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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=655403
• 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，我们有大量的大数据，在不同的领域中被称为大数据。互联网作为大量特征的函数该提案的一部分集中在FMR/MOE中的特征选择，估计和选择后的推理问题。分段研究，随着时间的流逝和不同市场的偏好，涉及异质功能数据。方法论和计算效率，特征选择以及选择后的推理，例如我的研究中的FMR/ AL点的假设测试和置信区间，这是我的研究关注的估计和特征选择。 -Dimansion OUS和依赖数据计算。在稀疏的FMR/MOE中的假设测试和置信区间将基于基于基于样本分裂技术的基于基于基于的基于基于基于的基于基于基于的基于VC-FMR模型。影响：我的支撑研究计划与高度的FMR/MOE模型中的未解决的统计信息以及VC-FMR模型中的相关性。作为生物学，工程，健康科学和市场研究。