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Efficient inference of dynamic gene regulatory networks using discrete penalty

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that an exact $\ell_0$ (zero-count) penalty can replace $\ell_1$ shrinkage in joint gene-network inference, and that the resulting mixed-integer problem is tractable for tree-structured populations.

desk verdict A genuinely scalable ℓ0 joint GRN estimator with a real positive-semidefiniteness problem at its core. read the letter →

arxiv 2507.23106 v1 pith:T7DYFGIY submitted 2025-07-30 stat.AP stat.COstat.OT

Visweswaran Ravikumar , Aaresh Bhathena , Wajd N Al-Holou , Salar Fattahi , Arvind Rao This is my paper
classification stat.APstat.COstat.OT
keywords generegulatorynetworksprecisionmatrixestimationl0penaltymixed-integerquadraticprogrammingdynamicspatialtranscriptomicsglioblastomaGaussianMarkovrandomfields
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a discrete $\ell_0$ penalty, which counts actual nonzero edges instead of shrinking them, can replace $\ell_1$ penalties in joint inference of dynamic gene regulatory networks, and that the resulting mixed-integer problem becomes tractable when populations are organized in a tree-structured hypergraph. The authors show Algorithm 1 runs in $O(Kp^2n + Kp^3 + K^2p^2)$ time and, on synthetic benchmarks, report F1 scores around 0.88 that beat the $\ell_1$-based ELEM-1 and far exceed joint graphical lasso and GRNBoost2. Applied to glioblastoma single-cell and spatial transcriptomics, the method reconstructs shared and population-specific networks, traces rewiring along a hypoxia gradient, and separates niche-specific primary-versus-recurrent changes. If the core estimator is valid, this gives biologists a way to control sparsity directly without trading away statistical accuracy for convexity.

What carries the argument

The load-bearing machinery is the element-wise decomposition of the objective (ELEM-0) combined with the tree-based dynamic program of [20]. For each off-diagonal coordinate $(i,j)$, the full joint problem reduces to minimizing over $K$ scalars a quadratic fit to the approximate backward mapping plus an $\ell_0$ penalty plus a tree-structured quadratic similarity term; [20, Algorithm 2] solves this mixed-integer quadratic program in $O(K^2)$ time. The second component is the approximate backward mapping $\tilde{F}^*(\hat\Sigma_k) = [ST_\nu(\hat\Sigma_k)]^{-1}$ from [24], which avoids the log-determinant term and keeps the objective quadratic. Together they convert a generally NP-hard $\ell_0$ problem into $p(p+1)/2$ small problems solvable in parallel.

What would settle it

Simulate data from a known precision matrix $\Theta^*_k$ with $n/p$ near 1 and compute $\| [ST_\nu(\hat\Sigma_k)]^{-1} - \Theta^*_k \|$; if ELEM-0's recovery error tracks this approximation error rather than the optimizer's gap, the backward-mapping proxy is the limiting assumption, while if recovery stays accurate despite large proxy error, the claim survives.

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Extended reading notes

Core claim

The central discovery is that unbiased sparsity control for joint Gaussian graphical model inference is computationally feasible at genomic scale. The paper's estimator, ELEM-0, minimizes the sum of a backward-mapping deviation, an $\ell_0$ off-diagonal penalty, and a quadratic similarity penalty over tree-structured populations; because the objective separates coordinate-wise, each off-diagonal entry becomes a $K$-variable mixed-integer quadratic program that can be solved exactly in $O(K^2)$ time by dynamic programming. This yields an exact $\ell_0$ joint precision-matrix estimator rather than an $\ell_1$ relaxation, avoiding uniform shrinkage of strong interactions. The categorical extension splits each precision matrix into shared global and category-local components, letting information pool across conditions. On synthetic data with $n/p$ from 0.5 to 30 and up to 100 populations, ELEM-0 maintains F1 scores around 0.88 to 0.91, and the glioblastoma applications demonstrate that the inferred networks align with known biology such as BACH1 centrality in recurrent tumors and hypoxia-driven modules.

Load-bearing premise

The method treats the inverse of the soft-thresholded sample covariance, $[ST_\nu(\hat\Sigma_k)]^{-1}$, as a faithful stand-in for the true precision matrix; if that proxy is poor in high-dimensional, low-sample data, the exact $\ell_0$ solver is solving the wrong estimation problem.

Editorial extensions

If this is right

  • Direct $\ell_0$ sparsity control removes the uniform shrinkage that $\ell_1$ penalties apply to strong edges, so inferred interaction strengths are less biased in the paper's synthetic comparisons.
  • The $O(Kp^2n + Kp^3 + K^2p^2)$ runtime makes joint inference practical for thousands of genes and dozens of populations; the paper demonstrates $p = 2000$ and $K$ up to 100.
  • The categorical decomposition into global and local components lets small per-category sample sizes borrow strength, improving F1 scores as category dissimilarity grows.
  • Tree-structured population hypergraphs cover pseudo-temporal, developmental, and spatial-gradient designs common in single-cell and spatial transcriptomics.
  • On glioblastoma data, the inferred networks recapitulate known regulators, including BACH1 in recurrence and SOX and FOX family factors in hypoxia, and suggest niche-specific rewiring.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Not stated but implied: the same element-wise $\ell_0$ machinery could extend to non-tree hypergraphs by iterative edge-removal or Lagrangian relaxation, though the exact $O(K^2)$ dynamic-programming guarantee would be lost.
  • A testable extension suggested by the paper's Section 7 limitations: replacing the fixed soft-threshold $\nu$ with per-population adaptive thresholds, or moving to count-valued generalized linear model losses, could remove the cluster-specific threshold tuning that the authors report as unresolved.
  • The authors' stated dependence on scVI-imputed counts and cluster-specific thresholds means the biological findings inherit the quality of the imputation and the tuning choice; the paper does not quantify how either affects edge recovery.
  • If the backward-mapping proxy is the true bottleneck, then a direct comparison of $\tilde{F}^*(\hat\Sigma_k)$ against $\Theta^*_k$ in synthetic low-sample regimes would isolate whether failures are optimization failures or approximation failures; this diagnostic is not run.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes ELEM-0, a joint estimator of multiple Gaussian precision matrices with an ℓ0 penalty, built on the approximate backward mapping of Yang et al. and on a dynamic-programming solver from prior work [20]. The main optimization is decomposed coordinate-wise over the off-diagonal entries, each subproblem being a mixed-integer quadratic program solved in O(K^2) time for tree-structured population hypergraphs; the total runtime is claimed as O(Kp²n + Kp³ + K²p²). The method is validated on synthetic data against ELEM-1, FASJEM, JGL, and GRNBoost2, and is applied to single-cell and spatial transcriptomics data from glioblastoma, including a categorical extension that separates global and local network components. The paper positions the contribution as an exact-ℓ0, scalable alternative to ℓ1-based joint graphical models with direct sparsity control.

