Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the performance has been impressive, the current implementations have limited capability to incorporate uncertainty in the graph structure. Almost all GCNNs process a graph as though it is a ground-truth depiction of the relationship between nodes, but often the graphs employed in applications are themselves derived from noisy data or modelling assumptions. Spurious edges may be included; other edges may be missing between nodes that have very strong relationships. In this paper we adopt a Bayesian approach, viewing the observed graph as a realization from a parametric family of random graphs. We then target inference of the joint posterior of the random graph parameters and the node (or graph) labels. We present the Bayesian GCNN framework and develop an iterative learning procedure for the case of assortative mixed-membership stochastic block models. We present the results of experiments that demonstrate that the Bayesian formulation can provide better performance when there are very few labels available during the training process.

Sequential state estimation in non-linear and non-Gaussian state spaces has a wide range of applications in statistics and signal processing. One of the most effective non-linear filtering approaches, particle filtering, suffers from weight degeneracy in high-dimensional filtering scenarios. Several avenues have been pursued to address high-dimensionality. Among these, particle flow particle filters construct effective proposal distributions by using invertible flow to migrate particles continuously from the prior distribution to the posterior, and sequential Markov chain Monte Carlo (SMCMC) methods use a Metropolis-Hastings (MH) accept-reject approach to improve filtering performance. In this paper, we propose to combine the strengths of invertible particle flow and SMCMC by constructing a composite Metropolis-Hastings (MH) kernel within the SMCMC framework using invertible particle flow. In addition, we propose a Gaussian mixture model (GMM)-based particle flow algorithm to construct effective MH kernels for multi-modal distributions. Simulation results show that for high-dimensional state estimation example problems the proposed kernels significantly increase the acceptance rate with minimal additional computational overhead and improve estimation accuracy compared with state-of-the-art filtering algorithms.Y. Li is with the

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