[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290358-105":59,"doc-detail-290358-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","efficient-representations-for-high-cardinality-categorical-variables-in-machine-learning-paper","Efficient Representations for High-Cardinality Categorical Variables in Machine Learning - Paper","","High-cardinality categorical variables create significant machine learning challenges, especially for computational efficiency and model interpretability. Traditional one-hot encoding yields high-dimensional sparse features, increasing overfitting risk and reducing scalability. The paper proposes new encoding strategies—means encoding, low-rank encoding, and multinomial logistic regression encoding—built on sufficient representations that produce compact, informative embeddings. Rigorous theoretical analysis and empirical experiments across multiple datasets show improved predictive performance and computational efficiency versus baseline methods.",{"@graph":69,"@context":122},[70,84,105],{"@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/efficient-representations-for-high-cardinality-categorical-variables-in-machine-learning-paper/290358/",{"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/efficient-representations-for-high-cardinality-categorical-variables-in-machine-learning-paper/290358.png","ImageObject",300,407,{"name":92,"@type":93},"Eliana","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":46},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why are high-cardinality categorical variables difficult for machine learning models?","Question",{"text":112,"@type":113},"They often cause computational inefficiency and poor interpretability. One-hot encoding becomes high-dimensional and sparse, which can increase overfitting and hurt scalability.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What limitations of fixed effect modeling are highlighted in the paper?",{"text":117,"@type":113},"Fixed effects can struggle with complex and non-linear signals, and the large number of group parameters can complicate statistical inference and stability.",{"name":119,"@type":110,"acceptedAnswer":120},"What encoding approaches does the paper propose to address these issues?",{"text":121,"@type":113},"It introduces means encoding, low-rank encoding, and multinomial logistic regression encoding. These methods use sufficient representations to form compact, informative embeddings while preserving predictive capacity.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},290358,1789641471,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":46,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":144,"preview_page_count":4},4398048949847,"https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267","Efficient Representations for High-Cardinality Categorical Variables in Machine Learning  \nZixuan Liang  \n[zliang1@my.harrisburgu.edu](zliang1@my.harrisburgu.edu)  \narXiv :2501 .05646v1 [ cs .LG] 10 Jan 2025  \nAbstract—High-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one-hot encoding often results in high-dimensional sparse feature spaces, increasing the risk of overfitting and reducing scalability. This paper introduces novel encoding techniques, including means encoding, low-rank encoding, and multinomial logistic regression encoding, to address these challenges. These methods leverage sufficient representations to generate compact and informative embeddings of categorical data. We conduct rigorous theoretical analyses and empirical validations on diverse datasets, demonstrating significant improvements in model performance and computational efficiency compared to baseline methods. The proposed techniques are particularly effective in domains requiring scalable solutions for large datasets, paving the way for more robust and efficient applications in machine learning.  \nI. INTRODUCTION  \nMany regression problems often arise when analyzing data collected across several groups, each of which can contribute uniquely to the statistical relevance of the model. For instance, in a healthcare context, if I want to model health outcomes using patient data from various hospitals, I need to account for hospital-specific effects that other covariates might not capture. This type of group effect is observed in numerous contexts, such as examining students from different schools, voters living in separate zip codes, employees at various firms, and many more scenarios.  \nA widely employed method for addressing such issues is fixed effect modeling. To illustrate, let’s assume that I have n samples {Xi , Gi , Yi } for i = 1 , . . . , n, where Xi ∈ Rp is a set of covariates pertaining to individual subjects, Gi ∈ G is a categorical variable denoting group membership, and Yi ∈ Ris the outcome of interest. My aim is to estimate:  \nµ (x, g) = E[Yi | Xi = x, Gi = g] . (1)  \nThe conventional fixed effects approach models this expectation as:  \nµ (x, g) = αg + xβ, (2)  \nwhere the parameters β and αg are estimated through ordinary least squares regression. Extensions of this basic approach can involve applying non-linear transformations to x, considering interactions between the group membership variable and other covariates, or adding regularization to improve stability and predictive power [1], [2], [3] .  \nHowever, in practice, I often observe that fixed effects modeling faces limitations when the underlying signal is complex and non-linear or when the number of groups, |G|, is large.  \nXi  \nFig. 1: This causal graph shows the core assumption that Yi and Xi are conditionally independent of group membership Gi when conditioned on latent state Li. Gray nodes denote observed variables.  \nThe rigidity of the model (2) can hinder its ability to capture complex signals, and the high number of αg parameters can lead to challenges with statistical inference [4] . In essence, the model might become too cumbersome to yield stable results while also lacking the flexibility to capture nuanced patterns in the data.  \nTo address these challenges, the focus of this paper is to propose a more efficient way to represent group membership. Specifically, I seek to develop a mapping ψ that transforms group membership Gi into a k-dimensional space without compromising predictive capacity:  \nψ : G → Rk , µ (x, g) = f(x,ψ(g)), (3)  \nwhere k is relatively small (i.e., k ≪ |G|) and the function f (·, ·) remains easy to learn. With such a mapping, the problem in (1) reduces to a standard regression problem with (p + k) -dimensional real-valued features (Xi ,ψ (Gi )), allowing me to apply off-the-shelf statistical learning tools.  \nTo create an ef","cbCaikc8t1UC5g8Y","https://ap.wps.com/l/cbCaikc8t1UC5g8Y","pdf",2908425,11,"English","# Introduction\n## Group effect modeling and fixed effects\n## Sufficient latent state assumption and representation mapping\n# Literature Review\n## Existing encodings and limitations","[{\"question\":\"Why are high-cardinality categorical variables difficult for machine learning models?\",\"answer\":\"They often cause computational inefficiency and poor interpretability. One-hot encoding becomes high-dimensional and sparse, which can increase overfitting and hurt scalability.\"},{\"question\":\"What limitations of fixed effect modeling are highlighted in the paper?\",\"answer\":\"Fixed effects can struggle with complex and non-linear signals, and the large number of group parameters can complicate statistical inference and stability.\"},{\"question\":\"What encoding approaches does the paper propose to address these issues?\",\"answer\":\"It introduces means encoding, low-rank encoding, and multinomial logistic regression encoding. These methods use sufficient representations to form compact, informative embeddings while preserving predictive capacity.\"}]","Efficient Representations for High-Cardinality Categorical Variables in Machine Learning - Paper | PDF",28]