Statistical inference in finite mixture of regressions and mixture-of-experts models in high-dimensional spaces, and varying coefficient finite mixture of regression models

高维空间中回归和专家混合模型的有限混合的统计推断，以及回归模型的变系数有限混合

• 批准号: RGPIN-2015-03805
• 负责人: Khalili, Abbas
• 金额: $ 1.02万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675441
• 关键词: Statistical; inference; finite; mixture; regressions

INTRODUCTION: In recent years, we have witnessed the rise of large scale data, colloquially referred to as big data, in different fields of scientific research ranging from biology and medicine to engineering, the social sciences and econometrics. A common statistical problem of interest in the analysis of such data is to model a response variable of interest as a function of a small subset of a large number of features. This is referred to as a feature selection problem. In addition to noise accumulation and spurious correlation, unobserved heterogeneity in high-dimensional data makes the feature selection problem even harder. Finite mixture of regressions (FMR) and mixture-of-experts (MOE) are powerful statistical models for capturing heterogeneity in data. The first part of this proposal focuses on feature selection, estimation and post-selection inference problems in FMR/MOE. The second part concerns varying coefficient finite mixture of regression (VC-FMR) models in which regression coefficients change as smooth functions of an index variable such as time. For example, in market segmentation research, consumer preferences for products often change over time and across different market segments. VC-FMR models provide a natural tool for modeling such phenomena which involves heterogeneous functional data. However, methodological and computational tools for these relatively new models are largely unexplored. ***OBJECTIVES: An emphasis of my research program is on developing sound statistical methodology and computationally efficient algorithms for estimation, feature selection, and also post-selection inference such as hypothesis testing and confidence intervals in FMR/MOE in high dimensions. Another focal point of my research concerns estimation and feature selection in VC-FMR. My longer term objectives focus on complex time series data and high-dimensional heterogeneous and dependent data. ***METHODS: I will study the regularization techniques LASSO/SCAD for simultaneous parameter estimation and feature selection in FMR/MOE models in high dimensions. Coordinate descent-type expectation-maximization (EM) algorithms will be investigated for numerical computations. Post-selection inference such as hypothesis testing and confidence intervals for parameters in sparse FMR/MOE will be explored based on sample splitting techniques. Regularized local kernel likelihood-based methods will be used for functional parameter estimation and feature selection in VC-FMR models. ****IMPACT: My proposed research program will address unresolved statistical issues in FMR/MOE models in high dimensions as well as in VC-FMR models, and offer solutions to practical problems of interest to a broader statistical audience. The proposed methods could then immediately be used to solve scientific problems in areas such as biology, engineering, the health sciences, and marketing research.    **

简介：近年来，我们目睹了大规模数据（俗称大数据）在生物学、医学、工程、社会科学和计量经济学等不同科学研究领域的兴起。在分析此类数据时，一个常见的统计问题是将感兴趣的响应变量建模为大量特征的小子集的函数。 这称为特征选择问题。 除了噪声积累和虚假相关性之外，高维数据中未观察到的异质性使特征选择问题变得更加困难。有限混合回归 (FMR) 和混合专家 (MOE) 是捕获数据异质性的强大统计模型。该提案的第一部分重点关注 FMR/MOE 中的特征选择、估计和选择后推理问题。第二部分涉及变系数有限混合回归 (VC-FMR) 模型，其中回归系数随着时间等指标变量的平滑函数而变化。例如，在市场细分研究中，消费者对产品的偏好通常会随着时间和不同细分市场的变化而变化。 VC-FMR 模型提供了一种对涉及异构功能数据的现象进行建模的自然工具。然而，这些相对较新的模型的方法和计算工具在很大程度上尚未被探索。 ***目标：我的研究计划的重点是开发合理的统计方法和计算高效的算法，用于估计、特征选择以及高维度 FMR/MOE 中的假设检验和置信区间等选择后推理。我研究的另一个重点是 VC-FMR 中的估计和特征选择。我的长期目标侧重于复杂的时间序列数据以及高维异构和依赖数据。 ***方法：我将研究正则化技术 LASSO/SCAD，用于高维 FMR/MOE 模型中的同步参数估计和特征选择。将研究坐标下降型期望最大化（EM）算法的数值计算。将基于样本分割技术探索稀疏 FMR/MOE 中参数的假设检验和置信区间等选择后推理。 基于正则局部核似然的方法将用于 VC-FMR 模型中的功能参数估计和特征选择。 ****影响：我提出的研究计划将解决高维 FMR/MOE 模型以及 VC-FMR 模型中未解决的统计问题，并为更广泛的统计受众感兴趣的实际问题提供解决方案。所提出的方法可以立即用于解决生物学、工程学、健康科学和营销研究等领域的科学问题。    **