Significance. If the statistical validity of the estimator were established, this would be a valuable contribution: it offers the first scalable joint precision-matrix estimator with an exact discrete penalty, with a clear complexity theorem (Theorem 2.1) and a proof that each element-wise MIQP is solved exactly by the dynamic program of [20]. The manuscript also ships open-source code and demonstrates the method on substantial real datasets, with biologically interpretable results. However, the central statistical claim currently rests on two unproven components: the approximate backward mapping target [ST_ν(Σ̂_k)]^{-1} may be indefinite, and the optimization in (ELEM-0) drops the positive-semidefinite constraint that is explicit in (MLE) and (JGL). The synthetic evaluation aligns the data-generating process with the tree-hypergraph assumption and scores only edge support, so the reported F1 gains do not fully address these concerns.

major comments (4)
  1. [Section 2, (ELEM-0) and Algorithm 1] The formulation (ELEM-0) omits the constraint Θ_k ∈ S_+^p that is present in both (MLE) and (JGL). Algorithm 1 optimizes each off-diagonal entry independently and then symmetrizes, with no mechanism that enforces positive semidefiniteness of the assembled {Θ̂_k}. This is load-bearing because (i) the eBIC criterion in Section 2.2 evaluates log det(Θ̂_k), which is undefined when det(Θ̂_k) ≤ 0; (ii) an indefinite symmetric matrix is not the precision matrix of any Gaussian Markov random field, so interpreting the output as a gene regulatory network is not justified; and (iii) the synthetic F1 scores measure only edge support, which can be correct even for indefinite matrices. The authors need to either add a PSD constraint and analyze how it interacts with the coordinate-wise decomposition, or prove that the solution of (ELEM-0) is PSD under stated conditions, or apply and document a post-processing projection.
  2. [Section 2, Equation (1)] The approximate backward mapping F̃*(Σ̂_k) = [ST_ν(Σ̂_k)]^{-1} is adopted from [24] without re-derivation or validation in the high-dimensional, low-sample regime typical of single-cell data. Elementwise soft-thresholding of a covariance matrix does not preserve positive semidefiniteness: for example, a 3×3 covariance with off-diagonals 0.9, 0.9, and 0.62 is PSD, but thresholding the 0.62 entry to zero gives an indefinite matrix whose inverse is indefinite. Consequently, even the ideal target of the objective can fail to be a valid precision matrix. The manuscript should provide conditions under which ST_ν(Σ̂_k) is invertible and PSD, or replace the backward mapping with a PSD-preserving estimator, or explicitly characterize the consequences of targeting a possibly indefinite quantity.
  3. [Section 2.2 and Discussion] The eBIC criterion in Section 2.2 includes a tunable parameter that is said to be fixed to a constant, but the constant is never specified, and the grid P includes a per-population ν_k. The Discussion further states that in the GBM single-cell case study, 'a single global threshold was insufficient and required cluster-specific adjustments.' This means the real-data networks are not produced by a single, pre-specified procedure with a documented threshold rule, which complicates reproducibility and weakens the claim of direct, unbiased sparsity control. The authors should report the exact eBIC constant, the threshold grid, and the protocol by which cluster-specific adjustments were made, preferably with a sensitivity analysis.
  4. [Section 3.1 and Table 1] The synthetic evaluation is closely aligned with the method's structural assumptions: the true precision matrices are generated as disjoint power-law modules, the population hypergraph is a minimum spanning tree, and the weight matrix W is set to the adjacency matrix of that same MST. This is exactly the tree structure for which the solver is designed, so the reported F1 gains over ELEM-1, FASJEM, and JGL may reflect favorable alignment rather than general superiority. In addition, GRNBoost2 is a directed GRN inference method not designed for precision-matrix estimation, and its reported F1=0 with recall=1 and precision=0 in Table 1 is not a meaningful comparison. I recommend additional simulations with non-tree population graphs or misspecified W, and either removal of GRNBoost2 from the headline comparison or a clear statement that it is an out-of-scope baseline.
minor comments (5)
  1. [Section 2.1, (Categorical ELEM-0)] The argmin in the categorical objective appears to contain a hat over Θ̂local in the domain, which is likely a typo; the domain should be over Θglobal_k and Θlocal_k,c without hats.
  2. [Section 2, equations (2) and (3)] The notation for the backward mapping is inconsistent: equation (2) uses F̃ while equation (1) and equation (3) use F̃*, and Algorithm 1 also uses F̃*. Please unify the notation.
  3. [Algorithm 1] Algorithm 1 lists input parameters as (μ, γ, ν), but the text and equations use λ for the sparsity penalty and ν for the soft-thresholding parameter; the symbol μ appears to be a typo for λ.
  4. [Figure 6] Figure 6 has a duplicated panel label: both panel (H) and panel (H) appear, and the key TFs panel is labeled (H) in one place and (I) in the text; the labels should be corrected.
  5. [Figure 7] The figure title contains the typo 'Supplemenatary'; it should be 'Supplementary'. Additionally, Figure 8D text refers to 'Fig8A–C' and 'Fig8D' with inconsistent spacing, which should be standardized.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the estimator is a new application of an independently published optimization solver, and the cited self-work is not used to smuggle in the target conclusion.

