A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
problem GCN's performance drops for deeper structures due to limited neighborhood information.
method Assumes higher-order neighbors are similar to first-order neighbors, learns weights through Lasso to minimize feature loss.
result HWGCN achieves state-of-the-art results on various datasets.
SPINEX improves clustering with explainable neighbors, outperforming other methods.
problem Improving clustering performance and explainability.
method Leverages similarity and higher-order interactions for clustering.
result SPINEX outperforms 13 clustering algorithms across various datasets.
Given a graph where every node has certain attributes associated with it and some nodes have labels associated with them, Collective Classification (CC) is the task of assigning labels to every unlabeled node using information from the node as well as its neighbors. It is often the case that a node is not only influenc…
We introduce nonlinear higher-order label spreading for semi-supervised learning.
problem Efficient semi-supervised learning on graphs with complex label spreading.
method We add nonlinearity to label spreading through higher-order graph structures, proving convergence and demonstrating efficiency on various datasets.
result Our nonlinear higher-order label spreading algorithm converges to the global solution and performs favorably compared to classical methods.
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and re…
GUIDE detects anomalies in attributed networks by reconstructing node attributes and higher-order structures.
problem Lack of effective mechanisms for detecting anomalies in complex network interactions.
method GUIDE uses attribute and structure autoencoders, graph attention, and reconstruction errors to identify anomalies.
result GUIDE significantly outperforms state-of-the-art methods on multiple real-world datasets.
New topological methods for hypergraph data improve community detection and pattern recognition.
problem Community detection and pattern recognition in hypergraph data.
method Introducing a new topological space structure of hypergraph data, proposing modified nearest neighbors methods.
result Improved methods for community detection and pattern recognition in hypergraph data.
SPINEX improves time series forecasting with explainable neighbors.
problem Enhancing time series forecasting accuracy and interpretability.
method Leverages similarity and higher-order temporal interactions across multiple scales.
result SPINEX consistently ranks among top performers in forecasting precision.
Algorithm finds adversarial examples for k-NN classifiers using Voronoi diagrams.
problem Ensuring robustness of k-NN classifiers against adversarial attacks.
method Geometric approach expanding outwards from input points to find minimum-norm adversarial examples.
result Our method outperforms existing approaches on various datasets.
New method uses information theory to uncover causal relationships in complex systems.
problem Discovering causal relationships in multivariate systems, especially in Bayesian networks and hypergraphs.
method Partial Information Decomposition (PID) to explicitly model higher-order interactions.
result PID components reveal direct causal neighbors and collider relationships in Bayesian networks and multi-tail hyperedges in causal hypergraphs.
Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operat…
Link prediction requires predicting which new links are likely to appear in a graph. Being able to predict unseen links with good accuracy has important applications in several domains such as social media, security, transportation, and recommendation systems. A common approach is to use features based on the common ne…
New method for learning on heterogeneous graphs without meta-paths.
problem Learning on heterogeneous graphs is sensitive to meta-paths choice, leading to poor performance.
method Decompose heterogeneous graph into homogeneous relation-type graphs, combine higher-order representations, use attention mechanisms.
result Our model outperforms state-of-the-art baselines in vertex classification tasks on heterogeneous graph datasets.
The weighted nearest neighbors (WNN) estimator has been popularly used as a flexible and easy-to-implement nonparametric tool for mean regression estimation. The bagging technique is an elegant way to form WNN estimators with weights automatically generated to the nearest neighbors; we name the resulting estimator as t…
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
Graph neural networks struggle with heterophily, but new designs improve their performance.
problem Graph neural networks struggle with heterophily (networks where connected nodes may have different class labels and dissimilar features).
method Ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations.
result The identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively.
Method estimates heterogeneous causal effects on networks using orthogonal learning.
problem Challenges in estimating causal effects on networks due to treatment effects on both treated and neighbors, and network homophily.
method Two-stage orthogonal learning framework: first stage uses graph neural networks for nuisance components, second stage residualizes and interpretable attention-based model for causal effects.
result Improves heterogeneous effect estimation and supports interpretable analyses.
ISP improves GNN expressivity by stratifying nodes based on graph invariants.
problem Graph Neural Networks struggle with expressivity and structural heterogeneity.
method Invariant-Stratified Propagation (ISP) using ISP-WL and ISPGNN.
result ISP achieves enhanced expressivity beyond 1-WL, with theoretical guarantees and practical improvements.
Improved neural model for social recommendation by integrating social and interest networks.
problem Data sparsity and lack of higher-order relationships in social recommendation.
method DiffNet++ models neural influence diffusion and interest diffusion in a unified framework using a multi-level attention network.
result Extensive experiments on real-world datasets show the effectiveness of DiffNet++.
LNPE enhances local connections in embeddings using extended neighbor propagation.
problem Improving local connections and interactions in nonlinear dimensionality reduction.
method Inspired by GCN, LNPE extends 1-hop neighbors to n-hop neighbors in LLE.
result LNPE produces more faithful and robust embeddings with better topological and geometrical properties.
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits …
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera o…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucia…
Stability of capillary hypersurfaces with higher order mean curvature.
problem Stability of capillary hypersurfaces with constant higher order mean curvature.
method Generalization of classical stability theory for capillary hypersurfaces.
result Results on stability for capillary hypersurfaces with higher order mean curvature.
