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Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the…

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…

We present two fully probabilistic Euler schemes, one explicit and one implicit, for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of super-linear growth and random initial condition. We provide a…

Bobkov, Houdr\'e, and the last author [2000] introduced a Poincar\'e-type functional parameter, $\lambda_\infty$, of a graph and related it to connectivity of the graph via Cheeger-type inequalities. A work by the second author,…

The rise of graph representation learning as the primary solution for many different network science tasks led to a surge of interest in the fairness of this family of methods. Link prediction, in particular, has a substantial social…

One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…

Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a…

We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…

Attributed graph clustering, which aims to group the nodes of an attributed graph into disjoint clusters, has made promising advancements in recent years. However, most existing methods face challenges when applied to large graphs due to…

Deep generative models (DGMs) have achieved remarkable advances. Semi-supervised variational auto-encoders (SVAE) as a classical DGM offer a principled framework to effectively generalize from small labelled data to large unlabelled ones,…

Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…

Graph anomaly detection has gained significant attention across various domains, particularly in critical applications like fraud detection in e-commerce platforms and insider threat detection in cybersecurity. Usually, these data are…

We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…

We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…

The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With…

Existing dehazing methods deal with real-world haze images with difficulty, especially scenes with thick haze. One of the main reasons is the lack of real-world paired data and robust priors. To avoid the costly collection of paired hazy…

Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current methods often fall short in capturing longer ranges, hierarchical structures, or community structures, which are common in various graphs…

Graph autoencoders (GAEs), as a kind of generative self-supervised learning approach, have shown great potential in recent years. GAEs typically rely on distance-based criteria, such as mean-square-error (MSE), to reconstruct the input…

Graph-based learning is a cornerstone for analyzing structured data, with node classification as a central task. However, in many real-world graphs, nodes lack informative feature vectors, leaving only neighborhood connectivity and class…

Classic variational autoencoders are used to learn complex data distributions, that are built on standard function approximators. Especially, VAE has shown promise on a lot of complex task. In this paper, a new autoencoder model -…