项目名称: 高维数据的图模型学习与统计推断
项目编号: No.11201479
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 尹建鑫
作者单位: 中国人民大学
项目金额: 22万元
中文摘要: 研究在高维数据情形下,图模型的结构学习及相关统计推断问题。在高维情形下,当均值受到另一组高维协变量影响时,我们用似然函数加惩罚的方法来估计无向图的结构。用惩罚似然方法研究array-型数据的无向图模型估计。对于高维有向图(DAG)采用基于约束的学习方法,其中关键的步骤是高维条件独立性检验。我们分别研究在有分布假定和无分布假定情况下的高维条件独立性检验。传统的检验统计量在高维情形下一般是无法工作的。需要提出在一定合理假定下(比如稀疏性或者结构上的假定)新的统计量和检验方法。研究所提出的检验的渐近相合性、功效以及最优性。条件独立性的推断结论本身也有意义。进一步该推断结果可以嵌入到有向无环图(DAG)整体或者部分的结构学习算法中去,比如PC,IC,递归, 或者局部学图算法。对于学得的高维图(无向或有向),我们评价在相依的多重检验下的整体错误发现率(FDR)等相关置信度度量,并研究它们的极限性质。
中文关键词: 图模型;高维数据;惩罚似然;马尔科夫毯子;自适应设计
英文摘要: We study the structral learning for graphical models and do related statistical inference under high-dimensional data setting. In the high-dimensional setting, when the mean vector is affected by another set of high dimensional covariates, we use the penalized likelihood method to estimate the structure for undirected graphs. The penalized likelihood method will also be applied to array-type of data to learn the undirected graphs. Undirected graphs can serve as the basis for the directed graphs' learning. Toward the structural learning for directed graphs, we use the constraint-based method in which the key is to test the conditional independence among two variables given a conditional variable set or two sets of variables given a conditional set in the high dimensional case. We consider both situations of with and without distributional assumptions. Traditional test statistics fail to work under such settings and we need new test statistics and method(under reasonable assumption like sparcity or structral assumption). We will study the consistency, efficiency and optimality of the proposed test. The conclusion of such test has an independent interest of itself. Furthermore, these inference conclusions can be plugged into many DAG learning algrithms(global or local) like PC, IC, Recursive and POLSL etc. For the
英文关键词: Graphical model;High Dimensional data;Penalized likelihood;Markov Blanket;Adaptive Design