Annals of Statistics最新文献_第2页

Order-of-addition orthogonal arrays to study the effect of treatment ordering 研究正交加法排序对处理排序的影响

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2317

Eric D. Schoen, Robert W. Mee

引用次数: 0

Matching recovery threshold for correlated random graphs 相关随机图的匹配恢复阈值

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2305

Jian Ding, Hang Du

引用次数: 13

Post-selection inference via algorithmic stability 通过算法稳定性进行后选择推理

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2303

Tijana Zrnic, Michael I. Jordan

引用次数: 2

Statistical inference on a changing extreme value dependence structure 变化极值依赖结构的统计推断

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2314

Holger Drees

引用次数: 2

Bridging factor and sparse models 桥接因子与稀疏模型

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2304

Jianqing Fan, Ricardo Masini, Marcelo C. Medeiros

引用次数: 0

Projected state-action balancing weights for offline reinforcement learning 用于离线强化学习的预估状态-行为平衡权值

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2302

Jiayi Wang, Zhengling Qi, Raymond K. W. Wong

{"title":"Projected state-action balancing weights for offline reinforcement learning","authors":"Jiayi Wang, Zhengling Qi, Raymond K. W. Wong","doi":"10.1214/23-aos2302","DOIUrl":"https://doi.org/10.1214/23-aos2302","url":null,"abstract":"Off-policy evaluation is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights, and show that the proposed value estimator is asymptotically normal under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we develop a necessary and sufficient condition for establishing the well-posedness of the operator that relates to the nonparametric Q-function estimation in the off-policy setting, which characterizes the difficulty of Q-function estimation and may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135055878","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: 6

A cross-validation framework for signal denoising with applications to trend filtering, dyadic CART and beyond 一个用于信号去噪的交叉验证框架，应用于趋势滤波，二元CART等

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2283

Anamitra Chaudhuri, Sabyasachi Chatterjee

引用次数: 0

Relaxing the i.i.d. assumption: Adaptively minimax optimal regret via root-entropic regularization 放宽i.i.d假设:基于根熵正则化的自适应最小最大最优后悔

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2315

Blair Bilodeau, Jeffrey Negrea, Daniel M. Roy

{"title":"Relaxing the i.i.d. assumption: Adaptively minimax optimal regret via root-entropic regularization","authors":"Blair Bilodeau, Jeffrey Negrea, Daniel M. Roy","doi":"10.1214/23-aos2315","DOIUrl":"https://doi.org/10.1214/23-aos2315","url":null,"abstract":"We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm—long known to be minimax (rate) optimal in the adversarial regime—was recently shown to be simultaneously minimax optimal for i.i.d. data. In this work, we propose to relax the i.i.d. assumption by seeking adaptivity at all levels of a natural ordering on constraint sets. We provide matching upper and lower bounds on the minimax regret at all levels, show that Hedge with deterministic learning rates is suboptimal outside of the extremes and prove that one can adaptively obtain minimax regret at all levels. We achieve this optimal adaptivity using the follow-the-regularized-leader (FTRL) framework, with a novel adaptive regularization scheme that implicitly scales as the square root of the entropy of the current predictive distribution, rather than the entropy of the initial predictive distribution. Finally, we provide novel technical tools to study the statistical performance of FTRL along the semi-adversarial spectrum.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135165186","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: 7

Graphical models for nonstationary time series 非平稳时间序列的图形模型

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/22-aos2205

Sumanta Basu, Suhasini Subba Rao

{"title":"Graphical models for nonstationary time series","authors":"Sumanta Basu, Suhasini Subba Rao","doi":"10.1214/22-aos2205","DOIUrl":"https://doi.org/10.1214/22-aos2205","url":null,"abstract":"We propose NonStGM, a general nonparametric graphical modeling framework, for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian graphical models (GGM) and stationary time series graphical models (StGM) and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGM, the proposed framework captures conditional noncorrelations (both intertemporal and contemporaneous) in the form of an undirected graph. In addition, to describe the more nuanced nonstationary relationships among the components of the time series, we introduce the new notion of conditional nonstationarity/stationarity and incorporate it within the graph. This can be used to search for small subnetworks that serve as the “source” of nonstationarity in a large system. We explicitly connect conditional noncorrelation and stationarity between and within components of the multivariate time series to zero and Toeplitz embeddings of an infinite-dimensional inverse covariance operator. In the Fourier domain, conditional stationarity and noncorrelation relationships in the inverse covariance operator are encoded with a specific sparsity structure of its integral kernel operator. We show that these sparsity patterns can be recovered from finite-length time series by nodewise regression of discrete Fourier transforms (DFT) across different Fourier frequencies. We demonstrate the feasibility of learning NonStGM structure from data using simulation studies.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134951510","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: 2

Learning low-dimensional nonlinear structures from high-dimensional noisy data: An integral operator approach 从高维噪声数据中学习低维非线性结构:一种积分算子方法

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2306

Xiucai Ding, Rong Ma

{"title":"Learning low-dimensional nonlinear structures from high-dimensional noisy data: An integral operator approach","authors":"Xiucai Ding, Rong Ma","doi":"10.1214/23-aos2306","DOIUrl":"https://doi.org/10.1214/23-aos2306","url":null,"abstract":"We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from noisy and high-dimensional observations, where the data sets are assumed to be sampled from a nonlinear manifold model and corrupted by high-dimensional noise. The algorithm employs an adaptive bandwidth selection procedure which does not rely on prior knowledge of the underlying manifold. The obtained low-dimensional embeddings can be further utilized for downstream purposes such as data visualization, clustering and prediction. Our method is theoretically justified and practically interpretable. Specifically, for a general class of kernel functions, we establish the convergence of the final embeddings to their noiseless counterparts when the dimension grows polynomially with the size, and characterize the effect of the signal-to-noise ratio on the rate of convergence and phase transition. We also prove the convergence of the embeddings to the eigenfunctions of an integral operator defined by the kernel map of some reproducing kernel Hilbert space capturing the underlying nonlinear structures. Our results hold even when the dimension of the manifold grows with the sample size. Numerical simulations and analysis of real data sets show the superior empirical performance of the proposed method, compared to many existing methods, on learning various nonlinear manifolds in diverse applications.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135055287","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