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support learning higher…
The paper improves CR Sobolev inequalities and classifies minimizers.
problem Higher-order CR Sobolev inequalities on the CR sphere.
method Improvement through vanishing higher order moments of the volume element.
result New direct proof of minimizers' classification and existence of minimizers in C2k(N). Study nearest-neighbor radii under dependent sampling, finding they remain informative.
problem Analyzing nearest-neighbor radii under dependent sampling.
method Consider strong mixing dependent observations, establish distribution-free almost sure convergence and sharp non-asymptotic moment bounds.
result Nearest-neighbor geometry remains informative under dependence sampling.
Deep nearest neighbors outperform self-supervised methods in anomaly detection.
problem Anomaly detection using self-supervised deep methods.
method Simple nearest-neighbor approach on Imagenet pretrained features.
result Nearest-neighbor method outperforms self-supervised methods in accuracy, few shot generalization, training time, and noise robustness.
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for this higher order situation and derive in this framework the phase equations fro…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significa…
The paper glosses different forms of an introducing of higher order tangent-like functors, especially functors derived from higher order nonholonomic tangent functors. A special attention is devoted to higher order osculating bundles: their identification with higher order tangent bundles is demonstrated as the main re…
A new method predicts higher-order interactions in evolving graphs using simplicial complexes.
problem Predicting higher-order interactions in dynamic graphs with theoretical guarantees.
method Capturing higher-order interactions as simplices, modeling neighborhoods with face-vectors, and developing a nonparametric kernel estimator.
result Our method outperforms existing higher-order prediction methods and is theoretically consistent.
Characterizes Lebesgue points using nearest neighbor methods.
problem Consistency of classification algorithms based on nearest neighbors.
method Characterization of Lebesgue points via 1-Nearest Neighbor regression.
result Proves convergence of 1-Nearest Neighbor classification algorithms in metric spaces.
Novel higher-order group synchronization for noisy local measurements on hypergraphs.
problem Synchronizing higher-order local measurements on hyperedges to global estimates on nodes.
method Message passing algorithm for global synchronization of higher-order measurements.
result Higher-order method outperforms standard pairwise synchronization methods in certain applications.
Higher-order tangent bundles have geometric structures compatible with their iterated bundle structure.
problem Connection towers and Sasaki metrics on higher-order tangent bundles
method Introduce the notion of a connection tower and study the geometric structures induced by such towers.
result Connection towers determine multiconnections, adapted splittings, and canonical vector bundle structures.
We use the Frölicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [14] to formulate and discuss t…
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type (r,s) in a vector space of signature (p,q). We then use these examples to establish some results concerning higher order Osserman and highe…
After defining cohomologically higher order BRST and anti-BRST operators for a compact simple algebra {\cal G}, the associated higher order Laplacians are introduced and the corresponding supersymmetry algebra Σ is analysed. These operators act on the states generated by a set of fermionic ghost fields transforming u…
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothn…
The paper explains how nearest neighbor methods succeed in prediction.
problem Explaining the success of nearest neighbor methods in prediction.
method The paper covers both theoretical and practical aspects of nearest neighbor methods, including statistical guarantees and practical algorithms.
result The paper provides nonasymptotic statistical guarantees and practical algorithms for nearest neighbor methods.
AWNN improves matrix completion by adaptively weighting nearest neighbors.
problem Matrix completion with optimal nearest neighbor weights and radii selection.
method Adaptively weighted nearest neighbor method for matrix completion.
result Theoretical guarantees and synthetic experiments support the effectiveness of AWNN.
Introduce Collapsed Effective Operators for higher-order structures.
problem Existing spectral operators decompose topology into separate ranks, leaving practitioners to fuse information back to vertices.
method Introduce Collapsed Effective Operators via Schur complementation of a graded Laplacian.
result Preserves positive semi-definiteness, lowers system energy under higher-order connectivity.
A new method uses nearest neighbors for importance weighting.
problem Data covariate shift problems in machine learning.
method Nearest neighbor classification scheme for determining importance weights.
result Demonstrated effectiveness through comparative experiments on various classification tasks.
Given a closed, oriented, connected 3-manifold, M, we define higher-order linking forms on the higher-order Alexander modules of M. These higher-order linking forms generalize similar linking forms for knots previously studied by the author, which were themselves generalizations of the classical Blanchfield linking for…
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
problem Comparing and characterizing random outcomes in risk assessment.
method Exploring the equivalence between higher order risk measures and stochastic dominance, using stochastic optimization and expectiles as examples.
result Higher order risk measures and stochastic dominance are equivalent and can be used to characterize random outcomes.
New estimator stabilizes higher-order influence functions for stable statistical inference.
problem Numerical instability in estimating inverse population Gram matrix.
method Proposes a new stabilized higher-order estimator without sample splitting.
result Stabilized estimator exhibits more stable performance and similar statistical guarantees.
This work explores higher-order algebroids via vector bundle comorphisms.
problem Generalizing concepts of higher-order tangent bundles and Lie algebroids.
method Introduces a vector bundle comorphism approach to describe higher-order algebroids.
result Establishes a one-to-one correspondence between higher-order Lie algebroids and specific algebraic structures.
New estimator stabilizes higher-order influence functions for bilinear forms.
problem Stability issues in estimating bilinear forms using higher-order influence functions.
method Proposes a new stabilized higher-order estimator for a class of bilinear forms without sample splitting.
result New estimator exhibits more stable finite-sample performance compared to the empirical higher-order estimator.