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，并根据它们做出判断，在认知和行为科学，消费者推荐系统，个性化教育，众包民主以及量化社会科学和政策制定的调查数据中起着至关重要的作用。使用人类判断的偏好和度量学习已经成为学习这种表示的强大工具。然而，这些学习算法中的大多数仅限于研究在总体上平均的模型，并且不能捕获组成总体的不同人群之间的变化。该项目旨在通过开发新的模型，分析其基本限制，并设计可以在不同粒度范围内学习的保证算法来缩小这一差距。这个项目的结果有可能在偏好和度量学习中引入一个新的范式。该项目还将通过为研究生和本科生提供课程模块、为本科生提供研究指导以及公共推广计划，产生重大的教育和推广影响。从生物科学到社会科学，许多科学研究都涉及在异质人群中收集的社会规模数据集，例如，不同的年龄，人口统计学等。这样的数据集通常也只有少数观察每个人（小数据制度）。一般来说，现成的机器学习算法并没有考虑到异质性和小数据等问题带来的统计挑战。该项目通过开发新的模型，基本限制方面的理论基础，以及保证从不同粒度级别的异构数据中学习的实用算法，解决了在偏好和度量学习中从小数据制度中的异构人群中学习时出现的挑战。具体而言，该项目旨在建立基本限制，开发具有理论保证的模型和算法，用于（1）学习人口偏好分布，（2）子组级别的学习指标，以及（3）该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的学术价值和更广泛的影响评审标准。

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.