Mark Cheung

Mark Cheung, John Shi, Lavender Yao Jiang et al.

Graph convolutional neural networks (GCNNs) are a powerful extension of deep learning techniques to graph-structured data problems. We empirically evaluate several pooling methods for GCNNs, and combinations of those graph pooling methods with three different architectures: GCN, TAGCN, and GraphSAGE. We confirm that graph pooling, especially DiffPool, improves classification accuracy on popular graph classification datasets and find that, on average, TAGCN achieves comparable or better accuracy than GCN and GraphSAGE, particularly for datasets with larger and sparser graph structures.

Abhinav Maurya, Mark Cheung

Gaussian graphical models (GGMs) are probabilistic tools of choice for analyzing conditional dependencies between variables in complex systems. Finding changepoints in the structural evolution of a GGM is therefore essential to detecting anomalies in the underlying system modeled by the GGM. In order to detect structural anomalies in a GGM, we consider the problem of estimating changes in the precision matrix of the corresponding Gaussian distribution. We take a two-step approach to solving this problem:- (i) estimating a background precision matrix using system observations from the past without any anomalies, and (ii) estimating a foreground precision matrix using a sliding temporal window during anomaly monitoring. Our primary contribution is in estimating the foreground precision using a novel contrastive inverse covariance estimation procedure. In order to accurately learn only the structural changes to the GGM, we maximize a penalized log-likelihood where the penalty is the $l_1$ norm of difference between the foreground precision being estimated and the already learned background precision. We modify the alternating direction method of multipliers (ADMM) algorithm for sparse inverse covariance estimation to perform contrastive estimation of the foreground precision matrix. Our results on simulated GGM data show significant improvement in precision and recall for detecting structural changes to the GGM, compared to a non-contrastive sliding window baseline.