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Topology Identification and Inference over Graphs

arXiv 2512.10183 ↗First posted 11 Dec 2025eess.SP cs.SI stat.MEcited by 0

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Abstract (arXiv)

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph topology identification and statistical inference methods for multidimensional relational data. Approaches for undirected links connecting graph nodes are outlined, going all the way from correlation metrics to covariance selection, and revealing ties with smooth signal priors. To account for directional (possibly causal) relations among nodal variables and address the limitations of linear time-invariant models in handling dynamic as well as nonlinear dependencies, a principled framework is surveyed to capture these complexities through judiciously selected kernels from a prescribed dictionary. Generalizations are also described via structural equations and vector autoregressions that can exploit attributes such as low rank, sparsity, acyclicity, and smoothness to model dynamic processes over possibly time-evolving topologies. It is argued that this approach supports both batch and online learning algorithms with convergence rate guarantees, is amenable to tensor (that is, multi-way array) formulations as well as decompositions that are well-suited for multidimensional network data, and can seamlessly leverage high-order statistical information.

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23 of 79 references.

References · 23

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  3. 2016Tensor Decomposition for Signal Processing and Machine Learningcited by 224
  4. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  5. 2016How to learn a graph from smooth signalscited by 146
  6. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  7. 2018Learning graphs from data: A signal representation perspectivecited by 119
  8. 2018Connecting the Dots: Identifying Network Structure via Graph Signal Processingcited by 111
  9. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  10. 2017Network Inference via the Time-Varying Graphical Lassocited by 55
  11. 2019A Unified Framework for Structured Graph Learning via Spectral Constraintscited by 53
  12. 2020Signal Processing on Directed Graphscited by 28
11 more
  1. 2014Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fieldscited by 19
  2. 2020Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Informationcited by 19
  3. 2021Accelerated Graph Learning from Smooth Signalscited by 16
  4. 2021Online Discriminative Graph Learning from Multi-Class Smooth Signalscited by 13
  5. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 13
  6. 2015Decentralized learning for wireless communications and networkingcited by 9
  7. 2016Kernel-Based Structural Equation Models for Topology Identification of Directed Networkscited by 8
  8. 2016Tensor Decompositions for Identifying Directed Graph Topologies and Tracking Dynamic Networkscited by 8
  9. 2018Semi-Blind Inference of Topologies and Dynamical Processes over Graphscited by 7
  10. 2013Nonparametric Basis Pursuit via Sparse Kernel-based Learningcited by 6
  11. 2020Topology Inference with Multivariate Cumulants: The M"obius Inference Algorithmcited by 1

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