Estimating the structure of a Bayesian network, in the form of a directed acyclic graph (DAG), from observational data is a statistically and computationally hard problem with essential applications in areas such as causal discovery. Bayesian approaches are a promising direction for solving this task, as they allow for uncertainty quantification and deal with well-known identifiability issues. From a probabilistic inference perspective, the main challenges are (i) representing distributions over graphs that satisfy the DAG constraint and (ii) estimating a posterior over the underlying combinatorial space. We propose an approach that addresses these challenges by formulating a joint distribution on an augmented space of DAGs and permutations. We carry out posterior estimation via variational inference, where we exploit continuous relaxations of discrete distributions. We show that our approach can outperform competitive Bayesian and non-Bayesian benchmarks on a range of synthetic and real datasets.

We propose a Bayesian approach to spectral graph convolutional networks (GCNs) where the graph parameters are considered as random variables. We develop an inference algorithm to estimate the posterior over these parameters and use it to incorporate prior information that is not naturally considered by standard GCN. The key to our approach is to define a smooth posterior parameterization over the adjacency matrix characterizing the graph, which we estimate via stochastic variational inference. Our experiments show that we can outperform standard GCN methods in the task of semi-supervised classification in noisy-graph regimes.

This paper presents multi-goal planning for an autonomous blasthole drill used in open pit mining operations. Given a blasthole pattern to be drilled and constraints on the vehicle's motion and orientation when drilling, we wish to compute the best order in which to drill the given pattern. Blasthole pattern drilling is an asymmetric Traveling Salesman Problem with precedence constraints specifying that some holes must be drilled before others. We wish to find the minimum cost tour according to criteria that minimize the distance travelled satisfying the precedence and vehicle motion constraints. We present an iterative method for solving the blasthole sequencing problem using the combination of a Genetic Algorithm and motion planning simulations that we use to determine the true cost of travel between any two holes.