Computationally intensive approaches to missing data

由于计算技术的进步和收集信息的普遍技术创新的爆炸性增长，现代科学研究在面临数据缺失时面临着独特的挑战。我的研究将尝试开发新的方法，在存在缺失观测的情况下分析数据，特别是对于本质上高维的数据，并解决模型选择的问题。我将使用和扩展先进的非参数聚类方法来改进高维分类变量的多重填充方法。我将展示如何通过使用自适应求积方法，特别是为计算机实验设计开发的方法，将多重填充算法的原始前提恢复为高维积分的估计，以帮助在少量副本的情况下提高推理的效率。我将研究机器和统计学习中常用的降维工具(如主成分分析、偏最小二乘法、神经网络和支持向量机)的使用，以允许生成使用尽可能多和实用的相关信息的完整数据集。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，在该框架中，从业者可以更容易和自动地测试在分析有缺失的数据时对建模假设的稳健性。

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.