The PC algorithm allows investigators to estimate a complete partially directed acyclic graph (CPDAG) from a finite dataset, but few groups have investigated strategies for estimating and controlling the false discovery rate (FDR) of the edges in the CPDAG. In this paper, we introduce PC with p-values (PC-p), a fast al…
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48 results for “Edge Values”
New graph learning model can approximate any function and handle edge values.
problem Graph learning models' limitations in approximating functions and handling edge values.
method Proposes a Graph Neural Network that can approximate any function and handle arbitrary edge values.
result Proves the model is strictly more expressive than existing models.
Study on network-valued processes with asynchronous updates, proving consistency in community and changepoint estimation.
problem Understanding the behavior of network-valued stochastic processes with asynchronous updates.
method Analysis of concentration properties of aggregated adjacency and Laplacian matrices for lazy network-valued stochastic processes.
result Demonstrates consistency of estimators in community and changepoint estimation problems.
Extends graph theory to hypergraphs with manifold-valued nodes.
problem Representing complex N-ary relationships on manifolds.
method Defined function spaces and symmetric products for manifold-valued nodes and edges.
result Generalized hypergraph Laplacians to manifold-valued hypergraphs.
Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…
On the Ricci flow on Treesmath.DG
Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
DistShap parallelizes GNN explanation for large graphs.
problem Computational expense in attributing GNN predictions to specific edges or features.
method Distributed Shapley values across multiple GPUs for scalable GNN explanations.
result DistShap outperforms existing methods and scales to models with millions of features.
New graph properties inherited by Frechet mean and median.
problem Characterizing the average of graph-valued samples.
method Analysis of Frechet mean and median graphs.
result Edge density is hereditary in Frechet mean and median graphs.
Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.
problem Determining the stick number and edge length of knots in a hexagonal lattice.
method Introducing a linear transformation between lattices to prove strict inequalities and classifying knots.
result Only trefoil and figure-eight knots are 11-stick knots in the hexagonal lattice.
SAM improves generalization by operating near the edge of stability.
problem Improving generalization in neural networks.
method Sharpness-Aware Minimization (SAM) approach to training neural networks.
result SAM operates near the 'edge of stability' identified by the analysis.
A new method learns DAG structures from data without false edges.
problem Learning DAG structures from observational data is hard due to combinatorial search space and non-sparse solutions.
method Developed NOTEARS-AL using adaptive Lasso to ensure sparsity and rule out false edges.
result NOTEARS-AL outperforms NOTEARS in synthetic and real-world datasets.
We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our microlocal heat kernel construction for algebraic boundary conditions is guided …
The paper develops formulas for hyperbolic simplices based on edge lengths.
problem Understanding the geometry of hyperbolic simplices using only edge lengths.
method Develops geometric formulas for hyperbolic simplices based on edge lengths.
result Distance and projection formulas in hyperbolic simplices.
The study characterizes homology 4-manifolds with combinatorially.
problem Characterizing homology 4-manifolds with specific values.
method Combinatorial approach using various operations on triangulated 4-spheres.
result Homology 4-manifolds with are triangulated spheres and can be derived from 4-spheres with .
Gradient descent on neural nets often operates at the Edge of Stability, where loss behavior is complex but loss decreases over time.
problem Understanding the optimization dynamics of neural networks at the Edge of Stability.
method Empirical demonstration of gradient descent behavior in neural network training.
result Gradient descent on neural networks typically occurs at the Edge of Stability, where loss behavior is non-monotonic but loss decreases over time.
VEC-SBM detects communities using side information like texts and images.
problem Community detection in social networks with side information.
method Proposes a novel algorithm based on iterative refinement techniques.
result Optimally recovers latent communities with side information.
This study examines how removing edges from complete graphs affects Ollivier Ricci curvature.
problem Conditions under which Ollivier Ricci curvature changes sign after edge removal.
method Defined and analyzed graphs obtained by removing matching, vertex incident, and cycle edges from complete graphs.
result Ollivier Ricci curvature remains positive or zero for graphs formed by removing edges from complete graphs.
Temporal Functional Circuits explain KAN forecasts with interpretable edge functions.
problem Lack of mechanistic explanations in KAN forecasting.
method Transform KAN edge functions into faithful, temporally grounded explanations using a gated residual KAN.
result Gated KAN achieves lower MSE than linear-only models on regime-switching signals.
Normal Form for Edge Metricsmath.AP
A normal form for edge metrics is derived under the necessary conditions that the metric be normalized and exact. The normal forms for such an edge metric are shown to be in 1-1 correspondence with representative metrics for a reduced conformal infinity on the boundary. The normal form is constructed via solution of a …
Federated learning technique improves convergence speed with communication delays.
problem Communication delays between edge nodes and aggregator in federated learning.
method Developed FedDelAvg, a technique that generalizes federated averaging to incorporate a weighting between current local model and delayed global model.
result FedDelAvg achieves a significant improvement in convergence speed, especially when optimizing the weighting scheme to account for delays.
It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural networks, the foundation of this hypothesis on generic non-linear systems remain…
Newly discovered Eguchi-Hanson metric arises from edge metrics.
problem Understanding limits of compact singular Einstein spaces.
method Constructing Kahler-Einstein edge metrics on Calabi-Hirzebruch manifolds.
result Eguchi-Hanson metric emerges as a Gromov-Hausdorff limit.
