Related papers: Gaussian process regression with Sliced Wasserstei…
Self supervised learning (SSL) is a machine learning paradigm where models learn to understand the underlying structure of data without explicit supervision from labeled samples. The acquired representations from SSL have demonstrated…
The isomorphism problem is a fundamental problem in network analysis, which involves capturing both low-order and high-order structural information. In terms of extracting low-order structural information, graph isomorphism algorithms…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive…
The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with…
Missing node attributes is a common problem in real-world graphs. Graph neural networks have been demonstrated power in graph representation learning while their performance is affected by the completeness of graph information. Most of them…
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
For semi-supervised learning on graphs, we study how initial kernels in a supervised learning regime can be augmented with additional information from known priors or from unsupervised learning outputs. These augmented kernels are…
Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive…
Graph convolutional networks gain remarkable success in semi-supervised learning on graph structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph…
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…
When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…
Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
Graph kernels are historically the most widely-used technique for graph classification tasks. However, these methods suffer from limited performance because of the hand-crafted combinatorial features of graphs. In recent years, graph neural…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…