Statistics and Computing最新文献_第2页

Nonconvex Dantzig selector and its parallel computing algorithm 非凸丹齐格选择器及其并行计算算法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-09-16 DOI: 10.1007/s11222-024-10492-8

Jiawei Wen, Songshan Yang, Delin Zhao

{"title":"Nonconvex Dantzig selector and its parallel computing algorithm","authors":"Jiawei Wen, Songshan Yang, Delin Zhao","doi":"10.1007/s11222-024-10492-8","DOIUrl":"https://doi.org/10.1007/s11222-024-10492-8","url":null,"abstract":"The Dantzig selector is a popular (ell _1)-type variable selection method widely used across various research fields. However, (ell _1)-type methods may not perform well for variable selection without complex irrepresentable conditions. In this article, we introduce a nonconvex Dantzig selector for ultrahigh-dimensional linear models. We begin by demonstrating that the oracle estimator serves as a local optimum for the nonconvex Dantzig selector. In addition, we propose a one-step local linear approximation estimator, called the Dantzig-LLA estimator, for the nonconvex Dantzig selector, and establish its strong oracle property. The proposed regularization method avoids the restrictive conditions imposed by (ell _1) regularization methods to guarantee the model selection consistency. Furthermore, we propose an efficient and parallelizable computing algorithm based on feature-splitting to address the computational challenges associated with the nonconvex Dantzig selector in high-dimensional settings. A comprehensive numerical study is conducted to evaluate the performance of the nonconvex Dantzig selector and the computing efficiency of the feature-splitting algorithm. The results demonstrate that the Dantzig selector with nonconvex penalty outperforms the (ell _1) penalty-based selector, and the feature-splitting algorithm performs well in high-dimensional settings where linear programming solver may fail. Finally, we generalize the concept of nonconvex Dantzig selector to deal with more general loss functions.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Robust singular value decomposition with application to video surveillance background modelling 将鲁棒奇异值分解应用于视频监控背景建模

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-09-11 DOI: 10.1007/s11222-024-10493-7

Subhrajyoty Roy, Abhik Ghosh, Ayanendranath Basu

{"title":"Robust singular value decomposition with application to video surveillance background modelling","authors":"Subhrajyoty Roy, Abhik Ghosh, Ayanendranath Basu","doi":"10.1007/s11222-024-10493-7","DOIUrl":"https://doi.org/10.1007/s11222-024-10493-7","url":null,"abstract":"The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination. In particular, background modelling of video surveillance data in the presence of camera tampering cannot be reliably solved by the classical SVD. In this paper, we propose a novel robust singular value decomposition technique based on the popular minimum density power divergence estimator. We have established the theoretical properties of the proposed estimator such as convergence, equivariance and consistency under the high-dimensional regime where both the row and column dimensions of the data matrix approach infinity. We also propose a fast and scalable algorithm based on alternating weighted regression to obtain the estimate. Within the scope of our fairly extensive simulation studies, our method performs better than existing robust SVD algorithms. Finally, we present an application of the proposed method on the video surveillance background modelling problem.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"39 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Optimal confidence interval for the difference between proportions 比例差异的最佳置信区间

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-09-02 DOI: 10.1007/s11222-024-10485-7

Almog Peer, David Azriel

{"title":"Optimal confidence interval for the difference between proportions","authors":"Almog Peer, David Azriel","doi":"10.1007/s11222-024-10485-7","DOIUrl":"https://doi.org/10.1007/s11222-024-10485-7","url":null,"abstract":"Estimating the probability of the binomial distribution is a basic problem, which appears in almost all introductory statistics courses and is performed frequently in various studies. In some cases, the parameter of interest is a difference between two probabilities, and the current work studies the construction of confidence intervals for this parameter when the sample size is small. Our goal is to find the shortest confidence intervals under the constraint of coverage probability being at least as large as a predetermined level. For the two-sample case, there is no known algorithm that achieves this goal, but different heuristics procedures have been suggested, and the present work aims at finding optimal confidence intervals. In the one-sample case, there is a known algorithm that finds optimal confidence intervals presented by Blyth and Still (J Am Stat Assoc 78(381):108–116, 1983). It is based on solving small and local optimization problems and then using an inversion step to find the global optimum solution. We show that this approach fails in the two-sample case and therefore, in order to find optimal confidence intervals, one needs to solve a global optimization problem, rather than small and local ones, which is computationally much harder. We present and discuss the suitable global optimization problem. Using the Gurobi package we find near-optimal solutions when the sample sizes are smaller than 15, and we compare these solutions to some existing methods, both approximate and exact. We find that the improvement in terms of lengths with respect to the best competitor varies between 1.5 and 5% for different parameters of the problem. Therefore, we recommend the use of the new confidence intervals when both sample sizes are smaller than 15. Tables of the confidence intervals are given in the Excel file in this link (https://technionmail-my.sharepoint.com/:f:/g/personal/ap_campus_technion_ac_il/El-213Kms51BhQxR8MmQJCYBDfIsvtrK9mQIey1sZnZWIQ?e=hxGunl).","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"9 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A comprehensive comparison of goodness-of-fit tests for logistic regression models 逻辑回归模型拟合优度检验的综合比较