full rationale

The paper's derivation chain is not circular. The objective (ELEM-0) is a new joint ℓ0-penalized estimator whose data-fidelity target is the externally defined approximate backward mapping F~*(Σ̂_k)=[ST_ν(Σ̂_k)]^{-1} from Yang et al. [24]; this target is not defined in terms of the output Θ̂_k, so the estimator is not self-definitional. The coordinate-wise decomposition in Equation (3) follows algebraically from the objective, and the ℓ0 subproblem is then handed to Bhathena et al. [20] as an optimization subroutine. Although [20] and the earlier framework [32] have overlapping authorship, the cited result is an independent, peer-reviewed mathematical theorem about tree-structured MIQPs with stated assumptions that do not include the GRN target, so this is ordinary self-citation rather than load-bearing circularity. The eBIC selection in Section 2.2 and the Discussion's admission (Section 7) that 'a single global threshold was insufficient and required cluster-specific adjustments' are genuine statistical-tuning weaknesses, and the lack of an explicit PSD constraint on Θ̂_k is a correctness/validity concern for the GMRF interpretation; but none of these makes the estimate equal to its own input by construction. The synthetic benchmarks are evaluated against externally generated ground-truth networks, and F1 is a support-recovery metric that is not forced by the fitting procedure. No specific equation-level reduction from output back to input can be exhibited, so the appropriate circularity score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The central claim depends on the Gaussian assumption, the tree topology, and the approximate backward mapping, none of which are derived in the paper. Five hyperparameters are fitted or tuned, and the global/local decomposition is an additional structural assumption with no independent evidence.

free parameters (5)
  • λ (sparsity penalty) = selected by eBIC grid search over Λ
    Controls the tradeoff between fit and the number of nonzero off-diagonal entries; grid-searched in synthetic and real experiments.
  • γ (similarity penalty) = selected by eBIC grid search over Γ
    Controls how strongly neighboring populations' precision matrices are pulled together; grid-searched.
  • ν_k (soft-thresholding parameter per population) = selected by eBIC grid search; cluster-specific adjustments in GBM single-cell analysis
    Defines the approximate backward mapping [ST_ν(Σ̂_k)]^{-1}; in the GBM application the authors found a single global value insufficient and tuned per cluster.
  • α (ridge penalty in categorical extension) = 0.01
    Fixed by hand to ensure numerical stability of the dynamic program in the categorical objective.
  • eBIC tilt parameter = not reported (described as fixed constant)
    The extended BIC has a tunable parameter controlling model complexity; the paper states it is fixed but does not give the value.
assumptions (5)
  • domain assumption Each population's gene expression follows a zero-mean multivariate Gaussian distribution.
    Invoked in Section 2 to justify precision-matrix sparsity as conditional independence; standard GMRF assumption.
  • domain assumption The population hypergraph H is a tree.
    Stated in Section 2 as 'a key structural assumption'; required for the O(K^2) dynamic programming solver from [20].
  • standard math The approximate backward mapping F~*(Σ̂_k) = [ST_ν(Σ̂_k)]^{-1} approximates the true precision matrix.
    Adopted from Yang et al. [24], Equation (1); the entire objective (ELEM-0) minimizes deviation from this proxy.
  • standard math The DP algorithm of Bhathena et al. [20] solves the element-wise MIQP subproblems exactly in O(K^2) for tree structures.
    Core computational premise; published in Mathematical Programming but self-cited and not re-derived here.
  • domain assumption Extended BIC selects hyperparameters that generalize to unseen data.
    Used for model selection (Section 2.2); no guarantee that eBIC-optimal parameters preserve edge recovery in high dimensions.
invented entities (1)
  • Global (Θ_global_k) and local (Θ_local_k,c) precision components
    purpose: Model shared network structure across categories plus category-specific deviations, enabling information borrowing when per-category samples are limited.
    Statistical decomposition introduced in Section 2.1; it is a latent modeling construct with no direct falsifiable handle outside the fitted model.

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Cite this review

Pith. "Pith review of Efficient inference of dynamic gene regulatory networks using discrete penalty." pith.science (2026). https://pith.science/paper/T7DYFGIY

@misc{pith2026250723106,
  author       = {Pith},
  title        = {Pith review of: Efficient inference of dynamic gene regulatory networks using discrete penalty},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T7DYFGIY}},
  note         = {Machine review of arXiv:2507.23106}
}
abstract

Gene regulatory networks (GRNs) orchestrate cellular decision making and survival strategies. Inferring the structure of these networks from high-dimensional transcriptomics data is a central challenge in systems biology. Traditional approaches to GRN inference, such as the graphical lasso and its joint extensions, rely on $\ell_1$ penalty to induce sparsity but can bias network recovery and require extensive hyperparameter tuning. Here, we present a scalable framework for the joint inference of dynamic GRNs using a discrete $\ell_0$ penalty, enabling direct and unbiased control over network sparsity. Leveraging recent algorithmic advances, we efficiently solve the resulting mixed-integer optimization problem for populations structured as arbitrary tree hypergraphs, accommodating both continuous and categorical distinctions among biological samples. After validating our method on synthetic benchmarks, we apply it to single-cell and spatial transcriptomics data from glioblastoma (GBM) patient tumors. Our approach reconstructs gene networks across tumor clusters, maps network rewiring along hypoxia gradients, and reveals niche-specific differences between primary and recurrent tumors. By providing a robust and interpretable tool for GRN inference in complex tissues, our work facilitates high-resolution dissection of tumor heterogeneity and adaptation, with broad applicability to emerging large-scale transcriptomic datasets.

Figures

Figures reproduced from arXiv: 2507.23106 by the authors.

