Marianne Huebner, Steven J. Pierce, Andrew J. Dennhardt, Hope Akaeze, Nicole Jess, Wenjuan Ma
The COVID‐19 pandemic led to unprecedented changes in all levels of society, including the statistical consulting field. This paper focuses on the experiences of graduate student consultants and clients at our statistical consulting center (SCC) that operates all year independent of semesters. During the lockdown period, work continued without interruption and was conducted remotely, but there was a temporary reduction in utilization. Advice on statistical methods, help with data analysis and educational offerings are the main appeals to utilize SCC services. We describe our mentoring approach for graduate student research assistants (RAs) and how pandemic changes affected RAs and clients. Based on experiences during the pandemic, we offer practical suggestions for SCCs' approaches to research support, work characteristics and collaborations to improve the experiences of graduate students, both as consultants and clients. Most collaboration meetings are now virtual by request from clients. Telecommuting supports flexible personal schedules and needs. Online educational offerings provide easier access for participants and more opportunities for a wider range of topics and presenters. However, mentoring sessions for RAs are best conducted in‐person, and every effort should be made to encourage in‐person interactions and collaborations between staff members to advance the effectiveness of post‐pandemic SCCs.
{"title":"What matters to graduate students? Experiences at a statistical consulting center from pre‐ to post‐COVID‐19 pandemic","authors":"Marianne Huebner, Steven J. Pierce, Andrew J. Dennhardt, Hope Akaeze, Nicole Jess, Wenjuan Ma","doi":"10.1002/sta4.659","DOIUrl":"https://doi.org/10.1002/sta4.659","url":null,"abstract":"The COVID‐19 pandemic led to unprecedented changes in all levels of society, including the statistical consulting field. This paper focuses on the experiences of graduate student consultants and clients at our statistical consulting center (SCC) that operates all year independent of semesters. During the lockdown period, work continued without interruption and was conducted remotely, but there was a temporary reduction in utilization. Advice on statistical methods, help with data analysis and educational offerings are the main appeals to utilize SCC services. We describe our mentoring approach for graduate student research assistants (RAs) and how pandemic changes affected RAs and clients. Based on experiences during the pandemic, we offer practical suggestions for SCCs' approaches to research support, work characteristics and collaborations to improve the experiences of graduate students, both as consultants and clients. Most collaboration meetings are now virtual by request from clients. Telecommuting supports flexible personal schedules and needs. Online educational offerings provide easier access for participants and more opportunities for a wider range of topics and presenters. However, mentoring sessions for RAs are best conducted in‐person, and every effort should be made to encourage in‐person interactions and collaborations between staff members to advance the effectiveness of post‐pandemic SCCs.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Differential privacy is a foundational concept for safeguarding sensitive individual information when releasing data or statistical analysis results. In this study, we concentrate on the protection of privacy in the context of goodness‐of‐fit (GOF) and independence tests, utilizing perturbed contingency tables that adhere to Gaussian differential privacy within the high‐privacy regime, where the degrees of privacy protection increase as the sample size increases. We introduce private test procedures for GOF, independence of two variables and the equality of proportions in paired samples, similar to McNemar's test. For each of these hypothesis testing situations, we propose private test statistics based on the statistics and establish their asymptotic null distributions. We numerically confirm that Type I error rates of the proposed private test procedures are well controlled and have adequate power for larger sample sizes and effect sizes. The proposal is demonstrated in private inferences based on the American Time Use Survey data.
差分隐私是在发布数据或统计分析结果时保护敏感个人信息的基本概念。在本研究中，我们将重点放在拟合优度（GOF）和独立性检验中的隐私保护上，利用扰动的或然率表，在高隐私机制下坚持高斯差分隐私，即隐私保护程度随着样本量的增加而增加。我们为 GOF、两个变量的独立性和配对样本中的比例相等（类似于 McNemar 检验）引入了隐私检验程序。对于上述每种假设检验情况，我们都提出了基于统计量的私有检验统计量，并建立了它们的渐近零分布。我们用数字证实了所提出的私人检验程序的 I 类错误率得到了很好的控制，并且对于较大的样本量和效应量具有足够的功率。我们在基于美国时间使用调查数据的私人推断中演示了这一建议。
{"title":"Highly private large‐sample tests for contingency tables","authors":"Sungkyu Jung, Seung Woo Kwak","doi":"10.1002/sta4.658","DOIUrl":"https://doi.org/10.1002/sta4.658","url":null,"abstract":"Differential privacy is a foundational concept for safeguarding sensitive individual information when releasing data or statistical analysis results. In this study, we concentrate on the protection of privacy in the context of goodness‐of‐fit (GOF) and independence tests, utilizing perturbed contingency tables that adhere to Gaussian differential privacy within the high‐privacy regime, where the degrees of privacy protection increase as the sample size increases. We introduce private test procedures for GOF, independence of two variables and the equality of proportions in paired samples, similar to McNemar's test. For each of these hypothesis testing situations, we propose private test statistics based on the statistics and establish their asymptotic null distributions. We numerically confirm that Type I error rates of the proposed private test procedures are well controlled and have adequate power for larger sample sizes and effect sizes. The proposal is demonstrated in private inferences based on the American Time Use Survey data.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a new ensemble framework for supervised learning, called machine collaboration (MaC), using a collection of possibly heterogeneous base learning methods (hereafter, base machines) for prediction tasks. Unlike bagging/stacking (a parallel and independent framework) and boosting (a sequential and top-down framework), MaC is a type of circular and recursive learning framework. The circular and recursive nature helps the base machines to transfer information circularly and update their structures and parameters accordingly. The theoretical result on the risk bound of the estimator from MaC reveals that the circular and recursive feature can help MaC reduce risk via a parsimonious ensemble. We conduct extensive experiments on MaC using both simulated data and 119 benchmark real datasets. The results demonstrate that in most cases, MaC performs significantly better than several other state-of-the-art methods, including classification and regression trees, neural networks, stacking, and boosting.
