CAREER: Learning from Heterogeneous Populations in Small Data Regime with Applications to Preference and Metric Learning

了解人类如何代表不同的概念，感知不同的选择，并根据这些概念做出判断，在认知和行为科学、消费者推荐系统、个性化教育、众包民主以及为社会科学和政策制定量化调查数据方面发挥着至关重要的作用。偏好和使用人类判断的度量学习已经成为学习这种表征的强大工具。然而，这些学习算法中的大多数仅限于研究总体平均的模型，而不能捕捉组成总体的不同人群之间的差异。该项目旨在通过开发新的模型、分析其基本限制并设计具有可在不同粒度尺度上学习的保证的算法来弥合这一差距。这个项目的结果有可能在偏好和度量学习中引入一种新的范式。该项目还将通过面向研究生和本科生的课程模块、为本科生提供的研究指导和公共推广方案产生重大的教育和推广影响。从生物科学到社会科学，许多科学研究涉及从不同人群收集的社会规模的数据集，例如不同的年龄、人口统计等。这种数据集通常也只有每个人的几个观察值(小数据制度)。一般来说，现成的机器学习算法的构建并没有考虑到由异质性和小数据等问题引起的统计挑战。该项目通过开发新的模型、基本限制方面的理论基础和具有保证从不同粒度的不同数据中学习的实用算法，解决了从小数据制度中的不同群体优先学习和度量学习时出现的挑战。具体地说，该项目旨在建立基本的限制，开发具有理论保证的模型和算法，以(1)了解总体偏好的分布，(2)在子组级别学习指标，以及(3)通过利用总体上了解的共同结构和先验知识来学习个人变异性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding how humans represent different concepts, perceive different options, and make judgements based on them plays a vital role in cognitive and behavioral sciences, consumer recommendation systems, individualized education, crowdsourced democracy and in quantifying survey data for social sciences and policy making. Preference and metric learning using judgment from humans have emerged as powerful tools to learn such representations. Most of these learning algorithms, however, are limited to studying models that are averaged over the population and do not capture the variations among the diverse set of people comprising the population. This project aims to close this gap by developing novel models, analyzing their fundamental limits, and designing algorithms with guarantees that can be learned at different scales of granularity. The results of this project have the potential to usher in a new paradigm in preference and metric learning. This project will also have significant educational and outreach impact through course modules for graduate and undergraduate students, research mentoring for undergraduate students, and public outreach programs.From biological sciences to social sciences, many scientific studies involve societal-scale datasets collected over heterogeneous populations, e.g., different ages, demographics, etc. Such datasets also usually have only a few observations per individual (small data regime). In general, off-the-shelf machine learning algorithms are not built with consideration to the statistical challenges arising from issues like heterogeneity and small data. This project addresses the challenges that arise when learning from heterogeneous populations in small data regimes in preference and metric learning by developing novel models, theoretical foundations in terms of fundamental limits, and practical algorithms with guarantees for learning from heterogeneous data at different levels of granularity. Specifically, the project aims to establish fundamental limits, develop models and algorithms with theoretical guarantees for (1) learning distribution of preferences over a population, (2) learning metrics at subgroup levels, and (3) learning individual variability by leveraging common structures and priors learned over the population.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.