Extending the use of machine learning algorithms to Sufficient Dimension Reduction

对于线性和非线性降维问题，研究者提出了充分降维的新方法。这位研究者和他的合作者最近开发了一种方法，该方法利用经典的两类支持向量机算法，在统一的框架下发展了一类新的线性和非线性充分降维算法。在这项工作中，研究人员在几个方向上扩展了这一方法。首先，对经典的支持向量机算法进行了不同的扩展，以改善原方法的性能和渐近性质。其次，将该方法扩展到允许多类分类的算法。第三，研究人员基于机器学习文献中的思想，为足够的维度技术开发了新的方法特定和无方法的变量选择方法。最后，基于新的方法开发了新的降维空间定阶算法。计算机科学的最新进展提高了计算机的计算能力，从而提高了高效存储大数据集的能力。因此，为了有效地分析生物学、气象学、遗传学和经济学等许多科学中的大数据集，需要新的技术来降低数据集的维度。这项工作创建了新的算法来有效地降低大数据集的维度，无论是对于变量之间的线性关系还是非线性关系。这些技术将高维回归或分类问题转化为低维问题，这有助于识别变量之间的隐藏关系。正在开发的方法将是科学家处理大数据集的有效工具，它将为统计学家开辟新的研究前沿，在降维领域提出新的想法。

The investigator develops new methodologies for sufficient dimension reduction both for linear and nonlinear dimension reduction problems. A method developed recently by the investigator and his collaborators utilizes classic two-class Support Vector Machine algorithms to develop a new class of algorithms for linear and nonlinear sufficient dimension reduction under a unified framework. In this work the investigator extends this methodology in several directions. First, different extensions of the classic Support Vector Machine algorithms are used to improve the performance and the asymptotic properties of the original method. Second, the method is extended to algorithms that allow for multi-class classification. Third, the investigator develops new method-specific and method-free variable selection methodologies for sufficient dimension techniques based on ideas in the machine learning literature. Finally, new algorithms for the order determination of the dimension reduction space based on the new methodology are developed.Recent advancements in computer science have increased computer power and, subsequently, the capability of storing large datasets efficiently. Thus, to analyze large datasets effectively in many sciences, like Biology, Meteorology, Genetics and Economics, new techniques are needed to reduce the dimensionality of the datasets. This work creates new algorithms to reduce the dimensionality of large datasets effectively, for both linear or nonlinear relationships between variables. These techniques transform a high-dimensional regression or classification problem to a lower-dimensional one, which helps to identify hidden relationships among variables. The methodology being developed will be an efficient tool for scientists working with large datasets, and it will open new research frontiers to statisticians to develop new ideas in the area of dimension reduction.