Time Series Prediction for Graphs in Kernel and Dissimilarity Spaces
This work addresses the need for predictive techniques that handle evolving graph structures in fields like distributed computing and social networks, though it is incremental as it applies existing regression methods to a new graph prediction task.
The paper tackled the problem of predicting future states of entire graphs, rather than single edges or nodes, by framing time series prediction as a regression problem using dissimilarity- or kernel-based techniques like kernel regression and Gaussian process regression. They found that kernel regression sufficed for theoretical models, but Gaussian process regression significantly reduced prediction error on real-world data from intelligent tutoring systems.
Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of nodes or edges. Predicting such changes within graphs can be expected to yield important insight with respect to the underlying dynamics, e.g. with respect to user behaviour. However, predictive techniques in the past have almost exclusively focused on single edges or nodes. In this contribution, we attempt to predict the future state of a graph as a whole. We propose to phrase time series prediction as a regression problem and apply dissimilarity- or kernel-based regression techniques, such as 1-nearest neighbor, kernel regression and Gaussian process regression, which can be applied to graphs via graph kernels. The output of the regression is a point embedded in a pseudo-Euclidean space, which can be analyzed using subsequent dissimilarity- or kernel-based processing methods. We discuss strategies to speed up Gaussian Processes regression from cubic to linear time and evaluate our approach on two well-established theoretical models of graph evolution as well as two real data sets from the domain of intelligent tutoring systems. We find that simple regression methods, such as kernel regression, are sufficient to capture the dynamics in the theoretical models, but that Gaussian process regression significantly improves the prediction error for real-world data.