We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous approaches either fail to encode the edge directionality or their encodings cannot be generalized across tasks. With our simple \emph{alternating random walk} strategy, we generate role specific vertex neighborhoods and train node embeddings in their corresponding source/target roles while fully exploiting the semantics of directed graphs. We also unearth the limitations of evaluations on directed graphs in previous works and propose a clear strategy for evaluating link prediction and graph reconstruction in directed graphs. We conduct extensive experiments to showcase our effectiveness on several real-world datasets on link prediction, node classification and graph reconstruction tasks. We show that the embeddings from our approach are indeed robust, generalizable and well performing across multiple kinds of tasks and graphs. We show that we consistently outperform all baselines for node classification task. In addition to providing a theoretical interpretation of our method we also show that we are considerably more robust than the other directed graph approaches.
This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture topological features of any arbitrary graph, and rank edge sets by different stages according to their contribution to topology reconstruction. Moreover, in addition to acting as an indicator of graph reconstruction, we find that these stages can also preserve important topological features in a graph.
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly identify the support of any multivariate normal distribution as a function of model parameters. For a model defined on a sparse graph with $p$ nodes, a maximum degree $d$ and minimum normalized edge strength $\kappa$, this necessary number of samples scales at least as $d \log p/\kappa^2$. The sample complexity requirements of existing methods for perfect graph reconstruction exhibit dependency on additional parameters that do not enter in the lower bound. The question of whether the lower bound is tight and achievable by a polynomial time algorithm remains open. In this paper, we constructively answer this question and propose an algorithm, termed DICE, whose sample complexity matches the information-theoretic lower bound up to a universal constant factor. We also propose a related algorithm SLICE that has a slightly higher sample complexity, but can be implemented as a mixed integer quadratic program which makes it attractive in practice. Importantly, SLICE retains a critical advantage of DICE in that its sample complexity only depends on quantities present in the information theoretic lower bound. We anticipate that this result will stimulate future search of computationally efficient sample-optimal algorithms.