Related papers: Graph Reconstruction by Discrete Morse Theory
We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures.…
Ensuring fairness in Graph Neural Networks is fundamental to promoting trustworthy and socially responsible machine learning systems. In response, numerous fair graph learning methods have been proposed in recent years. However, most of…
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
Recent studies have revealed that GNNs are vulnerable to adversarial attacks. To defend against such attacks, robust graph structure refinement (GSR) methods aim at minimizing the effect of adversarial edges based on node features, graph…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all…
This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…
Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…
We present a novel approach to post-quantum cryptography that employs directed-graph decryption of noise-enhanced high-memory convolutional codes. The proposed construction generates random-like generator matrices that effectively conceal…
In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has…
We consider the statistical problem of recovering a hidden "ground truth" binary labeling for the vertices of a graph up to low Hamming error from noisy edge and vertex measurements. We present new algorithms and a sharp finite-sample…