Measuring Mutual Information (MI) between high-dimensional, continuous, random variables from observed samples has wide theoretical and practical applications. Recent work, MINE (Belghazi et al. 2018), focused on estimating tight variational lower bounds of MI using neural networks, but assumed unlimited supply of samples to prevent overfitting. In real world applications, data is not always available at a surplus. In this work, we focus on improving data efficiency and propose a Data-Efficient MINE Estimator (DEMINE), by developing a relaxed predictive MI lower bound that can be estimated at higher data efficiency by orders of magnitudes. The predictive MI lower bound also enables us to develop a new meta-learning approach using task augmentation, Meta-DEMINE, to improve generalization of the network and further boost estimation accuracy empirically. With improved data-efficiency, our estimators enables statistical testing of dependency at practical dataset sizes. We demonstrate the effectiveness of our estimators on synthetic benchmarks and a real world fMRI data, with application of inter-subject correlation analysis.

We aim to better understand attention over nodes in graph neural networks and identify factors influencing its effectiveness. Motivated by insights from the work on Graph Isomorphism Networks (Xu et al., 2019), we design simple graph reasoning tasks that allow us to study attention in a controlled environment. We find that under typical conditions the effect of attention is negligible or even harmful, but under certain conditions it provides an exceptional gain in performance of more than 40% in some of our classification tasks. However, we have yet to satisfy these conditions in practice.

Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address this limitation by revisiting a particular family of spectral graph networks, Chebyshev GCNs, showing its efficacy in solving graph classification tasks with a variable graph structure and size. Chebyshev GCNs restrict graphs to have at most one edge between any pair of nodes. To this end, we propose a novel multigraph network that learns from multi-relational graphs. We model learned edges with abstract meaning and experiment with different ways to fuse the representations extracted from annotated and learned edges, achieving competitive results on a variety of chemical classification benchmarks.