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Annual Review of Statistics and Its Application最新文献

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A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions 知识蒸馏的统计视角：基础、经典方法和大型语言模型扩展
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-09-17 DOI: 10.1146/annurev-statistics-043025-102547
Luyang Fang, Haoran Lu, Jiazhang Cai, Tao Wang, Huimin Cheng, Wenxuan Zhong, Ping Ma
{"title":"A Statistical Perspective on Knowledge Distillation: Foundations, Classical Methods, and Large Language Model Extensions","authors":"Luyang Fang, Haoran Lu, Jiazhang Cai, Tao Wang, Huimin Cheng, Wenxuan Zhong, Ping Ma","doi":"10.1146/annurev-statistics-043025-102547","DOIUrl":"https://doi.org/10.1146/annurev-statistics-043025-102547","url":null,"abstract":"Knowledge distillation (KD) has emerged as a vital paradigm for transferring the capabilities of high-capacity models to efficient student counterparts, addressing critical challenges in computational cost, deployment constraints, and privacy-sensitive settings. Although KD is widely used in practice, it is often viewed primarily as an engineering technique, with a unified statistical perspective remaining less developed. This review bridges that gap by presenting a unified Bayesian formulation that formulates teacher predictions as prior information. This provides a principled interpretation of how teacher information is incorporated into student learning and establishes a rigorous connection to uncertainty quantification. We demonstrate how this foundational lens reconciles classical distillation with modern extensions in generative and foundation-model systems, showing that contemporary developments remain rooted in these same statistical principles. By synthesizing theory with emerging methodologies and diverse applications, this review provides a conceptual road map and identifies critical open problems for the future of the field.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"29 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149019964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistics for Climate Science: Differentiation and Integration 气候科学统计：分化与整合
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-09-08 DOI: 10.1146/annurev-statistics-042424-022358
Bo Li,Trevor Harris
{"title":"Statistics for Climate Science: Differentiation and Integration","authors":"Bo Li,Trevor Harris","doi":"10.1146/annurev-statistics-042424-022358","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042424-022358","url":null,"abstract":"Climate science increasingly relies on statistical tools to evaluate and synthesize diverse datasets, including observations, reanalyses, paleoclimate proxies, and model simulations. Climate data differentiation, which quantifies discrepancies between datasets, and climate integration, which combines information across them, play central roles in these efforts. This article reviews modern statistical approaches for climate data differentiation, including methods for quantifying discrepancies in means, dependence structures, distributions, extremes, spatial signals, and shapes. It also reviews approaches for climate data integration that combine information across models and observations through ensemble methods, bias correction, hierarchical modeling, and machine learning. We highlight how these methods address challenges such as high dimensionality, spatial dependence, limited observations, and structural model uncertainty. Together, these tools provide complementary perspectives for understanding differences among climate data sources and for synthesizing information across them, ultimately improving estimates of past, present, and future climate conditions.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"60 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148932636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical Methods in Generative Artificial Intelligence 生成式人工智能中的统计方法
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-08-14 DOI: 10.1146/annurev-statistics-042825-121454
Edgar Dobriban
{"title":"Statistical Methods in Generative Artificial Intelligence","authors":"Edgar Dobriban","doi":"10.1146/annurev-statistics-042825-121454","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042825-121454","url":null,"abstract":"Generative artificial intelligence (AI) is emerging as an important technology, promising to be transformative in many areas. At the same time, generative AI techniques are based on sampling from probabilistic models, and, by default, they come with no guarantees about correctness, safety, fairness, or other properties. Statistical methods offer a promising approach to improve the reliability of generative AI techniques. In addition, statistical methods are also promising for improving the quality and efficiency of AI evaluation, as well as for designing interventions and experiments in AI. In this article, we review some of the existing work on these topics, explaining both the general statistical techniques used and their applications to generative AI. We also discuss limitations and potential future directions.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"58 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148893994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recent Advances in Conditional Extreme Quantile Analysis 条件极值分位数分析的新进展
