Optimal and Robust Designs for Active Learning and Regression Analysis

主动学习和回归分析的最佳稳健设计

• 批准号: RGPIN-2020-05283
• 负责人: Xu, Xiaojian
• 金额: $ 1.31万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740480
• 关键词: Optimal; Robust; Designs; Active; Learning

My research program aims to develop both theory and methods of constructing optimal and robust designs of statistical experiments for regression, and of training data selection for active learning. My program consists of the following research problems that I intend to investigate for the next five years. (i) Robust designs for generalized linear mixed models (GLMM). Building on my previous research in this direction, I will continue to work on robust designs for GLMMs with imprecision. Frequently encountered GLMM departures will be considered. I intend to develop a design process that is robust against these departures. I plan to derive sequential designs for a general class of GLMM based on exponential dispersion distributions. Improvement and new methods are expected to better balance the computation complexity and design efficiencies. (ii) Optimal and robust designs for composite quantile regression (CQR). CQR enhances the robustness with least trade-off in efficiency. I intend to construct optimal and robust designs for CQR with two phases: First, I will consider equally weighted CQR and derive robust designs that minimize a specified loss function with respect to the degree of belief on the assumed CQR model. I will then introduce weighted CQR and aim to identify the optimal weights that minimize the estimation bias and further construct optimal designs in order to maximize estimation efficiency. (iii) Optimal and robust designs for accelerated life testing (ALT), incorporating step-stress loading schemes. Building on my research results obtained for optimal/robust constant-stress and simple step-stress ALT designs, I will continue to construct optimal and robust designs for ALT further with step-stress loading. Robustness of the designs will be emphasized to protect possible model departures, including imprecision in life-stress relationship and uncertainty in lifetime distribution. I will extend the previous study to the scenarios that involve heteroscedasticity, multiple factors, multiple step-stress loading, and/or semi-parametric ALT models. (iv) Optimal and robust active learning for linear regression and classification. I will construct optimal and robust designs of training data selection in active learning for both linear regression and classification problems. Optimal active learning is often based on an assumed linear regression model with imprecision, so robustification will be necessary. I also intend to develop optimal and robust active learning process for classification in order to identify a learned discriminant function which can classify the remaining input data points as accurately as possible. As such discriminant functions depend on the parameters in the assumed input distributions, we will use two-stage or sequential designs. Further, I will continue developing and applying the methods of optimal and robust design for various practical applications when optimal planning or finest data selection is needed.

我的研究计划旨在发展构建回归统计实验的最优和稳健设计的理论和方法，以及主动学习的训练数据选择。我的计划包括以下研究问题，我打算在接下来的五年里进行研究。(i)广义线性混合模型（GLMM）的稳健设计。基于我之前在这个方向上的研究，我将继续致力于不精确的glmm的稳健设计。经常遇到的GLMM偏离将被考虑。我打算开发一个强大的设计过程，以防止这些偏离。我计划推导出基于指数色散分布的通用类GLMM的顺序设计。改进和新方法有望更好地平衡计算复杂度和设计效率。（ii）复合分位数回归（CQR）的最优稳健设计。CQR以最小的效率代价增强了鲁棒性。我打算用两个阶段来构建CQR的最优和稳健设计：首先，我将考虑等加权的CQR，并推导出与假设的CQR模型的信任程度相关的最小化指定损失函数的稳健设计。然后，我将引入加权CQR，旨在确定使估计偏差最小化的最优权重，并进一步构建优化设计，以最大限度地提高估计效率。（iii）优化和稳健的加速寿命测试（ALT）设计，结合阶梯应力加载方案。基于我对恒应力和简单阶梯应力ALT设计的优化/稳健研究成果，我将继续构建阶梯应力加载ALT的优化和稳健设计。设计的稳健性将强调，以保护可能的模型偏离，包括不精确的生活-压力关系和不确定性的寿命分布。我将把之前的研究扩展到涉及异方差、多因素、多阶应力加载和/或半参数ALT模型的场景。（iv）线性回归和分类的最优鲁棒主动学习。我将为线性回归和分类问题构建主动学习中训练数据选择的最优和稳健设计。最优主动学习通常基于不精确的假设线性回归模型，因此鲁棒化是必要的。我还打算为分类开发最优和鲁棒的主动学习过程，以确定一个学习的判别函数，它可以尽可能准确地分类剩余的输入数据点。由于这种判别函数依赖于假设输入分布中的参数，我们将使用两阶段或顺序设计。此外，当需要最优规划或最佳数据选择时，我将继续开发和应用各种实际应用的最优和稳健设计方法。