Nonparametric Estimation via Mixed Derivatives

通过混合导数的非参数估计

基本信息

  • 批准号:
    2210504
  • 负责人:
  • 金额:
    $ 17.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-07-01 至 2025-06-30
  • 项目状态:
    未结题

项目摘要

Understanding the precise relationship between a specific variable of interest and a related set of covariables is a fundamental problem arising in many areas of science and engineering. It is usually necessary to combine two different sources of information to solve this problem. The first source of information is domain knowledge or theory, which often suggests certain basic forms for the relationship between the variables. The second source of information is observed data on the values of the variables for a set of experimental conditions or subjects. Effective solutions to the problem can only be obtained by efficiently combining both sources of information. The development of such a methodology is the primary goal of this project. Assuming the function governing the relationship between the variables is smooth in a certain sense, the observed data is then brought in to find the function satisfying the assumed smoothness that best explains the observed data. This project will explore different ways of carrying out this scheme and develop novel methods and computational algorithms useful to practitioners in broad scientific areas. Most existing methods for studying these problems either make strong prior assumptions that are unrealistic and lead to wrong conclusions on the relationship between the variables, or weak prior assumptions that lead to requiring unrealistically enormous sizes of datasets for reliable conclusions. The developed approach based on "mixed partial derivative smoothness constraints" effectively compromises these two extreme approaches and will lead to methods of great practical value. The material emanating from this research will be disseminated through seminars and undergraduate as well as graduate teaching. The methods from this project will be made available to the wider statistics and scientific community through the development of software packages. This project focuses on nonparametric function estimation problems under smoothness constraints involving mixed partial derivatives. The investigator plans to expand recently developed methodology for nonparametric regression under mixed partial derivatives of first and second orders to allow for restricted interaction orders, design faster algorithms for computation, and prove theoretical accuracy results under more general design assumptions. The possibility of near parametric rates under strong sparsity settings will be explored in a more general setting involving tensor product bases (including complex exponentials and radial basis functions). Uncertainty quantification will be systematically explored using Bayesian approaches with a main focus on Cauchy priors. New mixed derivative approaches will be explored in shape-constrained regression, including those based on Entire Monotonicity with restricted interactions and total Popoviciu convexity. Mixed derivative approaches for spectral density estimation of time series and density estimation will also be studied.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
理解一个特定的感兴趣的变量和一组相关的协变量之间的精确关系是在许多科学和工程领域出现的一个基本问题。通常有必要结合两个不同的信息源来解决这个问题。第一个信息源是领域知识或理论,它通常为变量之间的关系提出某些基本形式。第二个信息源是一组实验条件或实验对象的变量值的观测数据。只有有效地结合这两种信息来源,才能获得问题的有效解决方案。开发这样一种方法是这个项目的主要目标。假设控制变量之间关系的函数在某种意义上是平滑的,然后引入观测数据来寻找满足假设平滑的函数,该函数最好地解释了观测数据。本项目将探索实施该方案的不同方式,并开发对广泛科学领域的实践者有用的新方法和计算算法。大多数研究这些问题的现有方法要么做出不切实际的强先验假设,导致对变量之间的关系得出错误的结论,要么做出弱先验假设,导致需要不切实际的庞大数据集才能得出可靠的结论。基于“混合偏导数光滑性约束”的方法有效地折衷了这两种极端方法,将产生具有很大实用价值的方法。从这项研究中产生的材料将通过研讨会和本科及研究生教学传播。这个项目的方法将通过开发软件包提供给更广泛的统计和科学界。本课题主要研究包含混合偏导数的光滑约束下的非参数函数估计问题。研究人员计划扩展最近开发的一阶和二阶混合偏导数下的非参数回归方法,以允许受限制的交互顺序,设计更快的计算算法,并在更一般的设计假设下证明理论准确性结果。在强稀疏设置下近参数率的可能性将在涉及张量积基(包括复指数和径向基函数)的更一般设置中进行探讨。不确定性量化将系统地探索使用贝叶斯方法,主要集中在柯西先验。在形状约束回归中探索新的混合导数方法,包括基于受限相互作用的完全单调性和全波波维丘凸性的混合导数方法。时间序列的谱密度估计和密度估计的混合导数方法也将被研究。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Adityanand Guntuboyina其他文献

Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators
多维凸回归:最小二乘估计量的次优性
  • DOI:
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Gil Kur;Fuchang Gao;Adityanand Guntuboyina;B. Sen
  • 通讯作者:
    B. Sen
Covering numbers of $L_p$-balls of convex sets and functions
覆盖凸集和函数的 $L_p$-球的数量
  • DOI:
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Adityanand Guntuboyina
  • 通讯作者:
    Adityanand Guntuboyina
SUPPLEMENTARY MATERIAL TO ‘ ADAPTATION IN LOG-CONCAVE DENSITY ESTIMATION ’ By
“对数凹密度估计的适应”的补充材料
  • DOI:
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Arlene K. H. Kim;Adityanand Guntuboyina;R. Samworth
  • 通讯作者:
    R. Samworth
Supplement: A Statistical Perspective on Coreset Density Estimation
补充:核心集密度估计的统计视角
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Adityanand Guntuboyina;Dissertation Director;D. Pollard
  • 通讯作者:
    D. Pollard
Adaptation in log-concave density estimation
对数凹密度估计的适应
  • DOI:
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    4.5
  • 作者:
    Arlene K. H. Kim;Adityanand Guntuboyina;R. Samworth
  • 通讯作者:
    R. Samworth

Adityanand Guntuboyina的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Adityanand Guntuboyina', 18)}}的其他基金

CAREER: Nonparametric function estimation: shape constraints, adaptation, inference and beyond
职业:非参数函数估计:形状约束、适应、推理等
  • 批准号:
    1654589
  • 财政年份:
    2017
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Continuing Grant
Estimation of Convex Objects
凸物体的估计
  • 批准号:
    1309356
  • 财政年份:
    2013
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Continuing Grant

相似海外基金

CAREER: Solving Estimation Problems of Networked Interacting Dynamical Systems Via Exploiting Low Dimensional Structures: Mathematical Foundations, Algorithms and Applications
职业:通过利用低维结构解决网络交互动力系统的估计问题:数学基础、算法和应用
  • 批准号:
    2340631
  • 财政年份:
    2024
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Continuing Grant
Bayesian causal estimation via model misspecification
通过模型错误指定进行贝叶斯因果估计
  • 批准号:
    EP/Y029755/1
  • 财政年份:
    2024
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Research Grant
Data-driven selection of a convex loss function via shape-constrained estimation
通过形状约束估计来数据驱动选择凸损失函数
  • 批准号:
    2311299
  • 财政年份:
    2023
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Standard Grant
NSF-AoF: Collaborative Research: CIF: Small: 6G Wireless Communications via Enhanced Channel Modeling and Estimation, Channel Morphing and Machine Learning for mmWave Bands
NSF-AoF:协作研究:CIF:小型:通过增强型毫米波信道建模和估计、信道变形和机器学习实现 6G 无线通信
  • 批准号:
    2225617
  • 财政年份:
    2022
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Standard Grant
Estimation and Inference via Computational Statistics Algorithms
通过计算统计算法进行估计和推理
  • 批准号:
    RGPIN-2019-04142
  • 财政年份:
    2022
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Discovery Grants Program - Individual
Scalable Algorithm Design for Unbiased Estimation via Couplings of Markov Chain Monte Carlo Methods
通过马尔可夫链蒙特卡罗方法耦合进行无偏估计的可扩展算法设计
  • 批准号:
    2210849
  • 财政年份:
    2022
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Continuing Grant
Estimation and Inference via Computational Statistics Algorithms
通过计算统计算法进行估计和推理
  • 批准号:
    RGPIN-2019-04142
  • 财政年份:
    2021
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Discovery Grants Program - Individual
Solid tumour segmentation via principal axis estimation using weakly supervised adversarial deep learning
使用弱监督对抗性深度学习通过主轴估计进行实体瘤分割
  • 批准号:
    2565764
  • 财政年份:
    2020
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Studentship
Development of Evacuation Simulation Method Based on Human Flow Estimation via WiFi Signal Measurements
基于 WiFi 信号测量人流估计的疏散模拟方法的开发
  • 批准号:
    20K14989
  • 财政年份:
    2020
  • 资助金额:
    $ 17.5万
  • 项目类别:
    Grant-in-Aid for Early-Career Scientists
Spatial variable estimation in subsurface via kriging with machine learning mapping
通过克里格法和机器学习映射进行地下空间变量估计
  • 批准号:
    552550-2020
  • 财政年份:
    2020
  • 资助金额:
    $ 17.5万
  • 项目类别:
    University Undergraduate Student Research Awards
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了