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-03-09 DOI: 10.1146/annurev-statistics-042324-014139
Yiwei Tang, Junyu Chen, Deyuan Li, Huixia Judy Wang
{"title":"Recent Advances in Conditional Extreme Quantile Analysis","authors":"Yiwei Tang, Junyu Chen, Deyuan Li, Huixia Judy Wang","doi":"10.1146/annurev-statistics-042324-014139","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042324-014139","url":null,"abstract":"Estimating conditional extreme quantiles is essential for assessing tail risks in complex systems, with broad applications in finance, climate science, engineering, and beyond. While classical extreme value theory provides a foundational framework, recent advances, particularly semiparametric and nonparametric methods, including approaches based on quantile regression, machine learning, and deep learning, have greatly enriched the methodological landscape. This modern review synthesizes these developments, covering traditional likelihood-based methods, semiparametric approaches, and tree-based and deep learning techniques, including higher-order refinements.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"45 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical Modeling of the Ocean Environment 海洋环境的统计模型
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-03-09 DOI: 10.1146/annurev-statistics-042424-115755
Erik Vanem, Sheng Dong, Guillaume de Hauteclocque, Thomas Berge Johannessen, Tingyao Zhu, Jasna Prpic-Orsic, Sanne van Essen, Kevin Ewans, Ed Mackay, Philip Jonathan
{"title":"Statistical Modeling of the Ocean Environment","authors":"Erik Vanem, Sheng Dong, Guillaume de Hauteclocque, Thomas Berge Johannessen, Tingyao Zhu, Jasna Prpic-Orsic, Sanne van Essen, Kevin Ewans, Ed Mackay, Philip Jonathan","doi":"10.1146/annurev-statistics-042424-115755","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042424-115755","url":null,"abstract":"Statistical modeling of the ocean environment is important for many practical applications in science and engineering. Probabilistic descriptions of the ocean environment are important input for structural design and risk assessment of marine structures, including ships, offshore and coastal structures, and aquaculture installations. They are also essential for the safe operation of ships and other structures at sea. Additionally, they are critical for planning and decision-making in the exploitation of marine renewable energy sources such as waves, tides, and offshore wind. This article presents a review of recent developments with regard to statistical modeling of the ocean environment, with a particular focus on ocean waves. Such developments are driven by an increasing volume of available data, increasing computational capabilities, and demand from the industry for more accurate and uncertainty-aware descriptions of relevant oceanic variables. Hence, statistical modeling of the ocean environment remains an active area of research, with significant developments in various directions. These are reviewed in this article.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"60 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Theory of Random Forests 随机森林理论
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2026-03-09 DOI: 10.1146/annurev-statistics-112723-034707
Erwan Scornet, Giles Hooker
{"title":"Theory of Random Forests","authors":"Erwan Scornet, Giles Hooker","doi":"10.1146/annurev-statistics-112723-034707","DOIUrl":"https://doi.org/10.1146/annurev-statistics-112723-034707","url":null,"abstract":"Random forests (RFs) have a long history; they were originally defined by Leo but have antecedents in bagging methods introduced in 1996. They have become one of the most widely adopted machine learning tools thanks to their computational efficiency, relative insensitivity to tuning parameters, inbuilt cross validation, and interpretation tools. Despite their popularity, mathematical theory about the fundamental properties of RFs has been slow to emerge. Nonetheless, the past decade has seen significant advances in our understanding and analysis of these algorithms. In this review article, we describe several variations of RFs and how rates of consistency of these variants highlight the impact of different RF mechanisms on their performance. Another line of research focuses on establishing central limit theorems and confidence intervals for RFs. We also depict recent analyses in variable importance computed with RFs.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"54 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep Spatiotemporal Point Processes: Advances and New Directions 深度时空点过程：进展与新方向
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2025-12-22 DOI: 10.1146/annurev-statistics-042324-040052
Xiuyuan Cheng, Zheng Dong, Yao Xie