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …
We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on - regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods di…
New model detects communities in networks with signed, continuous weights.
problem Detect communities in networks with signed, continuous weights.
method Heterogeneous Block Covariance Model (HBCM) with variational EM algorithm.
result Provable consistent estimates of group memberships.
Gradient descent forces neural network eigenvalues to a specific threshold.
problem Understanding why gradient descent drives eigenvalues to a specific threshold.
method Introduced edge coupling, a functional on consecutive iterate pairs, to explain the trajectory towards the eigenvalue threshold.
result Gradient descent forces the Hessian eigenvalue to the threshold from arbitrary initialization.
Real-time anomaly detection for edge streams using MIDAS and MIDAS-F.
problem Detecting unusual behavior in dynamic graph edge streams.
method MIDAS-F focuses on microcluster anomalies, incorporating anomalies into internal states to reduce poisoning effect.
result MIDAS-F outperforms MIDAS in accuracy, with up to 62% higher ROC-AUC.
Multi-Likelihood Methods for Developing Stock Relationship Networks Using Financial Big Dataq-fin.ST
Development of stock networks is an important approach to explore the relationship between different stocks in the era of big-data. Although a number of methods have been designed to construct the stock correlation networks, it is still a challenge to balance the selection of prominent correlations and connectivity of …
Deep linear networks oscillate beyond the edge of stability in a predictable manner.
problem Understanding oscillations in deep linear networks beyond the edge of stability.
method Theoretical analysis of loss oscillations in deep matrix factorization loss.
result Loss oscillations in deep linear networks follow a period-doubling route to chaos and occur within a small subspace.
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm, we propose a new state-integral model for the Teichmüller TQFT, where the circle valued state variables live on the edges of oriented leveled shaped triangulations.
Cube edges curves minimize systole length.
problem Finding the shortest closed curve on a cube.
method Combining exact calculations and estimates, including branched covers, elliptic integrals, geodesic trajectories, and conformal maps.
result The extremal length systole is realized by 12 curves surrounding the cube's edges.
New method reveals true causal functions in nonlinear time series, not just scores.
problem Causal discovery in nonlinear time series often uses scalar edge scores, which hide true function-valued causal influence.
method Formalized function-valued causal influence for additive, contribution-decomposable architectures. Introduced a practical framework based on ICE for estimating causal response functions directly from trained models.
result Edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors.
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a realization from a random graph model, and estimate the underlying edge probability ma…
Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditi…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of dif…
The paper proposes a novel Kernelized image segmentation scheme for noisy images that utilizes the concept of Smallest Univalue Segment Assimilating Nucleus (SUSAN) and incorporates spatial constraints by computing circular colour map induced weights. Fuzzy damping coefficients are obtained for each nucleus or center p…
Paper proposes an AutoML framework for efficient device-edge co-inference.
problem Finding optimal hyper-parameters for model sparsity and feature compression.
method Sequential decision problem solved using deep reinforcement learning (DRL).
result Achieves better communication-computation trade-off and significant speedup.
A new method for identifying causal directions in complex systems.
problem Identifying causal relationships in nonlinear systems with limited data.
method Sequential edge orientation approach using pairwise additive noise model.
result The method can recover true causal DAGs under nonlinear additive noise models.
To accommodate heterogeneous tasks in Internet of Things (IoT), a new communication and computing paradigm termed mobile edge computing emerges that extends computing services from the cloud to edge, but at the same time exposes new challenges on security. The present paper studies online security-aware edge computing …
We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs (DAGs), where nodes represent hypotheses and edges specify a partial ordering in which hypotheses must be tested. The procedure is guaranteed to reject a sub-DAG with bounded false discovery rate (FDR) while satisf…
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity SAR d…
GRAPE uses graph representation to handle missing data in feature imputation and label prediction.
problem Handling missing data in machine learning tasks.
method GRAPE uses a bipartite graph where observations and features are nodes, and observed feature values are edges. It formulates feature imputation as edge-level prediction and label prediction as node-level prediction, solving these with Graph Neural Networks.
result GRAPE achieves 20% lower mean absolute error for imputation and 10% lower for label prediction compared to state-of-the-art methods.
Introduces Lax-Kirchhoff moduli spaces for quivers and Lie groups.
problem Constructing moduli spaces for quivers and Lie groups.
method Introduces Lax equations and Kirchhoff conditions, constructs slices, and uses Marsden-Weinstein reduction.
result Proves is a finite-dimensional smooth symplectic manifold with a Hamiltonian action of .
We give a unified description of tetrahedra with lightlike faces in 3d anti-de Sitter, de Sitter and Minkowski spaces and of their duals in 3d anti-de Sitter, hyperbolic and half-pipe spaces. We show that both types of tetrahedra are determined by a generalized cross-ratio with values in a commutative 2d real algebra t…
Paper proposes new methods for improving interatomic potentials.
problem Limitations of conventional SO(2) Linear architectures in MLIPs.
method Direct Cartesian construction, recursive Clebsch-Gordan construction, Edge Complex Product Basis, Radial Rotary Complex Attention.
result TECE-OAM-RRA-1.0 achieves SOTA performance on Matbench Discovery.
The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.