for systems equipped with four different families and generations of GPUs, scaling well to achieve 0.976 EFlop/s on 9,025 nodes (36,100 AMD MI250X multichip module (MCM) GPUs) of Frontier (nearly full system), 0.739 EFlop/s on 1,936 nodes (7,744 Grace-Hopper Superchips (GH200)) of Alps, 0.243 EFlop/s on 1,024 nodes (4,096 A100 GPUs) of Leonardo, and 0.375 EFlop/s on 3,072 nodes (18,432 V100 GPUs) of Summit.

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arXiv2024

Conjugacy properties of multivariate unified skew-elliptical distributions

The broad class of multivariate unified skew-normal (SUN) distributions has been recently shown to possess important conjugacy properties. When used as priors for the coefficients vector in probit, tobit, and multinomial probit models, these distributions yield posteriors that still belong to the SUN family. Although this result has led to important advancements in Bayesian inference and computation, its applicability beyond likelihoods associated with fully-observed, discretized, or censored realizations from multivariate Gaussian models remains yet unexplored. This article covers such a gap by proving that the wider family of multivariate unified skew-elliptical (SUE) distributions, which extends SUNs to more general perturbations of elliptical densities, guarantees conjugacy for broader classes of models, beyond those relying on fully-observed, discretized or censored Gaussians. Such a result leverages the closure under linear combinations, conditioning and marginalization of SUE to prove that this family is conjugate to the likelihood induced by multivariate regression models for fully-observed, censored or dichotomized realizations from skew-elliptical distributions. This advancement enlarges the set of models that enable conjugate Bayesian inference to general formulations arising from elliptical and skew-elliptical families, including the multivariate Student's t and skew-t, among others.

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