{"title":"Deep Spatiotemporal Point Processes: Advances and New Directions","authors":"Xiuyuan Cheng, Zheng Dong, Yao Xie","doi":"10.1146/annurev-statistics-042324-040052","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042324-040052","url":null,"abstract":"Spatiotemporal point processes model discrete events distributed in space and time, with applications in criminology, seismology, epidemiology, and social networks. Classical models rely on parametric kernels, limiting their ability to capture heterogeneous, nonstationary dynamics. Recent advances integrate deep neural architectures, either by modeling the conditional intensity directly or by learning flexible, data-driven influence kernels. This article reviews the deep influence kernel approach, which balances statistical interpretability by retaining explicit kernels to capture event propagation, with expressive power from neural architectures. We outline key components, including functional basis decomposition, graph neural networks for encoding spatial or network structures, and both likelihood-based and likelihood-free estimation methods, while addressing scalability for large data. We also highlight theoretical results on kernel identifiability. Applications in crime analysis, earthquake aftershock prediction, and sepsis modeling demonstrate the framework's effectiveness. We conclude with promising directions for developing explainable and scalable deep kernel point processes.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"84 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Why and How of Convex Clustering 凸聚类的原因和方法
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2025-12-03 DOI: 10.1146/annurev-statistics-112723-034107
Eric C. Chi, Aaron J. Molstad, Zheming Gao, Jocelyn T. Chi
{"title":"The Why and How of Convex Clustering","authors":"Eric C. Chi, Aaron J. Molstad, Zheming Gao, Jocelyn T. Chi","doi":"10.1146/annurev-statistics-112723-034107","DOIUrl":"https://doi.org/10.1146/annurev-statistics-112723-034107","url":null,"abstract":"This article reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from its predecessors. The optimization problem is free of spurious local minima, and its unique global minimizer is stable with respect to all its inputs, including the data, a tuning parameter, and weight hyperparameters. Its single tuning parameter controls the number of clusters and can be chosen using standard techniques from penalized regression. We give intuition into the behavior of and theory for convex clustering, as well as practical guidance. We highlight important algorithms and discuss how their computational costs scale with the problem size. Finally, we highlight the breadth of its uses and flexibility to be combined and integrated with other inferential methods.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"10 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145658281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical Aspects of Racial and Ethnic Health Disparities 种族和族裔健康差异的统计方面
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2025-11-26 DOI: 10.1146/annurev-statistics-042324-061403
Jay S. Kaufman
{"title":"Statistical Aspects of Racial and Ethnic Health Disparities","authors":"Jay S. Kaufman","doi":"10.1146/annurev-statistics-042324-061403","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042324-061403","url":null,"abstract":"Measurement and analysis of racial and ethnic health disparities are vital functions of government and academia in diverse societies, but the statistical methods for accomplishing this work are underdeveloped. Issues of measurement, aggregation, adjustment, choice of scale, internal validity, and generalizability are all paramount. Measurement of race and ethnicity is complicated by the fact that, as identities that form through historical and political processes, they are not stable over time and place, nor are they objectively verifiable. Similarly, it is impossible to specify an optimal adjustment set, because adjustments are functions of ethical judgments, not statistical criteria. Additional complications arise when decomposing disparities in relation to measured pathways, as well as in the modeling of multiple intersectional strata. The ethical considerations in model selection imply that measurement and modeling of health disparities can never be a purely statistical activity, but instead must be conducted in relation to a theory of justice.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"118 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145609859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Operator Learning: A Statistical Perspective 操作员学习：统计学视角
IF 7.9 1区 数学
Annual Review of Statistics and Its Application Pub Date : 2025-11-21 DOI: 10.1146/annurev-statistics-042424-070908
Unique Subedi, Ambuj Tewari
{"title":"Operator Learning: A Statistical Perspective","authors":"Unique Subedi, Ambuj Tewari","doi":"10.1146/annurev-statistics-042424-070908","DOIUrl":"https://doi.org/10.1146/annurev-statistics-042424-070908","url":null,"abstract":"Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the solution operators of partial differential equations (PDEs). These methods can also be used to develop black-box simulators to model system behavior from experimental data, even without a known mathematical model. In this article, we begin by formalizing operator learning as a function-to-function regression problem and review some recent developments in the field. We also discuss PDE-specific operator learning, outlining strategies for incorporating physical and mathematical constraints into architecture design and training processes. Finally, we end by highlighting key future directions such as active data collection and the development of rigorous uncertainty quantification frameworks.","PeriodicalId":48855,"journal":{"name":"Annual Review of Statistics and Its Application","volume":"29 1","pages":""},"PeriodicalIF":7.9,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145567648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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