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Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically…

This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…

The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…

Statistical analysis of network data has attracted considerable attention in recent years, due to the rapid advancement of well-trained network models and the accessibility of large public network datasets. In this article, we propose a…

Model-based optimization, in concert with conventional black-box methods, can quickly solve large-scale combinatorial problems. Recently, quantum-inspired modeling schemes based on tensor networks have been developed which have the…

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…

The prediction of configurational disorder properties, such as configurational entropy and order-disorder phase transition temperature, of compound materials relies on efficient and accurate evaluations of configurational energies. Previous…

Information is extracted from large and sparse data sets organized as 3-mode tensors. Two methods are described, based on best rank-(2,2,2) and rank-(2,2,1) approximation of the tensor. The first method can be considered as a generalization…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Text coherence is a fundamental problem in natural language generation and understanding. Organizing sentences into an order that maximizes coherence is known as sentence ordering. This paper is proposing a new approach based on the graph…

Network tomography is a crucial problem in network monitoring, where the observable path performance metric values are used to infer the unobserved ones, making it essential for tasks such as route selection, fault diagnosis, and traffic…