An Energy-Based View of Graph Neural Networks

Graph neural networks are a popular variant of neural networks that work with graph-structured data. In this work, we consider combining graph neural networks with the energy-based view of Grathwohl et al. (2019) with the aim of obtaining a more robust classifier. We successfully implement this framework by proposing a novel method to ensure generation over features as well as the adjacency matrix and evaluate our method against the standard graph convolutional network (GCN) architecture (Kipf & Welling (2016)). Our approach obtains comparable discriminative performance while improving robustness, opening promising new directions for future research for energy-based graph neural networks.

Graph Learning for Inverse Landscape Genetics

The problem of inferring unknown graph edges from numerical data at a graph's nodes appears in many forms across machine learning. We study a version of this problem that arises in the field of landscape genetics, where genetic similarity between populations of organisms living in a heterogeneous landscape is explained by a weighted graph that encodes the ease of dispersal through that landscape. Our main contribution is an efficient algorithm for inverse landscape genetics, which is the task of inferring this graph from measurements of genetic similarity at different locations (graph nodes). We reduced the problem to that of inferring graph edges from noisy measurements of effective resistances between graph nodes, which have been observed to correlate well with genetic similarity. Building on Hoskins et. al., we develop an efficient first-order optimization method for solving this problem. Despite its non-convex nature, extensive experiments on synthetic and real genetic data establish that our method provides fast and reliable convergence, significantly outperforming existing heuristics used in the field.