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-30 DOI: 10.1007/s11222-024-10487-5

Huiling Liu, Xinmin Li, Feifei Chen, Wolfgang Härdle, Hua Liang

{"title":"A comprehensive comparison of goodness-of-fit tests for logistic regression models","authors":"Huiling Liu, Xinmin Li, Feifei Chen, Wolfgang Härdle, Hua Liang","doi":"10.1007/s11222-024-10487-5","DOIUrl":"https://doi.org/10.1007/s11222-024-10487-5","url":null,"abstract":"We introduce a projection-based test for assessing logistic regression models using the empirical residual marked empirical process and suggest a model-based bootstrap procedure to calculate critical values. We comprehensively compare this test and Stute and Zhu’s test with several commonly used goodness-of-fit (GoF) tests: the Hosmer–Lemeshow test, modified Hosmer–Lemeshow test, Osius–Rojek test, and Stukel test for logistic regression models in terms of type I error control and power performance in small ((n=50)), moderate ((n=100)), and large ((n=500)) sample sizes. We assess the power performance for two commonly encountered situations: nonlinear and interaction departures from the null hypothesis. All tests except the modified Hosmer–Lemeshow test and Osius–Rojek test have the correct size in all sample sizes. The power performance of the projection based test consistently outperforms its competitors. We apply these tests to analyze an AIDS dataset and a cancer dataset. For the former, all tests except the projection-based test do not reject a simple linear function in the logit, which has been illustrated to be deficient in the literature. For the latter dataset, the Hosmer–Lemeshow test, modified Hosmer–Lemeshow test, and Osius–Rojek test fail to detect the quadratic form in the logit, which was detected by the Stukel test, Stute and Zhu’s test, and the projection-based test.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"4 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

New forest-based approaches for sufficient dimension reduction 基于森林的充分降维新方法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-30 DOI: 10.1007/s11222-024-10482-w

Shuang Dai, Ping Wu, Zhou Yu

{"title":"New forest-based approaches for sufficient dimension reduction","authors":"Shuang Dai, Ping Wu, Zhou Yu","doi":"10.1007/s11222-024-10482-w","DOIUrl":"https://doi.org/10.1007/s11222-024-10482-w","url":null,"abstract":"Sufficient dimension reduction (SDR) primarily aims to reduce the dimensionality of high-dimensional predictor variables while retaining essential information about the responses. Traditional SDR methods typically employ kernel weighting functions, which unfortunately makes them susceptible to the curse of dimensionality. To address this issue, we in this paper propose novel forest-based approaches for SDR that utilize a locally adaptive kernel generated by Mondrian forests. Overall, our work takes the perspective of Mondrian forest as an adaptive weighted kernel technique for SDR problems. In the central mean subspace model, by integrating the methods from Xia et al. (J R Stat Soc Ser B (Stat Methodol) 64(3):363–410, 2002. https://doi.org/10.1111/1467-9868.03411) with Mondrian forest weights, we suggest the forest-based outer product of gradients estimation (mf-OPG) and the forest-based minimum average variance estimation (mf-MAVE). Moreover, we substitute the kernels used in nonparametric density function estimations (Xia in Ann Stat 35(6):2654–2690, 2007. https://doi.org/10.1214/009053607000000352), targeting the central subspace, with Mondrian forest weights. These techniques are referred to as mf-dOPG and mf-dMAVE, respectively. Under regularity conditions, we establish the asymptotic properties of our forest-based estimators, as well as the convergence of the affiliated algorithms. Through simulation studies and analysis of fully observable data, we demonstrate substantial improvements in computational efficiency and predictive accuracy of our proposals compared with the traditional counterparts.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"57 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences SB-ETAS：使用基于模拟的推理方法对地震发生的 ETAS 模型进行可扩展的无似然推理

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-29 DOI: 10.1007/s11222-024-10486-6

Samuel Stockman, Daniel J. Lawson, Maximilian J. Werner

{"title":"SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences","authors":"Samuel Stockman, Daniel J. Lawson, Maximilian J. Werner","doi":"10.1007/s11222-024-10486-6","DOIUrl":"https://doi.org/10.1007/s11222-024-10486-6","url":null,"abstract":"The rapid growth of earthquake catalogs, driven by machine learning-based phase picking and denser seismic networks, calls for the application of a broader range of models to determine whether the new data enhances earthquake forecasting capabilities. Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as inlabru, which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with inlabru. Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from (mathcal {O}(n^2)) to (mathcal {O}(nlog n)). This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Sparse Bayesian learning using TMB (Template Model Builder) 使用 TMB（模板模型生成器）进行稀疏贝叶斯学习

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-28 DOI: 10.1007/s11222-024-10476-8

