[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85322-en":3,"doc-seo-85322-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85322,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Uncertainty Quantification for EO Regression Tasks","Earth Observation (EO) regression tasks such as building height, canopy height, and above-ground biomass estimation require not only high accuracy but also reliable per-pixel confidence. Most deep learning approaches output deterministic values and lack uncertainty characterization, while challenges like heterogeneous land surfaces, skewed targets, sensor noise, and saturation at high values make uncertainty estimation essential. The work models aleatoric uncertainty using Sentinel-1 SAR and Sentinel-2 MSI time series, comparing Gaussian and Quantile uncertainty methods at 10 m resolution.","Uncertainty Quantification for EO Regression Tasks: Building Height, Tree Canopy Height and Above-ground Biomass Estimation  \nRitu Yadav, Andrea Nascetti, and Yifang Ban  \narXiv :2607 . 11412v1 [ cs .CV] 13 Jul 2026  \nAbstract—Earth Observation regression tasks such as building height, canopy height, and above-ground biomass estimation underpin critical applications in urban planning, forest monitoring, and climate policy, where both accuracy and reliability are critical. Yet most deep learning models yield only deterministic predictions, providing no indication of per-pixel reliability. These regression tasks are inherently challenging due to heterogeneous land surfaces, skewed target distributions, sensor noise, and signal saturation at high target values, making uncertainty (UC) estimation essential for reliable inference. We address this gap by modeling aleatoric uncertainty using year-long Sentinel-1 SAR and Sentinel-2 MSI time series, proposing two complementary approaches: (i) Gaussian UC, which jointly predicts mean and standard deviation under a Gaussian assumption, and (ii) Quantile UC, which estimates the 10th, 50th, and 90th quantiles to capture asymmetric and heteroscedastic error distributions. Both models are evaluated on three representative EO regression tasks at 10 m spatial resolution. Results show that both approaches match or surpass deterministic benchmarks and existing global products, while delivering well-calibrated, interpretable, and operationally useful confidence estimates. Notably, both models outperform the current 10 m state-of-the-art uncertainty-aware model for canopy height estimation. Our implementation will be available at: [https://github.com/RituYadav92/EO-Regression](https://github.com/RituYadav92/EO-Regression)Uncertainty-Estimation  \nIndex Terms—Uncertainty Estimation, Epistemic, Quantile, Gaussian, Time Series, Regression.  \nI. INTRODUCTION  \nUNCERTAINTY estimation has become central to trust  \nworthy machine learning, particularly in safety-critical and large-scale deployment scenarios. In Earth Observation (EO), where satellite-derived products are used for decisionmaking in domains such as climate modeling, biodiversity monitoring, and urban planning, quantifying prediction uncertainty is equally essential. Errors arising from inherent sensor noise, atmospheric effects, or model limitations propagate through downstream applications; uncertainty estimates help distinguish reliable outputs from uncertain ones, improving trustworthiness and operational utility of EO products [1]–[3] . Despite significant progress in deep learning for EO, most models still produce single deterministic outputs, such as a class label for each pixel or a single scalar regression value per location. While aggregated evaluation metrics like RMSE or accuracy summarize performance over entire datasets, they do not convey the reliability of prediction at individual pixels. Uncertainty estimation addresses this gap by quantifying the variability or confidence associated with model outputs, enabling users to understand not only what a model predicts but also how certain it is about those predictions.  \nRitu Yadav, Andrea Nascetti and Yifang Ban is with Division of Geoinformatics, KTH Royal Institute of Technology, Sweden. (e-mail: [rituy@kth.se](rituy@kth.se), [nascetti@kth.se](nascetti@kth.se), [yifang@kth.se](yifang@kth.se)) 15 September, 2025  \nPredictive uncertainty formalizes this idea by characterizing the distribution over model outputs given an input, which may reflect either variability inherent in the data or uncertainty in the model itself. Depending on the source of variability, predictive uncertainty is typically decomposed into aleatoricand epistemic components. Aleatoric uncertainty stems from irreducible noise in the data, such as sensor errors, atmospheric interference, mixed pixels or inconsistencies in training labels. Epistemic uncertainty arises from limitations of the model itself, such as ","cbCaisSmjjOHxRuv","https://ap.wps.com/l/cbCaisSmjjOHxRuv","pdf",5348326,1,10,"English","en",105,"# Introduction\n## Predictive uncertainty and its components\n## Methods for epistemic and aleatoric uncertainty\n# (Background) Uncertainty estimation in EO regression","[{\"question\":\"Why is uncertainty estimation important for EO regression tasks like building height and biomass estimation?\",\"answer\":\"EO regression outputs feed into decision-making where both accuracy and reliability matter. Uncertainty estimation helps users identify which predictions are trustworthy at the pixel level rather than relying only on dataset-level metrics.\"},{\"question\":\"What does the document identify as the main difficulty for aleatoric uncertainty in EO regression?\",\"answer\":\"Irreducible aleatoric uncertainty is highlighted as dominant due to atmospheric noise, mixed pixels, and sensor saturation, which makes explicit aleatoric modeling necessary.\"},{\"question\":\"How do the proposed uncertainty approaches differ in modeling uncertainty?\",\"answer\":\"The document proposes two complementary aleatoric methods: Gaussian uncertainty that predicts mean and standard deviation under a Gaussian assumption, and Quantile uncertainty that estimates the 10th, 50th, and 90th quantiles to capture asymmetric and heteroscedastic errors.\"}]",1784202490,25,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"uncertainty-quantification-for-eo-regression-tasks","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/uncertainty-quantification-for-eo-regression-tasks/85322/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why is uncertainty estimation important for EO regression tasks like building height and biomass estimation?","Question",{"text":74,"@type":75},"EO regression outputs feed into decision-making where both accuracy and reliability matter. Uncertainty estimation helps users identify which predictions are trustworthy at the pixel level rather than relying only on dataset-level metrics.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What does the document identify as the main difficulty for aleatoric uncertainty in EO regression?",{"text":79,"@type":75},"Irreducible aleatoric uncertainty is highlighted as dominant due to atmospheric noise, mixed pixels, and sensor saturation, which makes explicit aleatoric modeling necessary.",{"name":81,"@type":72,"acceptedAnswer":82},"How do the proposed uncertainty approaches differ in modeling uncertainty?",{"text":83,"@type":75},"The document proposes two complementary aleatoric methods: Gaussian uncertainty that predicts mean and standard deviation under a Gaussian assumption, and Quantile uncertainty that estimates the 10th, 50th, and 90th quantiles to capture asymmetric and heteroscedastic errors.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":21,"slug":132},"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]