[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-290327-en":59,"doc-seo-290327-105":81},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":56,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":80,"preview_page_count":4},290327,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1786009248482753345","Locally varying geostatistical machine learning for spatial prediction - Journal Article","Machine learning methods for spatial prediction often focus on the spatial auto-correlation of the response variable, yet they typically assume a homogeneous relationship between response and predictors across the whole study area (spatial stationarity). This assumption is frequently unrealistic because contextual factors create spatial non-stationarity. Existing local methods also fail to model the response’s spatial auto-correlation and may rely on fewer observations, leading to over-fitting and dimensionality issues. The paper proposes a geostatistical ML framework that explicitly combines local stationarity, response auto-correlation–based local data augmentation, and spatially varying regression relationships. Experiments on synthetic and real spatial data show improved RMSE versus popular methods, and the approach supports interpreting spatially varying predictor significance.","Edith Cowan University  \nResearch Online  \nResearch outputs 2022 to 2026  \n12-1-2024  \nLocally varying geostatistical machine learning for spatial prediction  \nFrancky Fouedjio Edith Cowan University  \nEmet Arya  \nFollow this and additional works at: [https://ro.ecu.edu.au/ecuworks2022-2026](https://ro.ecu.edu.au/ecuworks2022-2026)  \n Part of the Applied Mathematics Commons  \n10.1016/j.aiig.2024.100081  \nFouedjio, F., & Arya, E. (2024) . Locally varying geostatistical machine learning for spatial prediction. Artificial Intelligence in Geosciences, 5, 100081. [https://doi.org/10.1016/j.aiig.2024.100081](https://doi.org/10.1016/j.aiig.2024.100081)  \n[This Journal Article is posted at Research Online.](This Journal Article is posted at Research Online.)[ ](This Journal Article is posted at Research Online.)[https://ro.ecu.edu.au/ecuworks2022-2026/4342](https://ro.ecu.edu.au/ecuworks2022-2026/4342)  \nArtificial Intelligence in Geosciences 5 (2024) 100081  \n| Original research articles\u003Cbr>Locally varying geostatistical machine learning for spatial prediction Francky Fouedjio a,b,c,∗, Emet Arya a,c\u003Cbr>a Rio Tinto, Data & Analytics, 152-158 St Georges Terrace, Perth, WA 6000, Australia\u003Cbr>b Kaplan Business School Pty Ltd, Perth Campus, 1325 Hay St, West Perth, WA, 6005, Australia c Edith Cowan University, School of Science, 270 Joondalup Drive, Joondalup, WA 6027, Australia |  |  |\n| --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |\n| Keywords:\u003Cbr>Data augmentation Geostatistics\u003Cbr>Local stationarity Machine learning Conditional simulation Spatial auto-correlation Spatial non-stationarity\u003Cbr>Spatial uncertainty |  | Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction. Nonetheless, under these methods, the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area. This assumption, known as spatial stationarity, is very questionable in real-world situations due to the influence of contextual factors. Therefore, allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable. However, existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself. Moreover, under these techniques, local machine learning models are effectively built using only fewer observations, which can lead to well-known issues such as over-fitting and the curse of dimensionality. This paper introducesa novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered. The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset. The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data. In the synthetic (resp. real) case study, the proposed method’s predictive accuracy, as indicated by the Root Mean Square Error (RMSE) on the test set, is 17%(resp. 7%) better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation. Additionally, this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space, and it can even be used to investigate the local significance of predictor variables. |\n\n1. Introduction  \nGeoreferenc","cbCaimlqgjHuaC6n","https://ap.wps.com/l/cbCaimlqgjHuaC6n","pdf",9513802,13,"English","en",105,"# Introduction\n## Spatial stationarity vs. non-stationarity in georeferenced data\n## Methods for spatial auto-correlation\n## Regression-kriging and related machine learning approaches\n## Motivation for the proposed locally varying approach","[{\"question\":\"Why is the spatial stationarity assumption problematic in real spatial prediction tasks?