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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=716158
• 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.

我的研究计划旨在开发理论和方法，构建回归统计实验的最佳和稳健设计，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，我打算在未来五年调查。 (i)广义线性混合模型的稳健设计。 基于我以前在这个方向上的研究，我将继续致力于不精确的GLP-R的鲁棒设计。将考虑经常遇到的GLMM偏离。我打算开发一个设计过程，对这些偏离是强大的。我计划推导出一般类的GLMM指数分散分布的基础上的序贯设计。改进和新的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）的最优和稳健设计。 CQR以最小的效率折衷增强了鲁棒性。我打算构造CQR的最优和鲁棒设计有两个阶段：首先，我将考虑等加权CQR和推导出鲁棒设计，最小化指定的损失函数的程度上的信念假设的CQR模型。然后，我将介绍加权CQR，旨在确定最佳的权重，最大限度地减少估计偏差，并进一步构建最佳的设计，以最大限度地提高估计效率。 (iii)加速寿命试验（ALT）的优化和稳健设计，包括步进应力加载方案。 在我对最佳/稳健恒定应力和简单步进应力ALT设计所获得的研究结果的基础上，我将继续构建进一步具有步进应力加载的ALT的最佳和稳健设计。将强调设计的稳健性，以保护可能的模型偏离，包括寿命-应力关系的不精确性和寿命分布的不确定性。我将把以前的研究扩展到涉及异方差、多因素、多阶跃应力加载和/或半参数ALT模型的场景。 (iv)线性回归和分类的最佳和鲁棒主动学习。 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鲁棒设计。最优主动学习通常是基于一个假设的线性回归模型，具有不精确性，所以鲁棒性将是必要的。我还打算开发用于分类的最佳和鲁棒的主动学习过程，以识别可以尽可能准确地对剩余输入数据点进行分类的学习判别函数。由于这种判别函数依赖于假设的输入分布中的参数，因此我们将使用两阶段或序贯设计。 此外，我将继续开发和应用最佳和稳健设计的方法，用于各种实际应用中，当需要最佳规划或最好的数据选择。