Ingvild M. Helgøy, Hans J. Skaug, Yushu Li

{"title":"Sparse Bayesian learning using TMB (Template Model Builder)","authors":"Ingvild M. Helgøy, Hans J. Skaug, Yushu Li","doi":"10.1007/s11222-024-10476-8","DOIUrl":"https://doi.org/10.1007/s11222-024-10476-8","url":null,"abstract":"Sparse Bayesian Learning, and more specifically the Relevance Vector Machine (RVM), can be used in supervised learning for both classification and regression problems. Such methods are particularly useful when applied to big data in order to find a sparse (in weight space) representation of the model. This paper demonstrates that the Template Model Builder (TMB) is an accurate and flexible computational framework for implementation of sparse Bayesian learning methods.The user of TMB is only required to specify the joint likelihood of the weights and the data, while the Laplace approximation of the marginal likelihood is automatically evaluated to numerical precision. This approximation is in turn used to estimate hyperparameters by maximum marginal likelihood. In order to reduce the computational cost of the Laplace approximation we introduce the notion of an “active set” of weights, and we devise an algorithm for dynamically updating this set until convergence, similar to what is done in other RVM type methods. We implement two different methods using TMB; the RVM and the Probabilistic Feature Selection and Classification Vector Machine method, where the latter also performs feature selection. Experiments based on benchmark data show that our TMB implementation performs comparable to that of the original implementation, but at a lower implementation cost. TMB can also calculate model and prediction uncertainty, by including estimation uncertainty from both latent variables and the hyperparameters. In conclusion, we find that TMB is a flexible tool that facilitates implementation and prototyping of sparse Bayesian methods.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"39 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A new maximum mean discrepancy based two-sample test for equal distributions in separable metric spaces 基于最大均值差异的新的可分离度量空间等分布双样本检验法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-25 DOI: 10.1007/s11222-024-10483-9

Bu Zhou, Zhi Peng Ong, Jin-Ting Zhang

{"title":"A new maximum mean discrepancy based two-sample test for equal distributions in separable metric spaces","authors":"Bu Zhou, Zhi Peng Ong, Jin-Ting Zhang","doi":"10.1007/s11222-024-10483-9","DOIUrl":"https://doi.org/10.1007/s11222-024-10483-9","url":null,"abstract":"This paper presents a novel two-sample test for equal distributions in separable metric spaces, utilizing the maximum mean discrepancy (MMD). The test statistic is derived from the decomposition of the total variation of data in the reproducing kernel Hilbert space, and can be regarded as a V-statistic-based estimator of the squared MMD. The paper establishes the asymptotic null and alternative distributions of the test statistic. To approximate the null distribution accurately, a three-cumulant matched chi-squared approximation method is employed. The parameters for this approximation are consistently estimated from the data. Additionally, the paper introduces a new data-adaptive method based on the median absolute deviation to select the kernel width of the Gaussian kernel, and a new permutation test combining two different Gaussian kernel width selection methods, which improve the adaptability of the test to different data sets. Fast implementation of the test using matrix calculation is discussed. Extensive simulation studies and three real data examples are presented to demonstrate the good performance of the proposed test.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"3 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Wasserstein principal component analysis for circular measures 用于循环测量的瓦瑟斯坦主成分分析法

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-24 DOI: 10.1007/s11222-024-10473-x

Mario Beraha, Matteo Pegoraro

引用次数: 0

Individualized causal mediation analysis with continuous treatment using conditional generative adversarial networks 利用条件生成对抗网络对连续治疗进行个性化因果中介分析

IF 2.2 2区数学

Statistics and Computing Pub Date : 2024-08-23 DOI: 10.1007/s11222-024-10484-8

Cheng Huan, Xinyuan Song, Hongwei Yuan

{"title":"Individualized causal mediation analysis with continuous treatment using conditional generative adversarial networks","authors":"Cheng Huan, Xinyuan Song, Hongwei Yuan","doi":"10.1007/s11222-024-10484-8","DOIUrl":"https://doi.org/10.1007/s11222-024-10484-8","url":null,"abstract":"Traditional methods used in causal mediation analysis with continuous treatment often focus on estimating average causal effects, limiting their applicability in precision medicine. Machine learning techniques have emerged as a powerful approach for precisely estimating individualized causal effects. This paper proposes a novel method called CGAN-ICMA-CT that leverages Conditional Generative Adversarial Networks (CGANs) to infer individualized causal effects with continuous treatment. We thoroughly investigate the convergence properties of CGAN-ICMA-CT and show that the estimated distribution of our inferential conditional generator converges to the true conditional distribution under mild conditions. We conduct numerical experiments to validate the effectiveness of CGAN-ICMA-CT and compare it with four commonly used methods: linear regression, support vector machine regression, decision tree, and random forest regression. The results demonstrate that CGAN-ICMA-CT outperforms these methods regarding accuracy and precision. Furthermore, we apply the CGAN-ICMA-CT model to the real-world Job Corps dataset, showcasing its practical utility. By utilizing CGAN-ICMA-CT, we estimate the individualized causal effects of the Job Corps program on the number of arrests, providing insights into both direct effects and effects mediated through intermediate variables. Our findings confirm the potential of CGAN-ICMA-CT in advancing individualized causal mediation analysis with continuous treatment in precision medicine settings.","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"7 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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