arXiv - STAT - Statistics Theory最新文献_第3页

RandALO: Out-of-sample risk estimation in no time flat RandALO：快速进行样本外风险评估

arXiv - STAT - Statistics Theory Pub Date : 2024-09-15 DOI: arxiv-2409.09781

Parth T. Nobel, Daniel LeJeune, Emmanuel J. Candès

引用次数: 0

Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting 近线性环境下卡尔曼滤波器的精度

arXiv - STAT - Statistics Theory Pub Date : 2024-09-15 DOI: arxiv-2409.09800

Edoardo Calvello, Pierre Monmarché, Andrew M. Stuart, Urbain Vaes

{"title":"Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting","authors":"Edoardo Calvello, Pierre Monmarché, Andrew M. Stuart, Urbain Vaes","doi":"arxiv-2409.09800","DOIUrl":"https://doi.org/arxiv-2409.09800","url":null,"abstract":"The filtering distribution captures the statistics of the state of a\u0000dynamical system from partial and noisy observations. Classical particle\u0000filters provably approximate this distribution in quite general settings;\u0000however they behave poorly for high dimensional problems, suffering weight\u0000collapse. This issue is circumvented by the ensemble Kalman filter which is an\u0000equal-weight interacting particle system. However, this finite particle system\u0000is only proven to approximate the true filter in the linear Gaussian case. In\u0000practice, however, it is applied in much broader settings; as a result,\u0000establishing its approximation properties more generally is important. There\u0000has been recent progress in the theoretical analysis of the algorithm,\u0000establishing stability and error estimates in non-Gaussian settings, but the\u0000assumptions on the dynamics and observation models rule out the unbounded\u0000vector fields that arise in practice and the analysis applies only to the mean\u0000field limit of the ensemble Kalman filter. The present work establishes error\u0000bounds between the filtering distribution and the finite particle ensemble\u0000Kalman filter when the model exhibits linear growth.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotics for irregularly observed long memory processes 不规则观测长记忆过程的渐近线

arXiv - STAT - Statistics Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09498

Mohamedou Ould-Haye, Anne Philippe

引用次数: 0

A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theorem 关于差异隐私的统计学观点：假设检验、表征和布莱克韦尔定理

arXiv - STAT - Statistics Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09558

Weijie J. Su

{"title":"A Statistical Viewpoint on Differential Privacy: Hypothesis Testing, Representation and Blackwell's Theorem","authors":"Weijie J. Su","doi":"arxiv-2409.09558","DOIUrl":"https://doi.org/arxiv-2409.09558","url":null,"abstract":"Differential privacy is widely considered the formal privacy for\u0000privacy-preserving data analysis due to its robust and rigorous guarantees,\u0000with increasingly broad adoption in public services, academia, and industry.\u0000Despite originating in the cryptographic context, in this review paper we argue\u0000that, fundamentally, differential privacy can be considered a textit{pure}\u0000statistical concept. By leveraging a theorem due to David Blackwell, our focus\u0000is to demonstrate that the definition of differential privacy can be formally\u0000motivated from a hypothesis testing perspective, thereby showing that\u0000hypothesis testing is not merely convenient but also the right language for\u0000reasoning about differential privacy. This insight leads to the definition of\u0000$f$-differential privacy, which extends other differential privacy definitions\u0000through a representation theorem. We review techniques that render\u0000$f$-differential privacy a unified framework for analyzing privacy bounds in\u0000data analysis and machine learning. Applications of this differential privacy\u0000definition to private deep learning, private convex optimization, shuffled\u0000mechanisms, and U.S.~Census data are discussed to highlight the benefits of\u0000analyzing privacy bounds under this framework compared to existing\u0000alternatives.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Random-effects Approach to Regression Involving Many Categorical Predictors and Their Interactions 涉及多个分类预测因子及其交互作用的随机效应回归方法

arXiv - STAT - Statistics Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09355

Hanmei Sun, Jiangshan Zhang, Jiming Jiang

引用次数: 0

Bounding the probability of causality under ordinal outcomes 限定序数结果下的因果关系概率

arXiv - STAT - Statistics Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09297

Hanmei Sun, Chengfeng Shi, Qiang Zhao

引用次数: 0

The Asymptotics of Wide Remedians 宽补数的渐近性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-14 DOI: arxiv-2409.09528

Philip T. Labo

引用次数: 0

Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts 高维计数的超常规局部尖锐拟合优度测试

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08871

Subhodh Kotekal, Julien Chhor, Chao Gao

引用次数: 0

High-dimensional regression with a count response 计数响应的高维回归

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08821

Or Zilberman, Felix Abramovich

引用次数: 0

Self-Organized State-Space Models with Artificial Dynamics 人工动力学自组织状态空间模型

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08928

Yuan Chen, Mathieu Gerber, Christophe Andrieu, Randal Douc

{"title":"Self-Organized State-Space Models with Artificial Dynamics","authors":"Yuan Chen, Mathieu Gerber, Christophe Andrieu, Randal Douc","doi":"arxiv-2409.08928","DOIUrl":"https://doi.org/arxiv-2409.08928","url":null,"abstract":"In this paper we consider a state-space model (SSM) parametrized by some\u0000parameter $theta$, and our aim is to perform joint parameter and state\u0000inference. A simple idea to perform this task, which almost dates back to the\u0000origin of the Kalman filter, is to replace the static parameter $theta$ by a\u0000Markov chain $(theta_t)_{tgeq 0}$ on the parameter space and then to apply a\u0000standard filtering algorithm to the extended, or self-organized SSM. However,\u0000the practical implementation of this idea in a theoretically justified way has\u0000remained an open problem. In this paper we fill this gap by introducing various\u0000possible constructions of the Markov chain $(theta_t)_{tgeq 0}$ that ensure\u0000the validity of the self-organized SSM (SO-SSM) for joint parameter and state\u0000inference. Notably, we show that theoretically valid SO-SSMs can be defined\u0000even if $|mathrm{Var}(theta_{t}|theta_{t-1})|$ converges to 0 slowly as\u0000$trightarrowinfty$. This result is important since, as illustrated in our\u0000numerical experiments, such models can be efficiently approximated using\u0000standard particle filter algorithms. While the idea studied in this work was\u0000first introduced for online inference in SSMs, it has also been proved to be\u0000useful for computing the maximum likelihood estimator (MLE) of a given SSM,\u0000since iterated filtering algorithms can be seen as particle filters applied to\u0000SO-SSMs for which the target parameter value is the MLE of interest. Based on\u0000this observation, we also derive constructions of $(theta_t)_{tgeq 0}$ and\u0000theoretical results tailored to these specific applications of SO-SSMs, and as\u0000a result, we introduce new iterated filtering algorithms. From a practical\u0000point of view, the algorithms introduced in this work have the merit of being\u0000simple to implement and only requiring minimal tuning to perform well.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0