我们提出了一种新的监督学习集合框架，称为机器协作（Machine Collaboration，简称 MaC），它使用一系列可能异构的基础学习方法（以下简称基础机器）来完成预测任务。与bagging/stacking（并行和独立框架）和boosting（顺序和自上而下框架）不同，MaC是一种循环和递归学习框架。循环和递归的特性有助于基础机器循环传递信息，并相应地更新其结构和参数。关于MaC估计器风险边界的理论结果表明，循环和递归特性可以帮助MaC通过准集合降低风险。我们使用模拟数据和 119 个基准真实数据集对 MaC 进行了大量实验。结果表明，在大多数情况下，MaC 的性能明显优于其他几种最先进的方法，包括分类和回归树、神经网络、堆叠和提升。
{"title":"Machine collaboration","authors":"Qingfeng Liu, Yang Feng","doi":"10.1002/sta4.661","DOIUrl":"https://doi.org/10.1002/sta4.661","url":null,"abstract":"We propose a new ensemble framework for supervised learning, called <i>machine collaboration</i> (MaC), using a collection of possibly heterogeneous base learning methods (hereafter, base machines) for prediction tasks. Unlike bagging/stacking (a parallel and independent framework) and boosting (a sequential and top-down framework), MaC is a type of <i>circular</i> and <i>recursive</i> learning framework. The <i>circular</i> and <i>recursive</i> nature helps the base machines to transfer information circularly and update their structures and parameters accordingly. The theoretical result on the risk bound of the estimator from MaC reveals that the <i>circular</i> and <i>recursive</i> feature can help MaC reduce risk via a parsimonious ensemble. We conduct extensive experiments on MaC using both simulated data and 119 benchmark real datasets. The results demonstrate that in most cases, MaC performs significantly better than several other state-of-the-art methods, including classification and regression trees, neural networks, stacking, and boosting.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As complex-survey data become more widely used in health and social science research, there is increasing interest in fitting a wider range of regression models. We describe an implementation of two-level linear mixed models in R using the pairwise composite likelihood approach of Rao and co-workers. We discuss the computational efficiency of pairwise composite likelihood and compare the estimator to the existing sequential pseudolikelihood estimator in simulations and in data from the Programme for International Student Assessment (PISA) educational survey.
随着复杂的调查数据越来越广泛地应用于健康和社会科学研究，人们对拟合更广泛的回归模型越来越感兴趣。我们介绍了使用 Rao 及其合作者的成对复合似然法在 R 中实现两级线性混合模型的方法。我们讨论了成对复合似然的计算效率，并在模拟和国际学生评估项目（PISA）教育调查数据中将该估计器与现有的顺序伪似然估计器进行了比较。
{"title":"Linear mixed models for complex survey data: Implementing and evaluating pairwise likelihood","authors":"Thomas Lumley, Xudong Huang","doi":"10.1002/sta4.657","DOIUrl":"https://doi.org/10.1002/sta4.657","url":null,"abstract":"As complex-survey data become more widely used in health and social science research, there is increasing interest in fitting a wider range of regression models. We describe an implementation of two-level linear mixed models in R using the pairwise composite likelihood approach of Rao and co-workers. We discuss the computational efficiency of pairwise composite likelihood and compare the estimator to the existing sequential pseudolikelihood estimator in simulations and in data from the Programme for International Student Assessment (PISA) educational survey.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139981455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deep learning has achieved unprecedented success in recent years. This approach essentially uses the composition of nonlinear functions to model the complex relationship between input features and output labels. However, a comprehensive theoretical understanding of why the hierarchical layered structure can exhibit superior expressive power is still lacking. In this paper, we provide an explanation for this phenomenon by measuring the approximation efficiency of neural networks with respect to discontinuous target functions. We focus on deep neural networks with rectified linear unit (ReLU) activation functions. We find that to achieve the same degree of approximation accuracy, the number of neurons required by a single‐hidden‐layer (SHL) network is exponentially greater than that required by a multi‐hidden‐layer (MHL) network. In practice, discontinuous points tend to contain highly valuable information (i.e., edges in image classification). We argue that this may be a very important reason accounting for the impressive performance of deep neural networks. We validate our theory in extensive experiments.
