Cauchy Graph Convolutional Networks

A common approach to learning Bayesian networks involves specifying an appropriately chosen family of parameterized probability density such as Gaussian. However, the distribution of most real-life data is leptokurtic and may not necessarily be best described by a Gaussian process. In this work we introduce Cauchy Graphical Models (CGM), a class of multivariate Cauchy densities that can be represented as directed acyclic graphs with arbitrary network topologies, the edges of which encode linear dependencies between random variables. We develop CGLearn, the resultant algorithm for learning the structure and Cauchy parameters based on Minimum Dispersion Criterion (MDC). Experiments using simulated datasets on benchmark network topologies demonstrate the efficacy of our approach when compared to Gaussian Graphical Models (GGM). Most Graph Convolutional Neural Networks (GCN) process input graphs as ground-truth representations of node relationships, yet these graphs are constructed based on modeling assumptions and noisy data and their use may lead to suboptimal performance on downstream prediction tasks. We propose Cauchy GCN which leverages CGM to infer graph topology that depicts latent relationships between nodes. We evaluate the effectiveness and quality of the structural graphs learned by CGM, and demonstrate that Cauchy-GCN achieves superior performance compared to widely used graph construction methods. • We propose Cauchy Graphical Models (CGM), a class of multivariate Cauchy densities that can be represented as directed acyclic graphs (DAGs) to model impulsive noise in random variables. • We introduce Minimum Dispersion Criterion (MDC), a score-based method to select the optimal DAG network of the CGM. • We conduct an extensive experimental campaign using synthetic data on benchmark Bayesian networks to validate the efficacy of our approach. • We introduce Cauchy Graph Convolutional Networks (Cauchy GCN) which leverages CGM to infer graph topology that depicts latent relationships between nodes. Our experimental results demonstrate that CGM produces quality graphs that improve the performance of GCN.