检索结果-内蒙古大学图书馆

Rates of contraction with respect to L2-distance for bayesian nonparametric regression

ELECTRONIC JOURNAL OF STATISTICS 2019年第2期13卷 3485-3512页

作者： Xie, Fangzheng Jin, Wei Xu, Yanxun Johns Hopkins Univ Dept Appl Math & Stat Baltimore MD 21218 USA

We systematically study the rates of contraction with respect to the integrated L-2-distance for bayesian nonparametric regression in a generic framework, and, notably, without assuming the regression function space to be uniformly bounded. The generic framework is very flexible and can be applied to a wide class of nonparametric prior models. Three non-trivial applications of the framework are provided: The finite random series regression of an alpha-Holder function, with adaptive rates of contraction up to a logarithmic factor;The un-modified block prior regression of an alpha-Sobolev function, with adaptive-and-exact rates of contraction;The Gaussian spline regression of an alpha-Holder function, with near optimal rates of contraction. These applications serve as generalization or complement of their respective results in the literature. Extensions to the fixed-design regression problem and sparse additive models in high dimensions are discussed as well.

关键词： bayesian nonparametric regression block prior finite random series Gaussian splines integrated L-2-distance rate of contraction

来源：评论

学校读者我要写书评

暂无评论

Adaptive bayesian nonparametric regression Using a Kernel Mixture of Polynomials with Application to Partial Linear Models

引用

bayesian ANALYSIS 2020年第1期15卷 159-186页

作者： Xie, Fangzheng Xu, Yanxun Johns Hopkins Univ Dept Appl Math & Stat Baltimore MD 21218 USA

We propose a kernel mixture of polynomials prior for bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal contraction rate of the full posterior distribution up to a logarithmic factor by estimating metric entropies of certain function classes. Under the assumption that the degree of the polynomials is larger than the unknown smoothness level of the true function, the posterior contraction behavior can adapt to this smoothness level provided an upper bound is known. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to partial linear models and obtain both the near-optimal rate of contraction for the nonparametric component and the Bernstein-von Mises limit (i.e., asymptotic normality) of the parametric component. The proposed method is illustrated with numerical examples and shows superior performance in terms of computational efficiency, accuracy, and uncertainty quantification compared to the local polynomial regression, DiceKriging, and the robust Gaussian stochastic process.

关键词： bayesian nonparametric regression Bernstein-von Mises limit metric entropies partial linear model rate of contraction

来源：评论

学校读者我要写书评

暂无评论

bayesian ADDITIVE regression TREES FOR GENOTYPE BY ENVIRONMENT INTERACTION MODELS

引用

ANNALS OF APPLIED STATISTICS 2023年第3期17卷 1936-1957页

作者： Sarti, Danilo A. Prado, Estevao B. Inglis, Alan N. Dos Santos, Antonia A. L. Hurley, Catherine B. Moral, Rafael A. Parnell, Andrew C. Maynooth Univ Insight Ctr Data Analyt Maynooth Ireland Maynooth Univ Hamilton Inst Dept Math & Stat Maynooth Ireland

We propose a new class of models for the estimation of genotype by environment (GxE) interactions in plant-based genetics. Our approach, named AMBARTI, uses semiparametric bayesian additive regression trees to accurately capture marginal genotypic and environment effects along with their interaction in a cut bayesian framework. We demonstrate that our approach is competitive or superior to similar models widely used in the literature via both simulation and a real world dataset. Furthermore, we introduce new types of visualisation to properly assess both the marginal and interactive predictions from the model. An R package that implements our approach is also available at https : //***/ebprado/ambarti.

关键词： bayesian nonparametric regression bayesian additive regression trees additive main effects multiplicative interactions model genotype-by-environment interactions

来源：评论

学校读者我要写书评

暂无评论

ACCOUNTING FOR SHARED COVARIATES IN SEMIPARAMETRIC bayesian ADDITIVE regression TREES

引用

ANNALS OF APPLIED STATISTICS 2025年第1期19卷 302-328页

作者： Prado, Estevao B. Parnell, Andrew C. Moral, Rafael A. Mcjames, Nathan O'shea, Ann Murphy, Keefe Univ Lancaster Sch Math Sci Lancaster England Maynooth Univ Hamilton Inst Maynooth Ireland Maynooth Univ Dept Math & Stat Maynooth Ireland Maynooth Univ Insight Ctr Data Analyt Maynooth Ireland

We propose some extensions to semiparametric models based on bayesian additive regression trees (BART). In the semiparametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for nonspecified interactions and nonlinearities. Previous semiparametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid poor coverage properties and reduce bias in the estimates of the parameters in the linear predictor. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias and resolve nonidentifiability issues between the parametric and nonparametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Our novel method is developed with a view to analysing data from an international education assessment, where certain predictors of students' achievements in mathematics are of particular interpretational interest. Through additional simulation studies and another application to a compared to regression models, alternative formulations of semiparametric BART, and other tree-based methods. The implementation of the proposed method is available at https://***/ebprado/CSP-BART.

