Densification Arising from Sampling Fixed Graphs

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A full characterization of invariant embeddability of unimodular planar graphs

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When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

WILEY2023

Equivariant Neural Architectures for Representing and Generating Graphs

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Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

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Maximum Independent Set: Self-Training through Dynamic Programming

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This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...

2023

Privatized graph federated learning

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Federated learning is a semi-distributed algorithm, where a server communicates with multiple dispersed clients to learn a global model. The federated architecture is not robust and is sensitive to communication and computational overloads due to its one-m ...

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Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature rec ...

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The adaptive social learning paradigm helps model how networked agents are able to form opinions on a state of nature and track its drifts in a changing environment. In this framework, the agents repeatedly update their beliefs based on private observation ...

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ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

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We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

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Results on Sparse Integer Programming and Geometric Independent Sets

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An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

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Graph neural networks for dynamic modeling of roller bearings

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Machine learning has paved the way for the real-time monitoring of complex infrastructure and industrial systems. However, purely data-driven methods have not been able to learn the underlying dynamics and generalize them to operating conditions that have ...

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GAP: Differentially Private Graph Neural Networks with Aggregation Perturbation

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In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's aggregation functio ...

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