network inference

This study systematically reviews machine learning—particularly deep learning—for gene regulatory network (GRN) inference, addressing the challenge of modeling nonlinear and dynamic regulatory interactions from high-throughput transcriptomic data (including bulk and single-cell RNA-seq). We propose, for the first time, a unified methodological taxonomy encompassing supervised, unsupervised, semi-supervised, and contrastive learning paradigms. We standardize benchmark datasets (e.g., DREAM, SINCERITIES) and evaluation metrics (AUPR, AUROC, F-score), and empirically delineate current model performance limits. Key contributions include: (1) synthesizing advances in deep neural architectures to elucidate their superior capacity for capturing complex, context-dependent regulatory logic; (2) establishing a reproducible, standardized benchmarking framework with practical implementation guidelines; and (3) laying a methodological foundation for both next-generation GRN algorithm development and mechanism-driven biological discovery.

Addressing the challenge of jointly performing variable clustering and network inference in high-dimensional Gaussian graphical models, this paper proposes Normal-Block: a method that jointly infers inter-cluster association networks atop a variable clustering structure. It introduces a unified framework for simultaneous clustering and graph structure learning, incorporating a zero-inflated normal mixture model to capture inherent sparsity in real-world data, and develops a penalized variational EM algorithm for end-to-end optimization. To ensure both sparsity and statistical consistency, it adopts a two-level Graphical Lasso penalty. The method is implemented as an open-source R package, *normalblockr*. Extensive evaluations on synthetic data and multiple real-world datasets—including proteomics, web text frequencies, and microbiome abundance—demonstrate substantial improvements in clustering accuracy, significant reduction in network false positives, and enhanced interpretability through cluster-level network representations.

This work addresses the modeling needs for molecules, proteins, reaction pathways, and industrial processes in chemical science. Method: We propose a unified graph-structured representation paradigm that abstracts multiscale chemical entities as learnable heterogeneous graphs. Integrating graph neural networks (GNNs) with domain-specific chemical priors, we develop an end-to-end graph representation learning framework supporting structure-aware embedding generation and cross-scale prediction—including molecular property estimation, reactivity assessment, and target binding affinity prediction. Contribution/Results: First, we introduce the first standardized chemical graph modeling protocol spanning atomic, molecular, protein, reaction, and process scales. Second, we design chemistry-aware edge-type encoding and subgraph-level attention mechanisms, substantially enhancing physical interpretability and generalization. Experiments demonstrate an average 9.3% improvement in prediction accuracy across 12 benchmark tasks. The framework has been deployed in real-world applications, including novel material discovery and drug candidate optimization.

Classical assumptions—such as strong homogeneity or graph denseness—frequently fail in latent-variable-driven network link regression, undermining the validity of standard linear regression inference. Method: We propose a linear regression framework valid under weaker, more realistic assumptions. Leveraging the Aldous–Hoover representation, we construct a jointly exchangeable regression array and develop a bias-corrected estimator that achieves consistent and asymptotically normal inference for natural target parameters—even under weak graph sparsity. The method employs network summary statistics—including local subgraph frequencies and spectral embeddings—as covariates, and its theoretical foundation ensures bootstrap consistency. Results: Extensive simulations and empirical analysis on real-world elementary-school academic interaction data demonstrate that our approach substantially improves robustness and accuracy in network link regression inference, effectively relaxing reliance on restrictive homogeneity or denseness assumptions.

This work addresses the joint modeling of causal relationships and nonlinear dynamic dependencies among nodes, along with topology inference, in dynamic graph scenarios—such as brain networks, transportation systems, and financial markets—where the underlying graph structure is unknown. To overcome the limitations of conventional linear time-invariant models in capturing time-varying, nonlinear, and directed dependencies, we propose a unified framework based on kernel dictionary selection. The framework seamlessly integrates structural priors including sparsity, acyclicity, low-rankness, and graph smoothness, supporting both batch and online learning, and naturally extending to tensor representations. It unifies covariance selection, structural equation modeling, nonlinear vector autoregression, kernelized modeling, tensor decomposition, and convex optimization. Theoretically guaranteed convergence is established. Experiments demonstrate significant improvements in leveraging higher-order statistical information, enabling high-accuracy and interpretable inference of dynamic graph topologies.

Existing graph generators often introduce systematic biases when modeling complex systems due to the scarcity of large-scale real-world multilayer network data. To address this limitation, this work proposes a data-driven inverse generative modeling approach that overcomes the strong coupling among mABCD generator parameters through a joint prediction strategy, enabling their coordinated calibration and surpassing the constraints of traditional independent parameter estimation. By integrating multilayer network feature matching with parameter error quantification, the method infers optimal generative configurations directly from empirical networks, thereby constructing high-fidelity digital twin networks. Experimental results demonstrate that the synthesized networks exhibit structural properties highly consistent with those of real systems, confirming the effectiveness of joint parameter estimation in enhancing generative fidelity.

This work proposes a statistical inference framework based on a hidden Markov network model to accurately estimate subgraph densities and enable joint multi-timepoint comparisons for non-i.i.d. dynamic network sequences subject to observation errors. By explicitly modeling edge-wise observation noise, the method achieves, for the first time, robust inference of subgraph densities across heterogeneous network snapshots and leverages information from multiple time points to enhance estimation efficiency. Theoretical analysis demonstrates that the proposed approach enjoys favorable asymptotic properties in large-scale networks, substantially improving both accuracy and computational efficiency in inferring subgraph structures from noisy dynamic networks.

This study addresses the challenge of estimating conditional independence graphs from high-dimensional Gaussian data while simultaneously controlling false discoveries and accurately identifying edges. The authors propose a novel Bayesian framework that integrates adaptive priors capturing node degree heterogeneity, edge sparsity, and graph topological structure, coupled with a multiple testing procedure to achieve false discovery rate (FDR) control in graph inference. Computationally, the method leverages an adaptive elastic net penalty and a variational expectation-maximization algorithm for efficient optimization. In simulations, the approach demonstrates substantially improved statistical power while rigorously maintaining FDR control. Applications to breast cancer gene expression and financial return networks yield sparse, stable, and biologically or economically interpretable conditional dependence graphs, particularly excelling in heterogeneous networks containing hub nodes.

This study addresses the computational and storage challenges posed by large-scale network data, which often exceed the capacity of existing statistical inference methods to balance efficiency and rigor. The authors propose a scalable subsampling inference framework under the generalized random dot product graph (GRDPG) model. By randomly selecting a small subset of nodes to construct a subgraph and leveraging graph interpolation techniques that exploit connections between the subgraph and the full graph, the method estimates global network features. This approach uniquely integrates predictive subsampling with an interpolation mechanism, achieving statistical consistency of estimators while substantially reducing computational complexity. Theoretical analysis establishes the consistency of the proposed estimator, and simulation studies demonstrate its high statistical power and computational efficiency in two-sample hypothesis testing.

This work addresses the challenges of model selection and hypothesis testing in network data, where strong dependencies and a single observed sample often render existing methods inadequate due to their lack of finite-sample guarantees and limited applicability. The authors propose a general framework based on Universal Inference, which employs edge sampling to partition the network into two subnetworks with controllable dependence structures. This approach yields the first e-value statistic tailored for dependent data, offering strict Type I error control in finite samples and logarithmic consistency under a broad class of alternative models. Empirical evaluations demonstrate that the method achieves both theoretical rigor and strong practical performance in tasks such as random graph model selection and community number estimation.