Gaussian processes on graphs

In the ever-growing field of machine learning research, the use of graphs has recently gathered significant interest for modelling on data with relational structures. Graphs and network-based data now exist ubiquitously in the real world, with examples including social networks, transportation, financial exchanges, and brain networks. Therefore, developing models on graphs is essential to allow users to understand and predict the complex nature observed in everyday phenomena. Currently, there is an abundance of literature on graph neural networks, but limited options are available that are probabilistic and Bayesian. In addressing this issue, we develop a series of Gaussian processes (GPs) for graph data in this thesis. Building GPs on graphs is now more feasible thanks to the emergence of graph signal processing, providing us with the tools to handle graph-structured information and smoothness modelling. The first problem we tackle is predicting the evolution of signals with a multi-output Gaussian process. We use kernels defined from the graph Laplacian with learnable spectral filters to predict with the smoothness level that matches the data. We then turn our focus to semi-supervised classification, designing three models for this task each emphasizing on a particular approach: multi-scale modelling, transductive learning, and sheaf modelling. The first approach provides a novel utilization of wavelets on graphs to fully exploit their ability to capture multi-scale properties in the data. Next, we present a unified definition of kernels on graphs with transductive properties, aiming to utilize the distribution of the full dataset to better inform the prediction. This naturally suits semi-supervised problems on graphs where training and testing nodes are generally connected and available at the same time. Finally, we introduce sheaves as a higher order representation of graphs, to design GPs with stronger separation power by learning additional topological structures. Collectively, this thesis represents not only a valuable contribution to the study of GPs for discrete and non-Euclidean data, but also useful alternatives to the more broadly used graph neural networks

Gaussian processes on graphs via spectral kernel learning

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible polynomial function in the graph spectral domain. Unlike most existing approaches, we propose to learn such a spectral kernel defined on a discrete space. In addition, this kernel has the interpretability of graph filtering achieved by a bespoke maximum likelihood learning algorithm that enforces the positivity of the spectrum. We demonstrate the interpretability of the model through synthetic experiments from which we show various ground truth spectral filters can be accurately recovered, and the adaptability translates to improved predictive performances compared to the baselines on real-world graph data of various characteristics

Graph classification Gaussian processes via spectral features

Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design two variants of Gaussian process models for graph classification. The first variant uses spectral features based on the distribution of energy of a node feature signal over the spectrum of the graph. We show that even such a simple approach, having no learned parameters, can yield competitive performance compared to strong neural network and graph kernel baselines. A second, more sophisticated variant is designed to capture multi-scale and localised patterns in the graph by learning spectral graph wavelet filters, obtaining improved performance on synthetic and real-world data sets. Finally, we show that both models produce well calibrated uncertainty estimates, enabling reliable decision making based on the model predictions

Transductive Kernels for Gaussian Processes on Graphs

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantages using synthetic data where the distribution of the whole graph can inform the pattern of the labels. Finally, by utilizing a flexible polynomial of the graph Laplacian within the kernel, the model also performed effectively in semi-supervised classification on graphs of various levels of homophily

Graph Classification Gaussian Processes via Spectral Features

Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design two variants of Gaussian process models for graph classification. The first variant uses spectral features based on the distribution of energy of a node feature signal over the spectrum of the graph. We show that even such a simple approach, having no learned parameters, can yield competitive performance compared to strong neural network and graph kernel baselines. A second, more sophisticated variant is designed to capture multi-scale and localised patterns in the graph by learning spectral graph wavelet filters, obtaining improved performance on synthetic and real-world data sets. Finally, we show that both models produce well calibrated uncertainty estimates, enabling reliable decision making based on the model predictions

3-(4-{3,3,4,4,5,5-Hexafluoro-2-[5-(3-methoxy­phen­yl)-2-methyl-3-thien­yl]cyclo­pent-1-en­yl}-5-methyl-2-thien­yl)benzonitrile