\",\"answer\":\"Many machine learning approaches assume the relationship between the response and predictors is homogeneous across the study area. The paper notes this is questionable in real-world settings because contextual factors can vary spatially, leading to non-stationarity.\"},{\"question\":\"What limitation do existing local machine learning techniques have according to the paper?\",\"answer\":\"The paper states that existing techniques accounting for spatially varying relationships between dependent and predictor variables do not capture the spatial auto-correlation of the dependent variable itself, and local models may be built using fewer observations.\"},{\"question\":\"How does the proposed method address both spatial auto-correlation and spatially varying regression relationships?\",\"answer\":\"The approach relies on local stationarity to build a collection of local machine learning models, while leveraging local spatial auto-correlation of the response variable to locally augment the training dataset. It explicitly accounts for both response auto-correlation and regression non-stationarity.\"}]","Locally varying geostatistical machine learning for spatial prediction - Journal Article | PDF",1789641373,48,{"code":4,"msg":82,"data":83},"ok",{"site_id":75,"language":74,"slug":84,"title":65,"keywords":85,"description":66,"schema_data":86,"social_meta":140,"head_meta":142,"extra_data":144,"updated_unix":79},"locally-varying-geostatistical-machine-learning-for-spatial-prediction-journal-article","",{"@graph":87,"@context":139},[88,102,122],{"@type":89,"itemListElement":90},"BreadcrumbList",[91,95,97,100],{"item":92,"name":93,"@type":94,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":96,"name":9,"@type":94,"position":14},"https://docshare.wps.com/document/",{"item":98,"name":40,"@type":94,"position":99},"https://docshare.wps.com/document/research-report/",3,{"item":101,"name":65,"@type":94,"position":19},"https://docshare.wps.com/document/locally-varying-geostatistical-machine-learning-for-spatial-prediction-journal-article/290327/",{"url":101,"name":65,"@type":103,"image":104,"author":109,"headline":65,"publisher":111,"fileFormat":114,"inLanguage":74,"description":66,"dateModified":115,"datePublished":116,"encodingFormat":114,"isAccessibleForFree":117,"interactionStatistic":118},"DigitalDocument",{"url":105,"@type":106,"width":107,"height":108},"https://docshare.wps.com/thumbnails/locally-varying-geostatistical-machine-learning-for-spatial-prediction-journal-article/290327.png","ImageObject",300,407,{"name":63,"@type":110},"Person",{"url":92,"name":112,"@type":113},"DocShare","Organization","application/pdf","2026-10-17","2026-09-17",true,{"@type":119,"interactionType":120,"userInteractionCount":72},"InteractionCounter",{"@type":121},"ViewAction",{"@type":123,"mainEntity":124},"FAQPage",[125,131,135],{"name":126,"@type":127,"acceptedAnswer":128},"Why is the spatial stationarity assumption problematic in real spatial prediction tasks?","Question",{"text":129,"@type":130},"Many machine learning approaches assume the relationship between the response and predictors is homogeneous across the study area. The paper notes this is questionable in real-world settings because contextual factors can vary spatially, leading to non-stationarity.","Answer",{"name":132,"@type":127,"acceptedAnswer":133},"What limitation do existing local machine learning techniques have according to the paper?",{"text":134,"@type":130},"The paper states that existing techniques accounting for spatially varying relationships between dependent and predictor variables do not capture the spatial auto-correlation of the dependent variable itself, and local models may be built using fewer observations.",{"name":136,"@type":127,"acceptedAnswer":137},"How does the proposed method address both spatial auto-correlation and spatially varying regression relationships?",{"text":138,"@type":130},"The approach relies on local stationarity to build a collection of local machine learning models, while leveraging local spatial auto-correlation of the response variable to locally augment the training dataset. It explicitly accounts for both response auto-correlation and regression non-stationarity.","https://schema.org",{"og:url":101,"og:type":141,"og:title":65,"og:site_name":112,"og:description":66},"article",{"robots":143,"canonical":101},"index,follow",{"doc_id":61,"site_id":75}]