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CRII: AF: Characterization and Complexity of Information Elicitation

CRII：AF：信息获取的特征和复杂性

基本信息

批准号：
1657598
负责人：
Rafael Frongillo
金额：
$ 17.5万
依托单位：
University of Colorado at Boulder
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-06-01 至 2020-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1657598&HistoricalAwards=false
关键词：
CRII AF Characterization Complexity Information

项目摘要

The way one judges the accuracy of predictions can greatly impact what predictions people or computers make. For example, Glenn Brier argued in 1950 that the way meteorologists were evaluated would actually give them an incentive to distort the true probability of rain. Brier's study inspired a growing body of work in statistics, economics, and now computer science, which studies evaluation metrics that incentivize accurate reports from people or machines. These evaluation metrics are also used in machine learning, a branch of artificial intelligence, where a designer implicitly tells the computer what statistic to predict by providing only the evaluation metric itself. This project seeks to mathematically characterize this link between statistics and evaluation metrics, and moreover, to understand the computational and statistical difficulty of evaluating different statistics. A precise understanding of this link would provide new evaluation metrics with the potential to increase predictive power across a vast array of applications such as climate simulations and smart cities. In particular, metrics for statistics that quantify uncertainty or risk could improve decision making in many fields, including healthcare, engineering, and finance.A dominant algorithmic paradigm in machine learning, encompassing most regression techniques and classification algorithms, is that of empirical risk minimization (ERM): choosing a model from some class that best fits the data, according to some evaluation metric called a loss function. A thread of research in theoretical machine learning called property elicitation gives a mathematical formalism to describe the link between loss functions and their corresponding statistics. In these terms, this project seeks to characterize the statistics which have calibrated loss functions, and determine how many regression parameters or data points are required for the calibration to hold. These questions are particularly relevant to machine learning when restricting attention to certain classes of loss functions which can be easily optimized or which have desirable statistical learning guarantees. The class of statistics from mathematical finance known as risk measures, which are used to regulate banks, form an important focus of the project.

人们判断预测准确性的方式会极大地影响人们或计算机做出的预测。例如，格伦·布里尔（Glenn Brier）在1950年指出，评估气象学家的方式实际上会激励他们扭曲降雨的真实概率。 Brier的研究激发了统计学、经济学以及现在的计算机科学领域越来越多的工作，这些工作研究了激励人或机器准确报告的评估指标。这些评估指标也用于机器学习，人工智能的一个分支，设计者通过只提供评估指标本身来隐含地告诉计算机预测什么统计数据。该项目力求从数学上描述统计数据和评价指标之间的这种联系，并了解评价不同统计数据的计算和统计困难。对这种联系的准确理解将提供新的评估指标，有可能提高气候模拟和智慧城市等大量应用的预测能力。特别是，量化不确定性或风险的统计指标可以改善许多领域的决策，包括医疗保健，工程和金融。机器学习中的一个主要算法范例，包括大多数回归技术和分类算法，是经验风险最小化（ERM）：根据称为损失函数的一些评估指标，从某些类别中选择最适合数据的模型。理论机器学习中的一个研究线索称为属性启发，它给出了一种数学形式来描述损失函数及其相应统计数据之间的联系。在这些术语中，该项目旨在描述具有校准损失函数的统计数据，并确定需要多少回归参数或数据点才能保持校准。这些问题与机器学习特别相关，因为它将注意力限制在某些类别的损失函数上，这些损失函数可以很容易地优化或具有理想的统计学习保证。被称为风险度量的数理金融统计类，用于监管银行，形成了该项目的一个重要焦点。