The title compound, C29H19F6NOS2, is a new unsymmetrical photochromic diarylethene derivative with different meta-phenyl substituents. The distance between the two reactive (i.e. can be irradiated to form a new chemical bond) C atoms is 3.501 (4) Å; the dihedral angles between the mean plane of the main central cyclo­pentene ring and the thio­phene rings are 47.7 (5) and 45.1 (2)°, and those between the thio­phene rings and the adjacent benzene rings are 29.4 (2) and 28.4 (3)°. The three C atoms and the F atoms of hexa­fuorocyclo­pentene ring are disordered over two positions, with site-occupancy factors of 0.751 (4) and 0.249 (4)

MicroRNA-29a-3p Downregulation Causes Gab1 Upregulation to Promote Glioma Cell Proliferation

Background/Aims: Glioma causes significant human mortalities annually. Molecularly-targeted therapy is a focus of glioma research. Methods: Grb2-associated binding 1 (Gab1) expression and microRNA-29a-3p (“miR-29a-3p”) expression in human glioma cells and tissues were tested by Western blotting assay and qRT-PCR assay. shRNA/siRNA strategy was applied to silence Gab1 in human glioma cells. miR-29a or anti-sense miR-29a construct was transfected to human glioma cells. Cell proliferation was tested by BrdU ELISA assay and cell counting assay. Results: We show that expression of Gab1 was significantly elevated in human glioma tissues and cells, which correlated with downregulation of its putative microRNA: miR-29a-3p. In A172 glioma cells and primary human glioma cells, Gab1 shRNA/siRNA inhibited Akt-Erk activation and cell proliferation. Forced-expression of miR-29a-3p downregulated Gab1, inhibiting glioma cell proliferation, whereas miR-29a-3p was in-effective on cell proliferation in Gab1-silenced A172 cells. Furthermore, introduction of a 3’-untranslated region (3’-UTR) mutant Gab1 (UTR-G160A) blocked miR-29a-3p-induced inhibition on Akt signaling and A172 cell proliferation. Conclusions: miR-29a-3p downregulation leads to Gab1 upregulation to promote glioma cell proliferation

Global trends and frontiers in research on exercise training for heart failure: a bibliometric analysis from 2002 to 2022

BackgroundHeart failure is a common cardiovascular disease that imposes a heavy clinical and economic burden worldwide. Previous research and guidelines have supported exercise training as a safe, effective, and cost-efficient treatment to intervene in heart failure. The aim of this study was to analyze the global published literature in the field of exercise training for heart failure from 2002 to 2022, and to identify hot spots and frontiers within this research field.MethodsBibliometric information on literature on the topic of exercise training for heart failure published between 2002 and 2022 was searched and collected in the Web of Science Core Collection. CiteSpace 6.1.R6 (Basic) and VOSviewer (1.6.18) were applied to perform bibliometric and knowledge mapping visualization analyses.ResultsA total of 2017 documents were retrieved, with an upward-stable trend in the field of exercise training for heart failure. The US authors were in the first place with 667 documents (33.07%), followed by Brazilian authors (248, 12.30%) and Italian authors (182, 9.02%). The Universidade de São Paulo in Brazil was the institution with the highest number of publications (130, 6.45%). The top 5 active authors were all from the USA, with Christopher Michael O'Connor and William Erle Kraus publishing the most documents (51, 2.53%). The International Journal of Cardiology (83, 4.12%) and the Journal of Applied Physiology (78, 3.87%) were the two most popular journals, while Cardiac Cardiovascular Systems (983, 48.74%) and Physiology (299, 14.82%) were the two most popular categories. Based on the results of keyword co-occurrence network and co-cited reference network, the hot spots and frontiers of research in the field of exercise training for heart failure were high-intensity interval training, behaviour therapy, heart failure with preserved ejection fraction, and systematic reviews.ConclusionThe field of exercise training for heart failure has experienced two decades of steady and rapid development, and the findings of this bibliometric analysis provide ideas and references for relevant stakeholders such as subsequent researchers for further exploration