Figure 1
Figure 1. Representative scenario for joint network inference across multiple spatial [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Schematic of condition-specific network inference on a global hypergraph [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Comparative performance of the proposed ELEM-0 (with [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Comparison of categorical and standard ELEM-0 across increasing local edge [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Performance comparison of categorical ELEM-0 and standard ELEM-0 at [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Joint network inference reveals shared and population-specific gene regulatory architecture across glioblastoma tumor populations.(A) UMAP embedding of cancer cell clusters across 24 patients (B) Distribution of primary and recurrent tumor cells across clusters (C) Nef…
Figure 7
Figure 7. Figure 7: Supplemenatary to [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Gene regulatory network rewiring along continuous hypoxia gradients in glioblastoma spatial transcriptomics. (A) Annotation of anatomical niches on a representative Visium tissue slide, delineating perivascular, tumor core, and perinecrotic regions. (B) Spatial distrib…
Figure 9
Figure 9. Figure 9: Niche-specific gene regulatory network rewiring in recurrent glioblastoma. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Supplementary to Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators

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Reference graph

Works this paper leans on

103 extracted references · 74 canonical work pages · cited by 1 Pith paper

  1. [20]

    A parametric approach for solving convex quadratic optimization with indicators over trees

    Bhathena A, Fattahi S, G´ omez A, K¨ u¸ c¨ ukyavuz S. A parametric approach for solving convex quadratic optimization with indicators over trees. Mathematical Programming. 2025;212(1):1–31. doi:10.1007/s10107-025-02222-3

    work page doi:10.1007/s10107-025-02222-3 2025

  2. [24]

    Elementary estimators for graphical models

    Yang E, Lozano AC, Ravikumar PK. Elementary estimators for graphical models. Advances in neural information processing systems. 2014;27

    2014

  3. [1]

    Network medicine: a network-based approach to human disease

    Barab´ asi AL, Gulbahce N, Loscalzo J. Network medicine: a network-based approach to human disease. Nature reviews genetics. 2011;12(1):56–68

    2011

  4. [2]

    Profiling cell identity and tissue architecture with single-cell and spatial transcriptomics

    Gulati GS, D’Silva JP, Liu Y, Wang X, Newman AM. Profiling cell identity and tissue architecture with single-cell and spatial transcriptomics. Nature Reviews Molecular Cell Biology. 2025;26:11–31. doi:10.1038/s41580-024-00768-2

    work page doi:10.1038/s41580-024-00768-2 2025

  5. [3]

    Advancements in single-cell RNA sequencing and spatial transcrip- tomics: transforming biomedical research

    Desta M, Birhanu A. Advancements in single-cell RNA sequencing and spatial transcrip- tomics: transforming biomedical research. Acta Biochimica Polonica. 2025;72(1):1–16

    2025

  6. [4]

    The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells

    Trapnell C, et al. The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells. Nature biotechnology. 2014;32(4):381–386

    2014

  7. [5]

    Network-based integration of multi-omics data for prioritizing cancer genes

    Dimitrakopoulos C, et al. Network-based integration of multi-omics data for prioritizing cancer genes. Bioinformatics. 2018;34(14):2441–2448

    2018

  8. [6]

    Topology-based metrics for finding the optimal sparsity in gene regulatory network inference

    Lundqvist N, Garbulowski M, Hillerton T, Sonnhammer EL. Topology-based metrics for finding the optimal sparsity in gene regulatory network inference. Bioinformatics. 2025;41(5):btaf120

    2025

Show all 103 references
  1. [7]

    Optimal Sparsity Selection Based on an Information Criterion for Gene Regulatory Network Inference

    Zhu Y, et al. Optimal Sparsity Selection Based on an Information Criterion for Gene Regulatory Network Inference. Frontiers in Genetics. 2022;13:855770

    2022

  2. [8]

    l {0} sparse inverse covariance estimation

    Marjanovic G, Hero AO. l {0} sparse inverse covariance estimation. IEEE Transactions on Signal Processing. 2015;63(12):3218–3231

    2015

  3. [9]

    Scalable inference of sparsely-changing Gaussian Markov random fields

    Fattahi S, Gomez A. Scalable inference of sparsely-changing Gaussian Markov random fields. Advances in Neural Information Processing Systems. 2021;34:6529–6541

    2021

  4. [10]

    Sparse inverse covariance estimation with the graphical lasso

    Friedman J, Hastie T, Tibshirani R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics. 2008;9(3):432–441. 25/31

    2008

  5. [11]

    The joint graphical lasso for inverse covariance estimation across multiple classes

    Danaher P, Wang P, Witten DM. The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2014;76(2):373–397

    2014

  6. [12]

    Network inference via the time-varying graphical lasso

    Hallac D, Park Y, Boyd S, Leskovec J. Network inference via the time-varying graphical lasso. In: Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining; 2017. p. 205–213

    2017

  7. [13]

    Breakdown in nonlinear regression

    Stromberg AJ, Ruppert D. Breakdown in nonlinear regression. Journal of the American Statistical Association. 1992;87(420):991–997

    1992

  8. [14]

    Robust Regression and Outlier Detection

    Rousseeuw PJ, Leroy AM. Robust Regression and Outlier Detection. John Wiley & Sons; 2005

    2005

  9. [15]

    Deleting outliers in robust regression with mixed integer program- ming

    Zioutas G, Avramidis A. Deleting outliers in robust regression with mixed integer program- ming. Acta Mathematicae Applicatae Sinica. 2005;21:323–334

    2005

  10. [16]

    Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models

    Xu T, Taeb A, K¨ u¸ c¨ ukyavuz S, Shojaie A. Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models. arXiv preprint arXiv:240412592. 2024

    2024

  11. [17]

    Consistent second-order conic integer programming for learning Bayesian networks

    K¨ u¸ c¨ ukyavuz S, Shojaie A, Manzour H, Wei L, Wu HH. Consistent second-order conic integer programming for learning Bayesian networks. Journal of Machine Learning Research. 2023;24(322):1–38

    2023

  12. [18]

    Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

    Manzour H, K¨ u¸ c¨ ukyavuz S, Wu HH, Shojaie A. Integer Programming for Learning Directed Acyclic Graphs from Continuous Data. INFORMS Journal on Optimization. 2021;3(1):46–73

    2021

  13. [19]

    Scalable network estimation with L0 penalty

    Kim J, Zhu H, Wang X, Do KA. Scalable network estimation with L0 penalty. Statistical Analysis and Data Mining: The ASA Data Science Journal. 2021;14(1):18–30

    2021

  14. [21]

    Joint Structural Estimation of Multiple Graphical Models

    Ma J, Michailidis G. Joint Structural Estimation of Multiple Graphical Models. Journal of Machine Learning Research. 2016;17(1):445–474

    2016

  15. [22]

    A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models

    Wang B, Gao J, Qi Y. A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models. In: Singh A, Zhu J, editors. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics. vol. 54 of Proceedings of Machine L...

