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Latent Dependence and Identifiable, Graphical, Deep Modeling of Discrete Latent Variables

离散潜在变量的潜在依赖性和可识别、图形化、深度建模

基本信息

批准号：
2210796
负责人：
Yuqi Gu
金额：
$ 15万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210796&HistoricalAwards=false
关键词：
Latent Dependence Identifiable Graphical Deep

项目摘要

In the data science era, complex dependent and heterogeneous data emerge in various subject areas, from education to psychology to medicine. Latent variable models are powerful statistical approaches to tackle such complex data. However, existing statistical methods for analysis of latent variables are mostly limited to relatively simple settings and cannot meet the need for modern high dimensional applications. For example, one critical motivating example for this project is personalized learning, for which educators aim to diagnose individual students’ latent strengths and weaknesses across many skills based on educational assessment data. In this scenario, it is highly desirable to make discrete statistical diagnoses about student’s fine-grained skills, to understand the relationships between various latent skills and the underlying cognitive processes, and to develop targeted remedial instructions. To achieve these goals, this project aims to develop a suite of new statistical tools for discrete latent variable modeling. The new statistical methodology is intended to apply not only to educational data, but also to data from psychology, medicine, genetics, and health sciences. The tools will be implemented in publicly available software. These research tools are expected to help practitioners to uncover hidden information about students, patients, and biological systems in a statistically principled manner. In addition, this project will provide multiple training opportunities for graduate and undergraduate students, introducing them to the important area of latent variable models in modern statistics. This project aims to advance the statistical theory and methodology of discrete latent variable modeling and providing novel statistical algorithms applicable to education and other applications. The project has three objectives. The first is to develop new mathematical machinery to study identifiability in general discrete models with latent and graphical components. These techniques will be used to derive sharp identifiability conditions for models motivated by education sciences. The second objective is to elaborate two new families of generative models with discrete latent variables: deep generative models with multilayer latent structures, and probabilistic graphical models encoding hard hierarchical latent constraints. Identifiability of these models will be established, which would guarantee the validity of statistical inference. The resulting models are expected to shed light on latent dependencies in several applications, particularly, in conjunction with educational diagnoses and personalized learning. The third objective is to develop novel hypothesis testing of identifiability, flexible Bayesian methods to simultaneously infer latent dimensions and other parameters, and efficient structure learning procedures to estimate the latent graphical constraints. The project will offer opportunities for professional development of trainees at the interface of statistics, data science, psychology, and educational sciences.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.

在数据科学时代，从教育到心理学再到医学，各个学科领域都出现了复杂的依赖性和异构性数据。潜变量模型是处理此类复杂数据的强大统计方法。然而，现有的潜变量统计分析方法大多局限于相对简单的设置，不能满足现代高维应用的需要。例如，这个项目的一个关键激励例子是个性化学习，教育工作者的目标是根据教育评估数据诊断个别学生在许多技能方面的潜在优势和弱点。在这种情况下，它是非常可取的离散的统计诊断学生的细粒度的技能，了解各种潜在的技能和潜在的认知过程之间的关系，并制定有针对性的补救指示。为了实现这些目标，本项目旨在开发一套新的离散潜变量建模的统计工具。新的统计方法不仅适用于教育数据，还适用于心理学、医学、遗传学和健康科学数据。这些工具将在公开提供的软件中实施。这些研究工具预计将帮助从业者发现隐藏的信息，学生，病人和生物系统在统计原则的方式。此外，该项目将为研究生和本科生提供多种培训机会，向他们介绍现代统计学中潜在变量模型的重要领域。该项目旨在推进离散潜变量建模的统计理论和方法，并提供适用于教育和其他应用的新颖统计算法。该项目有三个目标。第一个是开发新的数学机器来研究具有潜在和图形成分的一般离散模型的可识别性。这些技术将被用来获得尖锐的可识别性条件的教育科学的动机模型。第二个目标是阐述两个新的家庭的生成模型与离散的潜在变量：深层生成模型与多层潜在结构，和概率图形模型编码硬层次潜在的约束。这些模型的可识别性将被建立，这将保证统计推断的有效性。由此产生的模型有望揭示潜在的依赖关系在几个应用程序中，特别是在教育诊断和个性化学习。第三个目标是开发新的假设检验的可识别性，灵活的贝叶斯方法，同时推断潜在的尺寸和其他参数，和有效的结构学习程序来估计潜在的图形约束。该项目将为受训人员提供统计学、数据科学、心理学和教育科学等方面的专业发展机会。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。