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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612582
• 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的兴起，被称为大数据，在不同的科学研究领域，从生物学和医学到工程，社会科学和经济学。对此类数据的分析，一个常见的统计问题是对感兴趣的响应变量进行建模，这是大量特征的一小部分的函数。这被称为特征选择问题。除了噪声积累和虚假相关性外，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。回归（FMR）和专家混合物（MOE）的有限混合物是捕获数据中异质性的强大统计模型。该提案的第一部分着重于FMR/MOE中的特征选择，估计和选择后推断问题。第二部分涉及回归（VC-FMR）VC-FMR模型的临界有限混合物的不同，为建模涉及异质功能数据的现象提供了自然工具。但是，这些相对新模型的方法论和计算工具在很大程度上是出乎意料的。 目的：我的研究计划的重点是开发可靠的统计方法和计算有效的算法，用于估计，特征选择以及在高维度中FMR/MOE中的假设测试和置信区间等选择后推断。我的研究的另一个重点是VC-FMR中的估计和特征选择。我的长期目标集中在复杂的时间序列数据以及高维异质和依赖数据上。 方法：我将研究调节的技术套索/SCAD，以在高维度中的FMR/MOE模型中进行简单的参数估计和特征选择。将研究数值计算的坐标下降型期望最大化（EM）算法。根据样品分割技术，将探索选择后推理的推理，例如稀疏FMR/MOE参数的置信区间。基于局部内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度和VC-FMR模型中FMR/MOE模型中未解决的统计问题，并为更广泛的统计受众提供了感兴趣的实际问题的解决方案。然后，可以立即使用所提出的方法来解决生物学，工程，健康科学和市场研究等领域的科学问题。