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Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are…
Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both unnormalized and normalized Laplacians in…
Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…
We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single}…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…
Phase diagrams serve as a highly informative tool for materials design, encapsulating information about the phases that a material can manifest under specific conditions. In this work, we develop a method in which Bayesian inference is…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…
According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagation message passing scheme [Krzakala et al., PNAS 2007].…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…