    2017

  16. [23]

    A constrained ℓ 1 minimization approach to sparse precision matrix estimation

    Cai T, Liu W, Luo X. A constrained ℓ 1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association. 2011;106(494):594–607

    2011

  17. [25]

    Joint estimation of multiple precision matrices with common structures

    Lee W, Liu Y. Joint estimation of multiple precision matrices with common structures. The Journal of Machine Learning Research. 2015;16(1):1035–1062. 26/31

    2015

  18. [26]

    Solution Path of Time-varying Markov Random Fields with Discrete Regularization

    Fattahi S, G´ omez A. Solution Path of Time-varying Markov Random Fields with Discrete Regularization. arXiv preprint arXiv:230713750. 2023

    2023

  19. [27]

    BEST SUBSET SELECTION VIA A MODERN OPTIMIZATION LENS

    BERTSIMAS D, KING A, MAZUMDER R. BEST SUBSET SELECTION VIA A MODERN OPTIMIZATION LENS. The Annals of Statistics. 2016;44(2):813–852

    2016

  20. [28]

    Certifiably optimal sparse regression via mixed- integer optimization

    Bertsimas D, Pauphilet J, Van Parys B. Certifiably optimal sparse regression via mixed- integer optimization. Journal of Machine Learning Research. 2020;21(1):1–53

    2020

  21. [29]

    On polynomial-time solvability of combinatorial Markov random fields

    Han S, G´ omez A, Pang JS. On polynomial-time solvability of combinatorial Markov random fields. arXiv preprint arXiv:220913161. 2022

    2022

  22. [30]

    Graph learning with tridiagonal Hessians: Efficient algorithms and applications

    Liu Y, et al. Graph learning with tridiagonal Hessians: Efficient algorithms and applications. Annals of Statistics. 2023

    2023

  23. [31]

    Real-time solution of quadratic optimization problems with banded matrices and indicator variables

    Gomez A, Han S, Lozano L. Real-time solution of quadratic optimization problems with banded matrices and indicator variables. arXiv preprint arXiv:240503051. 2024

    2024

  24. [32]

    Efficient inference of spatially-varying Gaussian Markov random fields with applications in gene regulatory networks

    Ravikumar V, Xu T, Al-Holou WN, Fattahi S, Rao A. Efficient inference of spatially-varying Gaussian Markov random fields with applications in gene regulatory networks. IEEE/ACM transactions on computational biology and bioinformatics. 2023;20(5):2920–2932

    2023

  25. [33]

    SCANPY: large-scale single-cell gene expression data analysis

    Wolf F A, Angerer P, Theis FJ. SCANPY: large-scale single-cell gene expression data analysis. Genome biology. 2018;19:1–5

    2018

  26. [34]

    Dictionary learning for integrative, multimodal and scalable single-cell analysis

    Hao Y, Stuart T, Kowalski MH, Choudhary S, Hoffman P, Hartman A, et al. Dictionary learning for integrative, multimodal and scalable single-cell analysis. Nature biotechnology. 2024;42(2):293–304

    2024

  27. [35]

    A comparison of single-cell trajectory inference methods

    Saelens W, Cannoodt R, Todorov H, Saeys Y. A comparison of single-cell trajectory inference methods. Nature Biotechnology. 2019;37(5):547–554. doi:10.1038/s41587-019-0071-9

    2019 doi

  28. [36]

    Graphical models, exponential families, and variational inference

    Wainwright MJ, Jordan MI, et al. Graphical models, exponential families, and variational inference. Foundations and Trends in Machine Learning. 2008;1(1–2):1–305

    2008

  29. [37]

    Computer solution of large sparse positive definite

    George A, Liu JW. Computer solution of large sparse positive definite. Prentice Hall Professional Technical Reference; 1981

    1981

  30. [38]

    Chordal graphs and semidefinite optimization

    Vandenberghe L, Andersen MS. Chordal graphs and semidefinite optimization. Foundations and Trends in Optimization. 2015;1(4):241–433

    2015

  31. [39]

    Model selection and estimation in the Gaussian graphical model

    Yuan M, Lin Y. Model selection and estimation in the Gaussian graphical model. Biometrika. 2007;94(1):19–35

    2007

  32. [40]

    Extended Bayesian information criteria for Gaussian graphical models

    Foygel R, Drton M. Extended Bayesian information criteria for Gaussian graphical models. Advances in neural information processing systems. 2010;23

    2010

  33. [41]

    A fast and scalable joint estimator for learning multiple related sparse Gaussian graphical models

    Wang B, Gao J, Qi Y. A fast and scalable joint estimator for learning multiple related sparse Gaussian graphical models. In: Artificial Intelligence and Statistics. PMLR; 2017. p. 1168–1177

    2017

  34. [42]

    GRNBoost2 and Arboreto: efficient and scalable inference of gene regulatory networks

    Moerman T, Aibar Santos S, Bravo Gonz´ alez-Blas C, Simm J, Moreau Y, Aerts J, et al. GRNBoost2 and Arboreto: efficient and scalable inference of gene regulatory networks. Bioinformatics. 2019;35(12):2159–2161. 27/31

    2019

  35. [43]

    Statistical mechanics of complex networks

    Albert R, Barab´ asi AL. Statistical mechanics of complex networks. Reviews of modern physics. 2002;74(1):47

    2002

  36. [44]

    Glioblastoma heterogeneity at single cell resolution

    Eisenbarth D, Wang YA. Glioblastoma heterogeneity at single cell resolution. Oncogene. 2023;42(27):2155–2165

    2023

  37. [45]

    An integrative model of cellular states, plasticity, and genetics for glioblastoma

    Neftel C, Laffy J, Filbin MG, Hara T, Shore ME, Rahme GJ, et al. An integrative model of cellular states, plasticity, and genetics for glioblastoma. Cell. 2019;178(4):835–849

    2019

  38. [46]

    Pathway-based classi- fication of glioblastoma uncovers a mitochondrial subtype with therapeutic vulnerabilities

    Garofano L, Migliozzi S, Oh YT, D’Angelo F, Najac RD, Ko A, et al. Pathway-based classi- fication of glioblastoma uncovers a mitochondrial subtype with therapeutic vulnerabilities. Nature Cancer. 2021;2(2):141–156

    2021

  39. [47]

