Geometric Learning on Graph Structured Data

Graphs provide a ubiquitous and universal data structure that can be applied in many domains such as social networks, biology, chemistry, physics, and computer science. In this thesis we focus on two fundamental paradigms in graph learning: representation learning and similarity learning over graph-structured data. Graph representation learning aims to learn embeddings for nodes by integrating topological and feature information of a graph. Graph similarity learning brings into play with similarity functions that allow to compute similarity between pairs of graphs in a vector space. We address several challenging issues in these two paradigms, designing powerful, yet efficient and theoretical guaranteed machine learning models that can leverage rich topological structural properties of real-world graphs. This thesis is structured into two parts. In the first part of the thesis, we will present how to develop powerful Graph Neural Networks (GNNs) for graph representation learning from three different perspectives: (1) spatial GNNs, (2) spectral GNNs, and (3) diffusion GNNs. We will discuss the model architecture, representational power, and convergence properties of these GNN models. Specifically, we first study how to develop expressive, yet efficient and simple message-passing aggregation schemes that can go beyond the Weisfeiler-Leman test (1-WL). We propose a generalized message-passing framework by incorporating graph structural properties into an aggregation scheme. Then, we introduce a new local isomorphism hierarchy on neighborhood subgraphs. We further develop a novel neural model, namely GraphSNN, and theoretically prove that this model is more expressive than the 1-WL test. After that, we study how to build an effective and efficient graph convolution model with spectral graph filters. In this study, we propose a spectral GNN model, called DFNets, which incorporates a novel spectral graph filter, namely feedback-looped filters. As a result, this model can provide better localization on neighborhood while achieving fast convergence and linear memory requirements. Finally, we study how to capture the rich topological information of a graph using graph diffusion. We propose a novel GNN architecture with dynamic PageRank, based on a learnable transition matrix. We explore two variants of this GNN architecture: forward-euler solution and invariable feature solution, and theoretically prove that our forward-euler GNN architecture is guaranteed with the convergence to a stationary distribution. In the second part of this thesis, we will introduce a new optimal transport distance metric on graphs in a regularized learning framework for graph kernels. This optimal transport distance metric can preserve both local and global structures between graphs during the transport, in addition to preserving features and their local variations. Furthermore, we propose two strongly convex regularization terms to theoretically guarantee the convergence and numerical stability in finding an optimal assignment between graphs. One regularization term is used to regularize a Wasserstein distance between graphs in the same ground space. This helps to preserve the local clustering structure on graphs by relaxing the optimal transport problem to be a cluster-to-cluster assignment between locally connected vertices. The other regularization term is used to regularize a Gromov-Wasserstein distance between graphs across different ground spaces based on degree-entropy KL divergence. This helps to improve the matching robustness of an optimal alignment to preserve the global connectivity structure of graphs. We have evaluated our optimal transport-based graph kernel using different benchmark tasks. The experimental results show that our models considerably outperform all the state-of-the-art methods in all benchmark tasks

A randomized, double-blind, placebo-controlled trial on the role of preemptive analgesia with acetaminophen [paracetamol] in reducing headache following electroconvulsive therapy [ECT]

Abstract Background Electroconvulsive therapy (ECT) is a safe and efficient treatment for several severe psychiatric disorders, but its use is limited by side effects. Post-ECT headache is one of the commonest side effects. Preemptive analgesia is effective in post-surgical pain management. The most commonly used analgesic is acetaminophen (paracetamol). However, acetaminophen as a preemptive analgesic for post-ECT headache has not been studied adequately. This study was conducted to compare the incidence and severity of post-ECT headache in patients who were administered acetaminophen pre-ECT with a placebo group. Methods This study was a randomised, double-blind, placebo-controlled trial. Sixty-three patients received 1 g acetaminophen and 63 patients received a placebo identical to acetaminophen. The incidence and severity of headache 2 h before and after ECT were compared between placebo and acetaminophen groups. The severity was measured using a visual analog scale. Generalised linear models were used to evaluate variables associated with post ECT headache. Results Demographic and clinical variables of placebo and acetaminophen groups were comparable except for the energy level used to induce a seizure. Higher proportion of the placebo group (71.4%) experienced post-ECT headache when compared to the acetaminophen group (p < 0.001). The median pain score for headache was 0 (Inter quartile range: 0–2) in acetaminophen group whereas the score was 2 (IQR: 0–4) in placebo group (P < 0.001). Model fitting showed that the administration of acetaminophen is associated with less post-ECT headache (odds ratio = 0.23, 95% CI: 0.11–0.48, P < 0.001). Conclusion A significant reduction was seen in both the incidence and severity of post-ECT headache with preemptive analgesia with acetaminophen. Trial registration Ethical approval was granted by an Ethic review committee, University of Kelaniya, Sri Lanka (P/166/10/2015) and the trial was registered in the Sri Lanka Clinical Trials Registry ( SLCTR/2015/27 )