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Foundation models, such as Large Language Models (LLMs) or Large Vision Models (LVMs), have emerged as one of the most powerful tools in the respective fields. However, unlike text and image data, graph data do not have a definitive…

Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs…

Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…

Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely…

Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer…

Training graph neural networks on large datasets has long been a challenge. Traditional approaches include efficiently representing the whole graph in-memory, designing parameter efficient and sampling-based models, and graph partitioning…

Graph Neural Networks (GNN) have shown a strong potential to be integrated into commercial products for network control and management. Early works using GNN have demonstrated an unprecedented capability to learn from different network…

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…

Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs). Our framework is based on gating the output of GNN layers with a mechanism for multi-rate flow of message passing…

Although a number of studies have explored deep learning in neuroscience, the application of these algorithms to neural systems on a microscopic scale, i.e. parameters relevant to lower scales of organization, remains relatively novel.…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…