Ruan Ning, Jin Ruoming, Lee Victor E, Huang Kun
Department of Computer Science, Kent State University, Kent, OH 44242.
Proc IEEE Int Conf Data Min. 2009 Dec 6;2009:447-456. doi: 10.1109/ICDM.2009.67.
Temporal causal modeling can be used to recover the causal structure among a group of relevant time series variables. Several methods have been developed to explicitly construct temporal causal graphical models. However, how to best understand and conceptualize these complicated causal relationships is still an open problem. In this paper, we propose a decomposition approach to simplify the temporal graphical model. Our method clusters time series variables into groups such that strong interactions appear among the variables within each group and weak (or no) interactions exist for cross-group variable pairs. Specifically, we formulate the clustering problem for temporal graphical models as a regression-coefficient sparsification problem and define an interesting objective function which balances the model prediction power and its cluster structure. We introduce an iterative optimization approach utilizing the Quasi-Newton method and generalized ridge regression to minimize the objective function and to produce a clustered temporal graphical model. We also present a novel optimization procedure utilizing a graph theoretical tool based on the maximum weight independent set problem to speed up the Quasi-Newton method for a large number of variables. Finally, our detailed experimental study on both synthetic and real datasets demonstrates the effectiveness of our methods.
时态因果建模可用于恢复一组相关时间序列变量之间的因果结构。已经开发了几种方法来明确构建时态因果图形模型。然而，如何最好地理解和概念化这些复杂的因果关系仍然是一个悬而未决的问题。在本文中，我们提出了一种分解方法来简化时态图形模型。我们的方法将时间序列变量聚类成组，使得每组内的变量之间出现强相互作用，而跨组变量对之间存在弱（或无）相互作用。具体来说，我们将时态图形模型的聚类问题表述为回归系数稀疏化问题，并定义一个有趣的目标函数，该函数平衡模型预测能力及其聚类结构。我们引入一种迭代优化方法，利用拟牛顿法和广义岭回归来最小化目标函数并生成聚类时态图形模型。我们还提出了一种新颖的优化过程，利用基于最大权重独立集问题的图论工具来加速针对大量变量的拟牛顿法。最后，我们对合成数据集和真实数据集进行的详细实验研究证明了我们方法的有效性。