关键词： bayesian additive regression trees bayesian nonparametric regression generalised linear models semiparametric regression Trends in International Mathematics and Science Study TIMSS 2019

来源：评论

学校读者我要写书评

暂无评论

bayesian additive regression trees with model trees

引用

STATISTICS AND COMPUTING 2021年第3期31卷 1-13页

作者： Prado, Estevao B. Moral, Rafael A. Parnell, Andrew C. Maynooth Univ Hamilton Inst Maynooth Kildare Ireland Maynooth Univ Dept Math & Stat Maynooth Kildare Ireland Maynooth Univ Insight Ctr Data Analyt Maynooth Kildare Ireland

bayesian additive regression trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of nonlinearity and high-order interactions. In this paper, we introduce an extension of BART, called model trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a linear predictor is estimated considering the covariates that have been used as the split variables in the corresponding tree. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART. Via simulation studies and real data applications, we compare MOTR-BART to its main competitors. R code for MOTR-BART implementation is available at https://***/ebprado/MOTR-BART.

关键词： bayesian Trees Linear models Machine learning bayesian nonparametric regression

来源：评论

学校读者我要写书评

暂无评论

Posterior Contraction for Deep Gaussian Process Priors

引用

JOURNAL OF MACHINE LEARNING RESEARCH 2023年 24卷

作者： Finocchio, Gianluca Schmidt-Hieber, Johannes Univ Vienna Fac Business Econ & Stat A-1090 Vienna Austria Univ Twente Fac Elect Engn Math & Comp Sci NL-7522 NB Enschede Netherlands

We study posterior contraction rates for a class of deep Gaussian process priors in the nonparametric regression setting under a general composition assumption on the regression function. It is shown that the contraction rates can achieve the minimax convergence rate (up to log n factors), while being adaptive to the underlying structure and smoothness of the target function. The proposed framework extends the bayesian nonparametric theory for Gaussian process priors.

关键词： bayesian nonparametric regression contraction rates deep Gaussian processes uncertainty quantification neural networks

来源：评论

学校读者我要写书评

暂无评论

Posterior contraction for deep Gaussian process priors

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2023年第1期24卷 2861-2909页

作者： Gianluca Finocchio Johannes Schmidt-Hieber Faculty of Business Economics and Statistics University of Vienna Vienna Austria Faculty of Electrical Engineering Mathematics and Computer Science University of Twente Enschede The Netherlands

关键词： bayesian nonparametric regression contraction rates deep Gaussian processes uncertainty quantification neural networks

来源：评论

学校读者我要写书评

暂无评论

bayesian curve fitting for discontinuous functions using an overcomplete system with multiple kernels

引用

JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2020年第2期49卷 516-536页

作者： Lee, Youngseon Mano, Shuhei Lee, Jaeyong Samsung SDS Seoul South Korea Inst Stat Math Tachikawa Tokyo Japan Seoul Natl Univ Dept Stat Seoul South Korea

We propose a fully bayesian methodology for estimation of functions that have jump discontinuities. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system. In the proposed model, multiple kernels are used as the elements of an overcomplete system. Since these elements are composed of different types of functions such as Haar, Laplacian, and Gaussian kernel, the proposed model can estimate discontinuous as well as smooth functions without model selection. The location of jumps, the number of basis functions, and even the smoothness of the target function are automatically determined by the Levy random measure. A simulation study and a real data analysis illustrate that the proposed model performs better than the standard nonparametric methods for the estimation of discontinuous functions. Finally, we prove prior positivity of the model and show that the prior has sufficiently large support including discontinuous functions with a finite number of jumps.

关键词： bayesian nonparametric regression Overcomplete system Multiple kernels Levy random measure LARK

来源：评论

学校读者我要写书评

暂无评论

bayesian nonparametric regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

引用

BIOMETRICS 2011年第2期67卷 454-466页

作者： Ryu, Duchwan Li, Erning Mallick, Bani K. Med Coll Georgia Dept Biostat Augusta GA 30912 USA Texas A&M Univ Dept Stat College Stn TX 77843 USA

We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.

关键词： bayesian nonparametric regression Data augmentation Generalized additive model Longitudinal data Measurement error

来源：评论

学校读者我要写书评

暂无评论

A bayesian nonparametric meta-analysis model

引用

RESEARCH SYNTHESIS METHODS 2015年第1期6卷 28-44页

作者： Karabatsos, George Talbott, Elizabeth Walker, Stephen G. Univ Illinois Dept Educ Psychol Program Measurement Evaluat Stat & Assessments Coll Educ Chicago IL 60607 USA Univ Illinois Dept Special Educ Coll Educ Chicago IL 60607 USA Univ Texas Austin Div Stat & Sci Computat Austin TX 78712 USA

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： meta-analysis bayesian nonparametric regression meta-regression effect sizes publication bias

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：