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

研究人员为来自生物、医学和科学研究前沿的高维数据开发新的正则化和优化技术。提出了四个相关的研究课题以供研究。首先，提出了神经科学中对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，以响应时变刺激。其次，研究人员开发了高维空间曲线的基于曲率的形状分析，应用于比较生物形状、检测显示形状差异的关键解剖区域以及对功能数据对象进行分类。第三，研究了一般损失函数下正则化参数估计和非参数估计的统一理论和方法。第四，结合支持向量机和传统Logistic回归的优点，提出了一种高维伪Logistic回归和分类方法，生物信息学、环境、金融市场、信号和图像处理等领域产生的高维数据集和数据流对传统统计方法提出了许多挑战。该提案的一个主要目标是在方法和理论上为分析高维数据(如时空fMRI脑图像、功能数据对象和基因表达谱)中的重要和具有挑战性的正则化方法做出贡献。这些新的发展使科学家能够通过有效的降维和更高的可解释性来分析高维数据。此外，研究人员将把新的计算工具和数学理论与科学和工程中的工具和数学理论结合起来。这些进展的传播将促进新的知识发现和审慎的政策制定，并加强跨学科合作。这项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达到教育目的，并有利于本科生、研究生和代表性不足的少数群体的培训和学习。

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.