Computationally intensive approaches to missing data

由于计算技术的突飞猛进和信息收集技术的普遍创新，现代科学研究面临着数据缺失的独特挑战。我的研究将尝试开发新的方法来分析存在缺失观测的数据，特别是对于本质上是高维的数据和解决模型选择问题。我将采用并扩展先进的非参数聚类方法来改进高维分类变量的多重插值方法。我将展示如何通过使用自适应正交方法，特别是为设计计算机实验而开发的方法，将多重插值算法的原始前提返回为高维积分的估计，以帮助提高少量副本的推理效率。我将研究在机器和统计学习中常用的降维工具（如主成分分析、偏最小二乘、神经网络和支持向量机）的使用，以允许生成使用尽可能多的相关信息和实用的完整数据集。最后，我将使用功能数据分析（特别是广义轮廓估计）的新发展来构建一个框架，在这个框架中，从业者可以在分析缺失数据时更容易和自动地测试建模假设的鲁棒性。

Due to the explosion of computational advances and general technological innovation for gathering information, modern scientific research faces a unique challenge when faced with missing data. My research will attempt to develop new methods for analyzing data in the presence of missing observations, particularly for data that is high-dimensional in nature and addressing the question of model selection. I will employ and extend advanced nonparametric clustering methods to improve multiple imputation methods for high-dimensional categorical variables.I will show how returning the the original premise of the multiple imputation algorithm as estimation of a high-dimensional integral can help to improve the efficiency of inference with small numbers of copies through the use of adaptive quadrature methods, particularly methods that have been developed for the design of computer experiments. I will examine the use of tools for dimensionality reduction that are commonly used in machine and statistical learning (such as principal component analysis, partial least squares, neural networks, and support vector machines) to allow for generation of completed datasets that use as much relevant information as possible and practical. Finally, I will use new developments in functional data analysis (particularly generalized profile estimation) to construct a framework in which practitioners can more easily and automatically test for robustness to modelling assumptions when analyzing data with missingness.