A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
New hypergraph neural network learns variable-sized hyperedges.
problem Learning representations for non-uniform hypergraphs with variable cardinalities.
method Developed a hypergraph neural network exploiting incidence structure.
result Significant improvement in accuracy on real-world hypergraph datasets.
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.
problem Community detection in hypergraphs with large hyperedges.
method Extending Ricci flow to hypergraphs by defining edge probability measures and transporting them on the line expansion.
result Enhanced sensitivity to hypergraph structure, especially in large hyperedges.
HNHN learns from hypergraphs with hyperedge neurons for better classification.
problem Learning from hypergraphs with complex relationships.
method Hypergraph convolution network with hyperedge neurons and adaptive normalization.
result Improved classification accuracy and speed compared to state-of-the-art methods.
A framework infers hyperedges and overlapping communities in hypergraphs.
problem Characterizing the structural organization of hypergraphs with higher-order interactions.
method Statistical inference to infer missing hyperedges and detect overlapping communities.
result Efficient numerical implementation and strong performance on real-world systems.
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
problem Missing structure in pairwise Fisher graphs for multi-observable radiation patterns.
method Higher-order Fisher tensors and natural exponential-family coordinates.
result Exact triality of Fisher tensors, cumulants, and hypergraphs.
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly …
Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order structures in community detection problems over complex networks, we introduce the…
Improves hypergraph link prediction by breaking symmetry.
problem Limited expressivity of GWL-1 algorithm in hypergraph link prediction.
method Preprocessing algorithm to identify and replace symmetry-inducing subhypergraphs with covering hyperedges.
result Improves expressivity of GWL-1, leading to better link prediction.
Study learns random hypergraphs with queries, improving on previous results.
problem Learn random hypergraphs with non-adaptive queries.
method Equivalence to group testing, using Erdős-Rényi model for graphs.
result Generalization to random k-uniform hypergraphs. Paper proposes HGTAN for better stock trend prediction.
problem Predicting stock price trends is challenging and crucial for investors.
method Temporal-relational hypergraph tri-attention network (HGTAN).
result HGTAN outperforms existing methods in stock trend prediction.
Spectral algorithm recovers community structure in sparse hypergraphs.
problem Community detection in sparse random hypergraphs with community structure and higher-order interactions.
method Spectral algorithm with three steps: hyperedge selection, spectral partition, and correction/merging.
result Weak consistency achieved for weak signal-to-noise ratio.
We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with k blocks of equal size. More precisely, we consider a random d-uniform hypergraph H with n vertices partitioned into k clusters of size s=n/k. Hyperedges e are added independently with probability p if e is…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various lea…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex wei…
In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hy…
Bayesian hypergraph inference models disease pathways from EHR data.
problem Modeling rare diseases influenced by shared risk factors.
method Bayesian hypergraph inference framework reframing multi-disease modeling.
result Interpretable disease pathways and well-calibrated uncertainty quantification.
Paper learns hypergraph structures from signals with smoothness priors.
problem Learning hypergraph structures from signals with high-order relationships.
method Proposes HGSL framework with dual smoothness prior to map signals to hypergraph structure.
result HGSL efficiently infers meaningful hypergraph topologies from signals.
Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging sys…
HyperSAGE learns node representations in hypergraphs without losing information.
problem Learning node representations in hypergraphs is complex due to higher-order relations.
method Two-level neural message passing strategy for accurate information propagation.
result HyperSAGE outperforms state-of-the-art methods on benchmark datasets.
Wavelets model complex interactions in spatial transcriptomics.
problem Capturing higher-order relationships in spatial transcriptomics data.
method Hypergraph diffusion wavelets for representing hyperedges.
result Wavelets effectively represent disease-relevant cellular niches in Alzheimer's disease.
A new algorithm reduces frequentist regret in multi-agent bandit problems with sparse hypergraphs.
problem Deriving a frequentist regret bound for Thompson sampling in multi-agent settings with sparse hypergraphs.
method Proposed ε-exploring Multi-Agent Thompson Sampling (ε-MATS) algorithm that combines exploration and exploitation strategies. result Achieves a worst-case frequentist regret bound sublinear in time horizon and local arm size, optimal up to constants and logarithms for sparse hypergraphs.
The paper clusters hypergraphs to find diverse and experienced groups based on past experiences.
problem Finding diverse and experienced groups with respect to past experiences.
method Regularized edge-based hypergraph clustering objective with a 2-approximation algorithm.
result Demonstrates an efficient 2-approximation algorithm for clustering hypergraphs.
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
problem Capturing super-dyadic interactions in k-uniform hypergraphs.
method Tensor-based representation and tensor eigenvalue decomposition for capturing interactions.
result Improved min-cut solution on 2-uniform hypergraphs (graphs) compared to standard spectral partitioning.
A quantum framework optimizes collateral allocation for derivatives.
problem Legal constraints and operational rules in collateral allocation for derivatives.
method Certified higher-order quantum framework that normalizes margin requirements and builds a bounded neighborhood of actions.
result Quantum framework improves certified sample quality compared to classical methods.
Clustering on hypergraphs has been garnering increased attention with potential applications in network analysis, VLSI design and computer vision, among others. In this work, we generalize the framework of modularity maximization for clustering on hypergraphs. To this end, we introduce a hypergraph null model, analogou…
New hypergraph method improves scRNA-seq clustering.
problem Loss of higher-order information and overestimation in coexpression networks.
method Conceptualizing scRNA-seq data as hypergraphs and proposing novel clustering methods.
result Proposed methods outperform existing methods on simulated and real datasets.
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational data, which additionally describe relationships among instances. In this work we…
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
problem Understanding and improving the generalization of neural networks.
method Introducing weight expansion and showing that dropout leads to it.
result Dropout increases the generalization of neural networks by expanding the weight space.
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra D and a Mathematica implementation to compute ZD(K). result Derivation of large-color expansion from universal invariant.
This work explores functional expansions to handle path dependence in various fields.
problem Path dependence and infinite-dimensional problems in non-Markovian systems.
method Generalizes Wiener series and functional Taylor expansion to handle static and dynamic functionals.
result Elegant separation of functionals from future trajectories in dynamic cases.
In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…