{"title":"A note about why deep learning is deep: A discontinuous approximation perspective","authors":"Yongxin Li, Haobo Qi, Hansheng Wang","doi":"10.1002/sta4.654","DOIUrl":"https://doi.org/10.1002/sta4.654","url":null,"abstract":"Deep learning has achieved unprecedented success in recent years. This approach essentially uses the composition of nonlinear functions to model the complex relationship between input features and output labels. However, a comprehensive theoretical understanding of why the hierarchical layered structure can exhibit superior expressive power is still lacking. In this paper, we provide an explanation for this phenomenon by measuring the approximation efficiency of neural networks with respect to discontinuous target functions. We focus on deep neural networks with rectified linear unit (ReLU) activation functions. We find that to achieve the same degree of approximation accuracy, the number of neurons required by a single‐hidden‐layer (SHL) network is exponentially greater than that required by a multi‐hidden‐layer (MHL) network. In practice, discontinuous points tend to contain highly valuable information (i.e., edges in image classification). We argue that this may be a very important reason accounting for the impressive performance of deep neural networks. We validate our theory in extensive experiments.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Camille J. Hochheimer, Grace N. Bosma, Lauren Gunn-Sandell, Mary D. Sammel
With data and code sharing policies more common and version control more widely used in statistics, standards for reproducible research are higher than ever. Reproducible research practices must keep up with the fast pace of research. To do so, we propose combining modern practices of leadership with best practices for reproducible research in collaborative statistics as an effective tool for ensuring quality and accuracy while developing stewardship and autonomy in the people we lead. First, we establish a framework for expectations of reproducible statistical research. Then, we introduce Stephen M.R. Covey's theory of trusting and inspiring leadership. These two are combined as we show how stewardship agreements can be used to make reproducible coding a team norm. We provide an illustrative code example and highlight how this method creates a more collaborative rather than evaluative culture where team members hold themselves accountable. The goal of this manuscript is for statisticians to find this application of leadership theory useful and to inspire them to intentionally develop their personal approach to leadership.
{"title":"Reproducible research practices: A tool for effective and efficient leadership in collaborative statistics","authors":"Camille J. Hochheimer, Grace N. Bosma, Lauren Gunn-Sandell, Mary D. Sammel","doi":"10.1002/sta4.653","DOIUrl":"https://doi.org/10.1002/sta4.653","url":null,"abstract":"With data and code sharing policies more common and version control more widely used in statistics, standards for reproducible research are higher than ever. Reproducible research practices must keep up with the fast pace of research. To do so, we propose combining modern practices of leadership with best practices for reproducible research in collaborative statistics as an effective tool for ensuring quality and accuracy while developing stewardship and autonomy in the people we lead. First, we establish a framework for expectations of reproducible statistical research. Then, we introduce Stephen M.R. Covey's theory of trusting and inspiring leadership. These two are combined as we show how stewardship agreements can be used to make reproducible coding a team norm. We provide an illustrative code example and highlight how this method creates a more collaborative rather than evaluative culture where team members hold themselves accountable. The goal of this manuscript is for statisticians to find this application of leadership theory useful and to inspire them to intentionally develop their personal approach to leadership.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study addresses limitations in the nonparametric EWMA sign chart with fixed control limits (FCLs), particularly when facing time-varying sample sizes. The FCLs-based EWMA sign chart has a variable conditional false alarm rate (CFAR), especially at the startup of a process or after recovering from an out-of-control signal. To overcome these limitations, we propose a nonparametric EWMA sign chart based on dynamic probability control limits. This chart is capable of monitoring the process target with fixed, as well as time-varying sample sizes. Monte Carlo simulations are used to estimate the CFARs, zero-state (ZS) and steady-state (SS) average run-length profiles of the EWMA sign charts. It turns out that the proposed chart outperforms the existing chart, particularly in detecting shifts during the process startup, while maintaining the desired CFAR levels in both ZS and SS scenarios. A real data example is given to demonstrate the implementation of the EWMA sign charts.
