The need for mining causality, beyond mere statistical correlations, for real world problems has been recognized widely. Many of these applications naturally involve temporal data, which raises the challenge of how best to leverage the temporal information for causal modeling. Recently graphical modeling with the concept of “Granger causality”, based on the intuition that a cause helps predict its effects in the future, has gained attention in many domains involving time series data analysis. With the surge of interest in model selection methodologies for regression, such as the Lasso, as practical alternatives to solving structural learning of graphical models, the question arises whether and how to combine these two notions into a practically viable approach for temporal causal modeling. In this paper, we examine a host of related

The ability to predict linkages among data objects is central to many data mining tasks, such as product recommendation and social network analysis. A substantial literature has been devoted to the link prediction problem either as an implicitly embedded problem in specific applications or as a generic data mining task. This literature has mostly adopted a static graph representation where a snapshot of the network is analyzed to predict hidden or future links. However, this representation is only appropriate to investigate whether certain link will ever occur or not and does not apply to many applications for which the prediction of the repeated link occurrences are of main interest (e.g., communication network surveillance). In this paper, we introduce the time series link prediction problem, taking into consideration temporal evolutions of link occurrences to predict link occurrence probabilities at a particular time. Using the Enron email data and highenergy particle physics literature coauthorship data we have demonstrated that time series models of single link occurrences achieved comparable link prediction performance with commonly used static graph link prediction algorithms. Furthermore, combination of static graph link prediction algorithms and time series model produced significantly improved predictions than static graph link prediction methods, demonstrating the great potential of integrated methods that exploit both inter-link structural dependencies and intra-link temporal dependencies. Key words: analysis of algorithms; communication networks; link prediction; statistical analysis; time series analysis. 1.