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The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…

We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP). For solving the MCP penalized graphical model, we design an inexact proximal difference-of-convex algorithm…

The rise of digital ecosystems has exposed the financial sector to evolving abuse and criminal tactics that share operational knowledge and techniques both within and across different environments (fiat-based, crypto-assets, etc.).…

Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…

A long-standing goal in deep learning has been to characterize the learning behavior of black-box models in a more interpretable manner. For graph neural networks (GNNs), considerable advances have been made in formalizing what functions…

Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective…

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex…

We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…

Artificial intelligence for graphs has achieved remarkable success in modeling complex systems, ranging from dynamic networks in biology to interacting particle systems in physics. However, the increasingly heterogeneous graph datasets call…

Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…

Recent work in graph neural networks (GNNs) has led to improvements in molecular activity and property prediction tasks. Unfortunately, GNNs often fail to capture the relative importance of interactions between molecular substructures, in…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…

Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…

Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience…

Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…

The ability of Graph Neural Networks (GNNs) to capture long-range and global topology information is limited by the scope of conventional graph Laplacian, leading to unsatisfactory performance on some datasets, particularly on heterophilic…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…