{"title":"An EWMA sign chart for monitoring processes with fixed and variable sample sizes","authors":"Abdul Haq","doi":"10.1002/sta4.652","DOIUrl":"https://doi.org/10.1002/sta4.652","url":null,"abstract":"This study addresses limitations in the nonparametric EWMA sign chart with fixed control limits (FCLs), particularly when facing time-varying sample sizes. The FCLs-based EWMA sign chart has a variable conditional false alarm rate (CFAR), especially at the startup of a process or after recovering from an out-of-control signal. To overcome these limitations, we propose a nonparametric EWMA sign chart based on dynamic probability control limits. This chart is capable of monitoring the process target with fixed, as well as time-varying sample sizes. Monte Carlo simulations are used to estimate the CFARs, zero-state (ZS) and steady-state (SS) average run-length profiles of the EWMA sign charts. It turns out that the proposed chart outperforms the existing chart, particularly in detecting shifts during the process startup, while maintaining the desired CFAR levels in both ZS and SS scenarios. A real data example is given to demonstrate the implementation of the EWMA sign charts.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ruiwen Zhou, J. Philip Miller, Mae Gordon, Michael Kass, Mingquan Lin, Yifan Peng, Fuhai Li, Jiarui Feng, Lei Liu
Glaucoma is a major cause of blindness and vision impairment worldwide, and visual field (VF) tests are essential for monitoring the conversion of glaucoma. While previous studies have primarily focused on using VF data at a single time point for glaucoma prediction, there has been limited exploration of longitudinal trajectories. Additionally, many deep learning techniques treat the time-to-glaucoma prediction as a binary classification problem (glaucoma Yes/No), resulting in the misclassification of some censored subjects into the nonglaucoma category and decreased power. To tackle these challenges, we propose and implement several deep-learning approaches that naturally incorporate temporal and spatial information from longitudinal VF data to predict time-to-glaucoma. When evaluated on the Ocular Hypertension Treatment Study (OHTS) dataset, our proposed convolutional neural network (CNN)-long short-term memory (LSTM) emerged as the top-performing model among all those examined. The implementation code can be found online (https://github.com/rivenzhou/VF_prediction).
{"title":"Deep learning models to predict primary open-angle glaucoma","authors":"Ruiwen Zhou, J. Philip Miller, Mae Gordon, Michael Kass, Mingquan Lin, Yifan Peng, Fuhai Li, Jiarui Feng, Lei Liu","doi":"10.1002/sta4.649","DOIUrl":"https://doi.org/10.1002/sta4.649","url":null,"abstract":"Glaucoma is a major cause of blindness and vision impairment worldwide, and visual field (VF) tests are essential for monitoring the conversion of glaucoma. While previous studies have primarily focused on using VF data at a single time point for glaucoma prediction, there has been limited exploration of longitudinal trajectories. Additionally, many deep learning techniques treat the time-to-glaucoma prediction as a binary classification problem (glaucoma Yes/No), resulting in the misclassification of some censored subjects into the nonglaucoma category and decreased power. To tackle these challenges, we propose and implement several deep-learning approaches that naturally incorporate temporal and spatial information from longitudinal VF data to predict time-to-glaucoma. When evaluated on the Ocular Hypertension Treatment Study (OHTS) dataset, our proposed convolutional neural network (CNN)-long short-term memory (LSTM) emerged as the top-performing model among all those examined. The implementation code can be found online (https://github.com/rivenzhou/VF_prediction).","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age.
{"title":"Estimation of the density for censored and contaminated data","authors":"Ingrid Van Keilegom, Elif Kekeç","doi":"10.1002/sta4.651","DOIUrl":"https://doi.org/10.1002/sta4.651","url":null,"abstract":"Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In predictive modelling for high-stake decision-making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the coverage of prediction results with fewer theoretical assumptions. To obtain the prediction set by so-called full-CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split-CP is often employed where the data is split into two parts: one part for fitting and another for computing the prediction set. Unfortunately, because of the reduced sample size, split-CP is inferior to full-CP both in fitting as well as prediction set computation. In this paper, we develop a full-CP of sparse high-order interaction model (SHIM), which is sufficiently flexible as it can take into account high-order interactions among variables. We resolve the computational challenge for full-CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full-CP.
{"title":"A confidence machine for sparse high-order interaction model","authors":"Diptesh Das, Eugene Ndiaye, Ichiro Takeuchi","doi":"10.1002/sta4.633","DOIUrl":"https://doi.org/10.1002/sta4.633","url":null,"abstract":"In predictive modelling for high-stake decision-making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the coverage of prediction results with fewer theoretical assumptions. To obtain the prediction set by so-called full-CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split-CP is often employed where the data is split into two parts: one part for fitting and another for computing the prediction set. Unfortunately, because of the reduced sample size, split-CP is inferior to full-CP both in fitting as well as prediction set computation. In this paper, we develop a full-CP of sparse high-order interaction model (SHIM), which is sufficiently flexible as it can take into account high-order interactions among variables. We resolve the computational challenge for full-CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full-CP.","PeriodicalId":56159,"journal":{"name":"Stat","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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