CAREER: Sparse Modeling Driven by Large-Scale Genomic Data

在生物学和基因组学中，大量高维数据频繁出现。正则化和稀疏性是对此类数据建模和提取信息的关键组成部分。稀疏建模方法（如Lasso）的广泛成功促进了该领域的快速发展。然而，现有的方法大多是在线性模型和广义线性模型的框架下发展起来的。基因组数据中的复杂结构需要在现有方法之外进一步发展。为此，提出了基于大规模基因表达数据、蛋白质结合数据和DNA序列数据驱动的三种新型稀疏建模方法，这些方法具有复杂的模型结构。第一种方法的动机是建立蛋白质结合和基因表达之间的关系，在决策树的终端节点上构建线性回归模型。决策树根据预测因子将总体划分为子组。每个子群在响应和预测因子之间都有自己的稀疏线性回归模型。两种类型的正则化，一种是关于回归系数的，另一种是关于树的大小的，用来鼓励稀疏性。第二种方法是通过对两个紧密聚类之间以及紧密聚类与空聚类之间分组参数的差异进行惩罚来构建基因表达数据的紧密聚类。为了使正则似然函数最大化，提出了分块坐标下降与多数化相结合的方法。第三种方法由基序查找问题驱动，旨在发现序列模式。字典模型用于将句子划分为表示序列模式的单词和单个字母。提出了一种利用Kullback-Leibler散度对词的积多项模型进行正则化的新方法，该方法可以在估计单元概率时达到稀疏性。这种正则化被用来构造一个只包含少量单词的稀疏字典。提出了一种用于参数估计和解路径构造的广义电磁算法。由于大规模高维数据的有效分析在许多科学和工程领域都是至关重要的，因此提出的研究是当前的重大兴趣。特别是，所提出的方法已经准备好应用于基因组学和分子生物学等前沿研究领域，这些领域已经不断产生大量数据集。为了加速这类应用，人们正在开发免费的计算机软件包和独立软件，供用户分析自己的数据。另一方面，该提案包含许多创新的统计方法，可能对统计和计算科学做出重大贡献。最后，通过在本科和研究生阶段开发新的和改进现有课程，将拟议的研究与教育活动相结合。

Massive and high-dimensional data arise frequently in biology and genomics. Regularization and sparsity are critical components for modeling such data and extracting information. Broad success of sparse modeling methods, such as the Lasso, has encouraged fast development in this area. However, most existing methods were developed under the frameworks of linear models and generalized linear models. The complex structures in genomic data require further development beyond existing methods. To this end, proposed are three novel sparse modeling methods with sophisticated model structures driven by large-scale gene expression data, protein binding data and DNA sequence data. The first method, motivated by modeling the relationship between protein binding and gene expression, constructs linear regression models on the terminal nodes of a decision tree. The decision tree partitions the population into subgroups according to the predictors. Each subgroup has its own sparse linear regression model between the response and the predictors. Two types of regularization, one on the regression coefficients and the other on the size of the tree, are used to encourage sparsity. The second method concerns the construction of tight clusters for gene expression data by penalizing the difference in grouped parameters between two tight clusters and between a tight cluster and the null cluster. Block-wise coordinate descent in conjunction with majorization is developed to maximize the regularized likelihood function. The third method, motivated by the motif finding problem, aims at sequence pattern discovery. A dictionary model is used to partition a sentence into words, which represent sequence patterns, and single letters. A novel regularization through the Kullback-Leibler divergence is developed for the product-multinomial model for words, which can achieve sparsity in estimating the cell probabilities. This regularization is used to construct a sparse dictionary that contains only a small number of words. A generalized EM algorithm is proposed for parameter estimation and solution path construction.As efficient analysis of large-scale high-dimensional data is critical in many fields of science and engineering, the proposed research is of great current interest. Particularly, the proposed methods are ready for applications to front-edge research areas in genomics and molecular biology, where massive data sets have been continuously generated. To accelerate such applications, free computer packages and self-contained software are being developed for users to analyze their own data. On the other hand, this proposal contains many innovative statistical methodologies that may contribute significantly to statistics and computational sciences. Finally, the proposed research is integrated with educational activities by developing new and improving existing courses at both undergraduate and graduate levels.