    Cancer cell heterogeneity and plasticity: A paradigm shift in glioblastoma

    Yabo YA, Niclou SP, Golebiewska A. Cancer cell heterogeneity and plasticity: A paradigm shift in glioblastoma. Neuro-oncology. 2022;24(5):669–682

    2022

  40. [48]

    Collagen in the central nervous system: contributions to neurodegeneration and promise as a therapeutic target

    Wareham LK, Baratta RO, Del Buono BJ, Schlumpf E, Calkins DJ. Collagen in the central nervous system: contributions to neurodegeneration and promise as a therapeutic target. Molecular Neurodegeneration. 2024;19(1):11

    2024

  41. [49]

    Phosphorylation, dephosphorylation, and multiprotein assemblies regulate dynamic behavior of neuronal cytoskeleton: a mini-review

    Kurochkina N, Bhaskar M, Yadav SP, Pant HC. Phosphorylation, dephosphorylation, and multiprotein assemblies regulate dynamic behavior of neuronal cytoskeleton: a mini-review. Frontiers in Molecular Neuroscience. 2018;11:373

    2018

  42. [50]

    Phenotypic and functional consequences of haploinsufficiency of genes from exocyst and retinoic acid pathway due to a recurrent microdeletion of 2p13

    Wen J, Lopes F, Soares G, Farrell SA, Nelson C, Qiao Y, et al. Phenotypic and functional consequences of haploinsufficiency of genes from exocyst and retinoic acid pathway due to a recurrent microdeletion of 2p13. 2. Orphanet journal of rare diseases. 2013;8:1–12

    2013

  43. [51]

    Exploring the pathological mechanisms underlying Cohen syndrome

    Vacca F, Yalcin B, Ansar M. Exploring the pathological mechanisms underlying Cohen syndrome. Frontiers in neuroscience. 2024;18:1431400

    2024

  44. [52]

    Single-cell transcriptomics unveils gene regulatory network plasticity

    Iacono G, Massoni-Badosa R, Heyn H. Single-cell transcriptomics unveils gene regulatory network plasticity. Genome biology. 2019;20:1–20

    2019

  45. [53]

    Transcription factor BACH1 in cancer: roles, mechanisms, and prospects for targeted therapy

    Hu D, Zhang Z, Luo X, Li S, Jiang J, Zhang J, et al. Transcription factor BACH1 in cancer: roles, mechanisms, and prospects for targeted therapy. Biomarker Research. 2024;12(1):21

    2024

  46. [54]

    Single-cell multi-omics sequencing uncovers region-specific plasticity of glioblastoma for complementary therapeutic targeting

    Wang X, Sun Q, Liu T, Lu H, Lin X, Wang W, et al. Single-cell multi-omics sequencing uncovers region-specific plasticity of glioblastoma for complementary therapeutic targeting. Science Advances. 2024;10(47):eadn4306

    2024

  47. [55]

    TopicNet: a framework for measuring transcriptional regulatory network change

    Lou S, Li T, Kong X, Zhang J, Liu J, Lee D, et al. TopicNet: a framework for measuring transcriptional regulatory network change. Bioinformatics. 2020;36(Supplement 1):i474–i481

    2020

  48. [56]

    Inference of cell type-specific gene regulatory networks on cell lineages from single cell omic datasets

    Zhang S, Pyne S, Pietrzak S, Halberg S, McCalla SG, Siahpirani AF, et al. Inference of cell type-specific gene regulatory networks on cell lineages from single cell omic datasets. Nature Communications. 2023;14(1):3064

    2023

  49. [57]

    topicmodels: An R package for fitting topic models

    Gr¨ un B, Hornik K. topicmodels: An R package for fitting topic models. Journal of statistical software. 2011;40:1–30

    2011

  50. [58]

    Package ‘ldatuning’; 2016

    Nikita M, Nikita MM. Package ‘ldatuning’; 2016. 28/31

    2016

  51. [59]

    ZHX2 Interacts with Ephrin-B and regulates neural progenitor maintenance in the developing cerebral cortex

    Wu C, Qiu R, Wang J, Zhang H, Murai K, Lu Q. ZHX2 Interacts with Ephrin-B and regulates neural progenitor maintenance in the developing cerebral cortex. Journal of Neuroscience. 2009;29(23):7404–7412

    2009

  52. [60]

    Transcription factor AP2 epsilon (Tfap2e) regulates neural crest specification in Xenopus

    Hong CS, Devotta A, Lee YH, Park BY, Saint-Jeannet JP. Transcription factor AP2 epsilon (Tfap2e) regulates neural crest specification in Xenopus. Developmental neurobiology. 2014;74(9):894–906

    2014

  53. [61]

    The expanding roles of Nr6a1 in development and evolution

    Li J, Mascarinas P, McGlinn E. The expanding roles of Nr6a1 in development and evolution. Frontiers in Cell and Developmental Biology. 2024;12:1357968

    2024

  54. [62]

    Current understanding of hypoxia in glioblastoma multiforme and its response to immunotherapy

    Park JH, Lee HK. Current understanding of hypoxia in glioblastoma multiforme and its response to immunotherapy. Cancers. 2022;14(5):1176

    2022

  55. [63]

    Integrative spatial analysis reveals a multi-layered organization of glioblastoma

    Greenwald AC, Darnell NG, Hoefflin R, Simkin D, Mount CW, Castro LNG, et al. Integrative spatial analysis reveals a multi-layered organization of glioblastoma. Cell. 2024;187(10):2485– 2501

    2024

  56. [64]

    The molecular signatures database hallmark gene set collection

    Liberzon A, Birger C, Thorvaldsd´ ottir H, Ghandi M, Mesirov JP, Tamayo P. The molecular signatures database hallmark gene set collection. Cell systems. 2015;1(6):417–425

    2015

  57. [65]

    Pathway centric analysis for single-cell RNA-seq and spatial transcriptomics data with GSDensity

    Liang Q, Huang Y, He S, Chen K. Pathway centric analysis for single-cell RNA-seq and spatial transcriptomics data with GSDensity. Nature communications. 2023;14(1):8416

    2023

  58. [66]

    Epithelial-mesenchymal transition in glioblastoma progression

    Iwadate Y. Epithelial-mesenchymal transition in glioblastoma progression. Oncology letters. 2016;11(3):1615–1620

