Related papers: Learnable Kernel Density Estimation for Graphs and…
We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…
Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are…
For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…
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…
This paper presents a novel density estimation method for anomaly detection using density matrices (a powerful mathematical formalism from quantum mechanics) and Fourier features. The method can be seen as an efficient approximation of…
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…
Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…
Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and…
This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate…
Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of…
Recent work on graph generative models has made remarkable progress towards generating increasingly realistic graphs, as measured by global graph features such as degree distribution, density, and clustering coefficients. Deep generative…
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
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…
Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
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…