[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290395-105":59,"doc-detail-290395-en":131},{"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":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","probabilities-informed-machine-learning-study-framework-and-applications","Probabilities-Informed Machine Learning - Study Framework and Applications","","Machine learning (ML) is a powerful tool for regression and classification, but performance depends strongly on training data quality. This study proposes a probabilities-informed ML paradigm that injects the probabilistic structure of the output function into training, such as the target variable’s cumulative distribution function. The probabilistic information is obtained from historical data or estimated via structural reliability techniques during experimental design. Embedding these probabilistic insights improves accuracy and reduces overfitting and underfitting. Applications in regression, image denoising, and classification validate real-world effectiveness.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/probabilities-informed-machine-learning-study-framework-and-applications/290395/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/probabilities-informed-machine-learning-study-framework-and-applications/290395.png","ImageObject",300,407,{"name":92,"@type":93},"Eliana","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the core idea of probabilities-informed machine learning in this study?","Question",{"text":113,"@type":114},"The study incorporates probabilistic structure of the output function into the ML training process, using information such as a cumulative distribution function.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the probabilistic information about the output variable obtained?",{"text":118,"@type":114},"It is derived from historical data or estimated using structural reliability methods during experimental design.",{"name":120,"@type":111,"acceptedAnswer":121},"Why does the paper argue that error metrics like RMSE may be insufficient for model selection?",{"text":122,"@type":114},"When the output variable has complex or probabilistic behavior, RMSE-only selection may choose an inadequate model that fails to represent the underlying data distribution, leading to overfitting or underfitting.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290395,1789641598,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":31,"preview_page_count":4},4398048949847,"https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267","Probabilities-Informed Machine Learning  \nMohsen Rashki  \nDepartment of Architectural Engineering, University of Sistan and Baluchestan, Zahedan, Iran  \nEmail [address: Mrashki@eng.usb.ac.ir](address: Mrashki@eng.usb.ac.ir)  \nAbstract  \nMachine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge of the structure of output function, akin to physics-informed ML, but rooted in probabilistic principles rather than physical laws. The proposed approach integrates the probabilistic structure of the target variable—such as its cumulative distribution function—into the training process. This probabilistic information is obtained from historical data or estimated using structural reliability methods during experimental design. By embedding domain-specific probabilistic insights into the learning process, the technique enhances model accuracy and mitigates risks of overfitting and underfitting. Applications in regression, image denoising, and classification demonstrate the approach's effectiveness in addressing real-world problems.  \nKeywords: Probabilistic Machine Learning, Reliability Theory, Informed Machine Learning, Support Vector Machine (SVM), Artificial Neural Networks (ANN), Optimization-Based Learning, Uncertainty.  \n1. Introduction  \nOver the last decade, Machine Learning (ML) has emerged as a transformative tool for solving complex prediction and classification problems [1], [2] . As a natural evolution of traditional regression methods [3], ML models such as Support Vector Regression (SVR) [4] and Artificial Neural Networks (ANN) [5] have been developed to handle non-linear relationships and highdimensional datasets [6] with increasing accuracy and robustness.  \nFor instance, SVR has proven to be a robust regression tool because it can generalize well with limited data and capture nonlinear relationships using kernel functions [7] . Similarly, ANN, inspired by the neural architecture of the human brain, has become foundational to ML [5] . Typically, these methods use inputs (X) and outputs (Y) to construct surrogate models that aim to minimize the difference between the predicted and actual output values. These models have found applications across diverse fields, including engineering, medicine, and economics, demonstrating their versatility and potential [8],[9],[10] .  \nIn many real-world applications, additional prior information regarding the output model can be leveraged to enhance its accuracy and robustness [11] [12] . For instance, in physical systems, knowledge of the governing laws of physics has been successfully incorporated into ML by developing physics-informed neural networks (PINNs) [13], leading to improved efficiency and accuracy in prediction tasks [14] .  \nIn addition to physical laws, probabilistic information about the structure of the problem may also exist in practical scenarios [15] . Moreover, in many systems, the output variable is inherently probabilistic, necessitating models to approximate the probabilistic structure of the output [16] . Methods such as the Gaussian Processes (GPs) [17][18], Bayesian neural networks [19], quantiles [20] and generative modeling [21] have shown great potential for integrating such probabilistic  \narXiv:2412 .11526 1 December 16, 2024  \nissues in ML. Furthermore, as demonstrated in [15], [22] and [23], probabilities-informed modeling enhances robust decision-making and ensures reliable predictions, particularly in complex systems (see also [24] and [25] where the concept of failure probability is utilized to improve the training process in PINNs) . These findings underscore the critical role of leveraging the complete probabilistic structure of the output function during model selection and training in ML.  \nThis paper develops probabilities-informed modeling as an explicit framework for ","cbCaiuAPVY6Xl7rn","https://ap.wps.com/l/cbCaiuAPVY6Xl7rn","pdf",5734966,"English","# 1. Introduction\n# 2. Problem Statement and Study Motivation\n## Overfitting and Underfitting\n## Role of Probabilistic Output Structure\n# 3. Probabilities-Informed Modeling Framework","[{\"question\":\"What is the core idea of probabilities-informed machine learning in this study?\",\"answer\":\"The study incorporates probabilistic structure of the output function into the ML training process, using information such as a cumulative distribution function.\"},{\"question\":\"How is the probabilistic information about the output variable obtained?\",\"answer\":\"It is derived from historical data or estimated using structural reliability methods during experimental design.\"},{\"question\":\"Why does the paper argue that error metrics like RMSE may be insufficient for model selection?\",\"answer\":\"When the output variable has complex or probabilistic behavior, RMSE-only selection may choose an inadequate model that fails to represent the underlying data distribution, leading to overfitting or underfitting.\"}]","Probabilities-Informed Machine Learning - Study Framework and Applications | PDF"]