    2016

  59. [67]

    Adapt to persist: Glioblas- toma microenvironment and epigenetic regulation on cell plasticity

    Uribe D, Niechi I, Rackov G, Erices JI, San Mart ´ ın R, Quezada C. Adapt to persist: Glioblas- toma microenvironment and epigenetic regulation on cell plasticity. Biology. 2022;11(2):313

    2022

  60. [68]

    The role of hypoxia in glioblastoma invasion

    Monteiro AR, Hill R, Pilkington GJ, Madureira PA. The role of hypoxia in glioblastoma invasion. Cells. 2017;6(4):45

    2017

  61. [69]

    Cancer genetics and genomics of human FOX family genes

    Katoh M, Igarashi M, Fukuda H, Nakagama H, Katoh M. Cancer genetics and genomics of human FOX family genes. Cancer letters. 2013;328(2):198–206

    2013

  62. [70]

    Har- monized single-cell landscape, intercellular crosstalk and tumor architecture of glioblastoma

    Ruiz-Moreno C, Salas SM, Samuelsson E, Brandner S, Kranendonk ME, Nilsson M, et al. Har- monized single-cell landscape, intercellular crosstalk and tumor architecture of glioblastoma. BioRxiv. 2022; p. 2022–08

    2022

  63. [71]

    Hypoxia coordinates the spatial landscape of myeloid cells within glioblastoma to affect survival

    Haley MJ, Bere L, Minshull J, Georgaka S, Garcia-Martin N, Howell G, et al. Hypoxia coordinates the spatial landscape of myeloid cells within glioblastoma to affect survival. Science Advances. 2024;10(20):eadj3301

    2024

  64. [72]

    Multiomics analyses reveal DARS1-AS1/YBX1–controlled posttranscriptional circuits promoting glioblastoma tumori- genesis/radioresistance

    Zheng C, Wei Y, Zhang Q, Sun M, Wang Y, Hou J, et al. Multiomics analyses reveal DARS1-AS1/YBX1–controlled posttranscriptional circuits promoting glioblastoma tumori- genesis/radioresistance. Science advances. 2023;9(31):eadf3984

    2023

  65. [73]

    Spatially resolved multi-omics deciphers bidirectional tumor-host interdependence in glioblastoma

    Ravi VM, Will P, Kueckelhaus J, Sun N, Joseph K, Sali´ e H, et al. Spatially resolved multi-omics deciphers bidirectional tumor-host interdependence in glioblastoma. Cancer cell. 2022;40(6):639–655

    2022

  66. [74]

    Chromatin remodeler HELLS maintains glioma stem cells through E2F3 and MYC

    Zhang G, Dong Z, Prager BC, Kim LJ, Wu Q, Gimple RC, et al. Chromatin remodeler HELLS maintains glioma stem cells through E2F3 and MYC. JCI insight. 2019;4(7):e126140. 29/31

    2019

  67. [75]

    Glioblastoma stem-like cells, metabolic strategy to kill a challenging target

    Garnier D, Renoult O, Alves-Guerra MC, Paris F, Pecqueur C. Glioblastoma stem-like cells, metabolic strategy to kill a challenging target. Frontiers in oncology. 2019;9:118

    2019

  68. [76]

    Tumor cell plasticity, heterogene- ity, and resistance in crucial microenvironmental niches in glioma

    Jung E, Osswald M, Ratliff M, Dogan H, Xie R, Weil S, et al. Tumor cell plasticity, heterogene- ity, and resistance in crucial microenvironmental niches in glioma. Nature communications. 2021;12(1):1014

    2021

  69. [77]

    Mechanism of notch signaling pathway in malignant progression of glioblastoma and targeted therapy

    Wang S, Gu S, Chen J, Yuan Z, Liang P, Cui H. Mechanism of notch signaling pathway in malignant progression of glioblastoma and targeted therapy. Biomolecules. 2024;14(4):480

    2024

  70. [78]

    Identification of key genes involved in the recurrence of glioblastoma multiforme using weighted gene co-expression network analysis and differential expression analysis

    Ren P, Wang J, Li L, Lin X, Wu G, Chen J, et al. Identification of key genes involved in the recurrence of glioblastoma multiforme using weighted gene co-expression network analysis and differential expression analysis. Bioengineered. 2021;12(1):3188–3200

    2021

  71. [79]

    Transcription factor EHF drives cholangio- carcinoma development through transcriptional activation of glioma-associated oncogene homolog 1 and chemokine CCL2

    Luo Y, Li Z, Zhu H, Lu J, Lei Z, Su C, et al. Transcription factor EHF drives cholangio- carcinoma development through transcriptional activation of glioma-associated oncogene homolog 1 and chemokine CCL2. MedComm. 2024;5(5):e535

    2024

  72. [80]

    Vascular regulation of glioma stem-like cells: a balancing act

    Brooks LJ, Parrinello S. Vascular regulation of glioma stem-like cells: a balancing act. Current Opinion in Neurobiology. 2017;47:8–15

    2017

  73. [81]

    Tumor cell plasticity, heterogeneity, and resistance in crucial microenvironments of glioblastoma

    Wang L, Babikir H, M¨ uller S, Yagnik G, Shamardani K, Catalan F, et al. Tumor cell plasticity, heterogeneity, and resistance in crucial microenvironments of glioblastoma. Nature Communications. 2021;12:5376. doi:10.1038/s41467-021-21117-3

    2021 doi

  74. [82]

    Computational modelling of perivascular- niche dynamics for the optimization of glioblastoma treatment schedules

    Ghaffari L, Mumenthaler SM, Sadeghi H, et al. Computational modelling of perivascular- niche dynamics for the optimization of glioblastoma treatment schedules. Nature Biomedical Engineering. 2021;5:964–978. doi:10.1038/s41551-021-00756-2

    2021 doi

  75. [83]

    Joint inference of gene regulatory networks from multiple single-cell RNA-seq datasets

    Wang X, et al. Joint inference of gene regulatory networks from multiple single-cell RNA-seq datasets. Scientific Reports. 2016;6:20533. doi:10.1038/srep20533

    2016 doi

  76. [84]

    Adaptive penalization improves gene regulatory network inference from single-cell RNA-seq data

