Regularization and Optimization for High Dimensional Regression and Classification with Biological Applications

研究者开发新的正则化和优化技术，从生物，医学和科学研究的前沿出现的高维数据。提出了四个相互关联的研究课题。首先，提出了神经科学功能磁共振成像数据的功能稀疏推理，以便更准确地定位大脑区域对时变刺激的响应。其次，研究者开发了基于曲率的高维空间曲线形状分析，并应用于生物形状的比较、表现形状差异的关键解剖区域的检测以及功能数据对象的分类。第三，研究了一类损失函数下正则化参数估计量和非参数估计量的统一理论和方法。第四，提出了一种结合支持向量机和传统逻辑回归优点的高维伪逻辑回归分类方法。来自生物信息学、环境、金融市场、信号和图像处理的高维数据集和数据流对传统的统计方法提出了许多挑战。该提案的主要目标是为高维数据分析中的重要和具有挑战性的正则化方法做出方法和理论贡献，如时空fMRI脑图像，功能数据对象和基因表达谱。这些新的发展使科学家能够分析高维数据，有效地减少维数，提高可解释性。此外，研究者将整合新的计算工具和数学理论与那些在科学和工程。传播这些发展将促进新知识的发现和审慎的政策制定，并加强跨学科合作。该研究还将通过关于当代最先进的数据挖掘和机器学习的多学科课程服务于教育目的，并有利于本科生、研究生和未被充分代表的少数民族的培训和学习。

The investigator develops new regularization and optimization techniques for high dimensional data that arise from frontiers of biological, medical and scientific research. Four interrelated research topics are proposed for investigation. First, the functional sparse inference for functional magnetic resonance imaging data in neuroscience is proposed for more accurate localization of brain areas in response to the time-varying stimuli. Second, the investigator develops curvature-based shape analysis for high-dimensional space curves with applications to comparing biological shapes, detecting key anatomical regions which exhibit shape difference, and classifying functional data objects. Third, the investigator studies unified theory and methodology for regularized parametric and nonparametric estimators under a general class of loss functions. Fourth, a high-dimensional pseudo logistic regression and classification approach is proposed which simultaneously combines the strengths of both support vector machine and traditional logistic regression.High-dimensional data sets and streams arising from bioinformatics, environment, financial markets, and signal and image processing pose numerous challenges to conventional statistical methods. A majorgoal of the proposal is to make methodological and theoretical contributions to the important and challenging regularization approach in the analysis of high-dimensional data, like spatio-temporal fMRI brain images, functional data objects and gene expression profiles. These new developments allow scientists to analyze high-dimensional data with efficient dimension reduction and increased interpretability. In addition, the investigator will integrate new computational tools and mathematical theories with those in sciences and engineering. Dissemination of these developments will enhance new knowledge discoveries and prudentpolicy making, and strengthen interdisciplinary collaborations. The research will also serve an educational purpose through multi-disciplinary courses on the contemporary state-of-the-art data mining and machine learning, and benefit the training and learning of undergraduate, graduate students and underrepresented minorities.