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1. Recursive nearest neighbor co‐kriging models for big multi‐fidelity spatial data sets

   https://doi.org/10.1002/env.2844  

   Cheng, Si; Konomi, Bledar A.; Karagiannis, Georgios; Kang, Emily L. (February 2024, Environmetrics)

   Abstract Big datasets are gathered daily from different remote sensing platforms. Recently, statistical co‐kriging models, with the help of scalable techniques, have been able to combine such datasets by using spatially varying bias corrections. The associated Bayesian inference for these models is usually facilitated via Markov chain Monte Carlo (MCMC) methods which present (sometimes prohibitively) slow mixing and convergence because they require the simulation of high‐dimensional random effect vectors from their posteriors given large datasets. To enable fast inference in big data spatial problems, we propose the recursive nearest neighbor co‐kriging (RNNC) model. Based on this model, we develop two computationally efficient inferential procedures: (a) the collapsed RNNC which reduces the posterior sampling space by integrating out the latent processes, and (b) the conjugate RNNC, an MCMC free inference which significantly reduces the computational time without sacrificing prediction accuracy. An important highlight of conjugate RNNC is that it enables fast inference in massive multifidelity data sets by avoiding expensive integration algorithms. The efficient computational and good predictive performances of our proposed algorithms are demonstrated on benchmark examples and the analysis of the High‐resolution Infrared Radiation Sounder data gathered from two NOAA polar orbiting satellites in which we managed to reduce the computational time from multiple hours to just a few minutes. 

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2. REDS: Random ensemble deep spatial prediction

   https://doi.org/10.1002/env.2780  

   Daw, Ranadeep; Wikle, Christopher_K (December 2022, Environmetrics)

   Abstract There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there has been growing interest in the machine learning community for such methods, primarily driven by the success of deep Gaussian process regression approaches and deep convolutional neural networks. These methods are often computationally expensive to train and implement and consequently, there has been a resurgence of interest in random projections and deep learning models based on random weights—so called reservoir computing methods. Here, we combine several of these ideas to develop the random ensemble deep spatial (REDS) approach to predict spatial data. The procedure uses random Fourier features as inputs to an extreme learning machine (a deep neural model with random weights), and with calibrated ensembles of outputs from this model based on different random weights, it provides a simple uncertainty quantification. The REDS method is demonstrated on simulated data and on a classic large satellite data set. 

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3. Distributed model building and recursive integration for big spatial data modeling

   https://doi.org/10.1093/biomtc/ujae159  

   Hector, Emily_C; Reich, Brian_J; Eloyan, Ani (January 2025, Biometrics)

   ABSTRACT Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional likelihoods. We propose a shift in viewpoint from whole to local data perspectives that is rooted in distributed model building and integrated estimation and inference. The framework’s backbone is a computationally and statistically efficient integration procedure that simultaneously incorporates dependence within and between spatial resolutions in a recursively partitioned spatial domain. Statistical and computational properties of our distributed approach are investigated theoretically and in simulations. The proposed approach is used to extract new insights into autism spectrum disorder from the autism brain imaging data exchange. 

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4. Spatial Classification with Limited Observations Based on Physics-Aware Structural Constraint

   https://doi.org/10.1609/aaai.v34i01.5436  

   Sainju, Arpan Man; He, Wenchong; Jiang, Zhe; Yan, Da (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain regions or partial responses are collected in field surveys. Existing research mostly focuses on addressing incomplete or missing data, e.g., data cleaning and imputation, classification models that allow for missing feature values, or modeling missing features as hidden variables and applying the EM algorithm. These methods, however, assume that incomplete feature observations only happen on a small subset of samples, and thus cannot solve problems where the vast majority of samples have missing feature observations. To address this issue, we propose a new approach that incorporates physics-aware structural constraints into the model representation. Our approach assumes that a spatial contextual feature is observed for all sample locations and establishes spatial structural constraint from the spatial contextual feature map. We design efficient algorithms for model parameter learning and class inference. Evaluations on real-world hydrological applications show that our approach significantly outperforms several baseline methods in classification accuracy, and the proposed solution is computationally efficient on a large data volume. 

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5. spOccupancy: An R package for single‐species, multi‐species, and integrated spatial occupancy models

   https://doi.org/10.1111/2041-210X.13897  

   Doser, Jeffrey W.; Finley, Andrew O.; Kéry, Marc; Zipkin, Elise F. (May 2022, Methods in Ecology and Evolution)

   Abstract Occupancy modelling is a common approach to assess species distribution patterns, while explicitly accounting for false absences in detection–nondetection data. Numerous extensions of the basic single‐species occupancy model exist to model multiple species, spatial autocorrelation and to integrate multiple data types. However, development of specialized and computationally efficient software to incorporate such extensions, especially for large datasets, is scarce or absent.We introduce thespOccupancy Rpackage designed to fit single‐species and multi‐species spatially explicit occupancy models. We fit all models within a Bayesian framework using Pólya‐Gamma data augmentation, which results in fast and efficient inference.spOccupancyprovides functionality for data integration of multiple single‐species detection–nondetection datasets via a joint likelihood framework. The package leverages Nearest Neighbour Gaussian Processes to account for spatial autocorrelation, which enables spatially explicit occupancy modelling for potentially massive datasets (e.g. 1,000s–100,000s of sites).spOccupancyprovides user‐friendly functions for data simulation, model fitting, model validation (by posterior predictive checks), model comparison (using information criteria and k‐fold cross‐validation) and out‐of‐sample prediction. We illustrate the package's functionality via a vignette, simulated data analysis and two bird case studies.ThespOccupancypackage provides a user‐friendly platform to fit a variety of single and multi‐species occupancy models, making it straightforward to address detection biases and spatial autocorrelation in species distribution models even for large datasets. 

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