    Zhang Y, et al. Adaptive penalization improves gene regulatory network inference from single-cell RNA-seq data. Nature Communications. 2021;12:8687. doi:10.1038/s41467-021- 28970-9

    2021 doi

  77. [85]

    Challenges and advances in gene regulatory network infer- ence from single-cell data

    Smith J, Doe A. Challenges and advances in gene regulatory network infer- ence from single-cell data. Computational Biology and Chemistry. 2022;100:107682. doi:10.1016/j.compbiolchem.2022.107682

    2022

  78. [86]

    Single-cell multi-omics reveals regulatory programs in glioblastoma

    Lee S, et al. Single-cell multi-omics reveals regulatory programs in glioblastoma. Science Advances. 2024;10(5):eabc1234. doi:10.1126/sciadv.abc1234

    2024 doi

  79. [87]

    Deep learning for gene regulatory network inference from single-cell data

    Wang X, et al. Deep learning for gene regulatory network inference from single-cell data. Nature Machine Intelligence. 2022;4:1234–1245. doi:10.1038/s42256-022-00567-8

    2022 doi

  80. [88]

    BACH1 as a potential target for immunotherapy in glioblastomas

    Li Y, et al. BACH1 as a potential target for immunotherapy in glioblastomas. Frontiers in Oncology. 2022;12:825252. doi:10.3389/fonc.2022.825252

    2022

  81. [90]

    BACH1 promotes temozolomide resistance in glioblastoma

    Zhang X, et al. BACH1 promotes temozolomide resistance in glioblastoma. Scientific Reports. 2016;6:39743. doi:10.1038/srep39743

    2016 doi

  82. [91]

    Heterogeneity of glioblastoma stem cells in the context of the tumor microenvironment

    Pombo Antunes AR, et al. Heterogeneity of glioblastoma stem cells in the context of the tumor microenvironment. Frontiers in Oncology. 2022;12:1022716. doi:10.3389/fonc.2022.1022716

    2022

  83. [92]

    Glioma Stem Cell Niches in Human Glioblastoma Are Periarteriolar

    Hira VVV, et al. Glioma Stem Cell Niches in Human Glioblastoma Are Periarteriolar. Cancers. 2018;10(4):96. doi:10.3390/cancers10040096

    2018 doi

  84. [93]

    Glioblastoma: Microenvironment and Niche Concept

    Pacioni S, et al. Glioblastoma: Microenvironment and Niche Concept. Frontiers in Immunol- ogy. 2018;9:2496. doi:10.3389/fimmu.2018.02496

    2018

  85. [94]

    Targeting the Glioblastoma Perivascular Stem Cell Niche

    Calabrese C, Poppleton H, et al. Targeting the Glioblastoma Perivascular Stem Cell Niche. Cancer Cell. 2007;11(1):69–82. doi:10.1016/j.ccr.2006.11.020

    2007 doi

  86. [95]

    Glioblastoma: Defining Tumor Niches

    Charles N, Holland EC. Glioblastoma: Defining Tumor Niches. Cancer Journal. 2015;21(4):254–261. doi:10.1097/PPO.0000000000000131

    2015 doi

  87. [96]

    Tumor microenvironment in glioblastoma: Current and emerging concepts

    Yue Q, et al. Tumor microenvironment in glioblastoma: Current and emerging concepts. Frontiers in Oncology. 2023;13:10034917. doi:10.3389/fonc.2023.10034917

    2023

  88. [97]

    Covariate-adjusted construction of gene regulatory networks using generalized linear models

    Chatrabgoun O, Ganjtabesh M, Sadeghi M. Covariate-adjusted construction of gene regulatory networks using generalized linear models. PLOS ONE. 2025;20(1):e0309556. doi:10.1371/journal.pone.0309556

    2025 doi

  89. [98]

    Data integration for inferring context-specific gene regulatory networks

    Baur B, Shin J, Zhang S, Roy S. Data integration for inferring context-specific gene regulatory networks. Current opinion in systems biology. 2020;23:38–46

    2020

  90. [99]

    Leveraging chromatin accessibility for transcriptional regulatory network inference in T Helper 17 Cells

    Miraldi ER, Pokrovskii M, Watters A, Castro DM, De Veaux N, Hall JA, et al. Leveraging chromatin accessibility for transcriptional regulatory network inference in T Helper 17 Cells. Genome Research. 2019;29(3):449–463. doi:10.1101/gr.238253.118

    2019 doi

  91. [100]

    Dissecting cell identity via network-based in silico perturbation of single-cell transcriptomes

    Kamimoto K, et al. Dissecting cell identity via network-based in silico perturbation of single-cell transcriptomes. Nature Communications. 2023;14:12345. doi:10.1038/s41467-023- 36137-1

    2023 doi

  92. [101]

    SCENIC+: single-cell multiomic inference of enhancers and gene regulatory networks

    Bravo Gonz´ alez-Blas C, De Winter S, Hulselmans G, Hecker N, Matetovici I, Christiaens V, et al. SCENIC+: single-cell multiomic inference of enhancers and gene regulatory networks. Nature methods. 2023;20(9):1355–1367

    2023

  93. [102]

    Harnessing the power of single-cell multi-omic data for gene regulatory network inference

    Kim D, Tran A, Kim HJ, Lin Y, Yang JYH, Yang P. Harnessing the power of single-cell multi-omic data for gene regulatory network inference. npj Systems Biology and Applications. 2023;9(1):51. doi:10.1038/s41540-023-00312-6

    2023 doi

  94. [103]

    Predicting transcriptional outcomes of novel multigene perturbations with GEARS

    Roohani Y, Huang K, Leskovec J. Predicting transcriptional outcomes of novel multigene perturbations with GEARS. Nature Biotechnology. 2024;42(6):927–935. doi:10.1038/s41587- 023-01905-6

    2024 doi

  95. [104]

    A mini-review on perturbation modelling across single-cell omic modalities

    Gavriilidis GI, Vasileiou V, Orfanou A, Ishaque N, Psomopoulos F. A mini-review on perturbation modelling across single-cell omic modalities. Computational and Structural Biotechnology Journal. 2024;23:1886–1896. doi:10.1016/j.csbj.2024.04.058. 31/31

    2024 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.