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AF: Small: Optimal algorithms and new models for statistical estimation

AF：小：统计估计的最佳算法和新模型

基本信息

批准号：
2127806
负责人：
Paul Valiant
金额：
$ 45万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-10-01 至 2024-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2127806&HistoricalAwards=false
关键词：
AF Small Optimal algorithms new

项目摘要

Data is becoming both more valuable, yet harder to effectively analyze. Across many areas of statistics and machine learning, one desires algorithms that 1) give more accurate predictions, 2) require less data to operate, and 3) are robust to the wide array of errors that show up in real data. This project focuses on addressing this challenge in two archetypal settings. First, this project seeks to develop new algorithms and analysis tools for one of the most useful and versatile primitives of statistics: estimating the mean of a probability distribution, given data from it. Second, it seeks to develop new models that identify, unify, and hope to resolve the challenges of dealing with data that come from a non-ideal sampling process. These problems lie at the intersection of statistics, machine learning, and computer science. More broadly, this project will help build a pipeline of future researchers, by creating new pathways for undergraduates towards research and to graduate school, and by exploring with computer science students the role of research, the thought process of research, the mechanics of research, and the impact of research.In more detail, the first target of this project is the fundamental problem of "mean estimation", often considered the most important classical estimation problem in statistics: given samples from a probability distribution in one or more dimensions, estimate its mean as accurately and robustly as possible. Surprisingly, there are many important settings in which good solutions to this basic question remain to be found. This project will focus primarily on the setting of high-dimensional data, and will aim to develop algorithms that are efficient, accurate, and flexible. The second area of focus is the challenge of making accurate statistical inferences from data, despite the data originating from a non-uniform, biased sample. This project develops new frameworks for how to leverage insights about the data-collection process to improve the accuracy of statistics, a challenge that has been grappled with by many fields including computer graphics, econometrics, sociology, and statistical physics. The techniques developed to tackle these problems will reveal new algorithms and subtle probabilistic phenomena that will inform the next generation of solutions to the challenges of effectively using valuable data.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.

数据变得越来越有价值，但更难有效分析。在统计和机器学习的许多领域，人们希望算法1）给出更准确的预测，2）需要更少的数据来操作，3）对真实的数据中出现的各种错误具有鲁棒性。这个项目的重点是在两个原型设置解决这一挑战。首先，该项目旨在为统计学中最有用和最通用的基本要素之一开发新的算法和分析工具：估计概率分布的平均值，给出来自它的数据;其次，它旨在开发新的模型，识别，统一，并希望解决处理来自非理想抽样过程的数据的挑战。这些问题位于统计学、机器学习和计算机科学的交叉点。更广泛地说，这个项目将有助于建立一个未来的研究人员的管道，通过创造新的途径，为本科生走向研究和研究生院，并与计算机科学的学生探索研究的作用，研究的思维过程，研究的机制，研究的影响。更详细地说，这个项目的第一个目标是“均值估计”的基本问题，通常被认为是统计学中最重要的经典估计问题：给定一维或多维概率分布的样本，尽可能准确和稳健地估计其均值。令人惊讶的是，在许多重要的设置中，这个基本问题的好的解决方案仍然有待发现。本项目将主要关注高维数据的设置，并将致力于开发高效，准确和灵活的算法。第二个重点领域是从数据中做出准确的统计推断的挑战，尽管数据来自不均匀的、有偏见的样本。该项目为如何利用对数据收集过程的见解来提高统计数据的准确性开发了新的框架，这是一个由包括计算机图形学，计量经济学，社会学和统计物理学在内的许多领域所面临的挑战。为解决这些问题而开发的技术将揭示新的算法和微妙的概率现象，为下一代解决方案提供信息，以有效利用有价值的数据。该奖项反映了NSF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。