Structural Inference; Benchmark; AI4Science; Interaction Graphs; Dynamical Systems
Abstract :
[en] Understanding complex dynamical systems begins with identifying their topological structures, which expose the organization of the systems. This requires robust structural inference methods that can deduce structure from observed behavior. However, existing methods are often domain-specific and lack a standardized, objective comparison framework. We address this gap by benchmarking 13 structural inference methods from various disciplines on simulations representing two types of dynamics and 11 interaction graph models, supplemented by a biological experimental dataset to mirror real-world application. We evaluated the methods for accuracy, scalability, robustness, and sensitivity to graph properties. Our findings indicate that deep learning methods excel with multi-dimensional data, while classical statistics and information theory based approaches are notably accurate and robust. Additionally, performance correlates positively with the graph's average shortest path length. This benchmark should aid researchers in selecting suitable methods for their specific needs and stimulate further methodological innovation.
Disciplines :
Computer science
Author, co-author :
WANG, Aoran ✱; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Computer Science > Team Jun PANG
TONG, Tsz Pan ✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
MIZERA, Andrzej; IDEAS-NCBR > IDEAS-NCBR ; Institute of Informatics > Faculty of Mathematics, Informatics and Mechanics > University of Warsaw
PANG, Jun ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
✱ These authors have contributed equally to this work.
External co-authors :
yes
Language :
English
Title :
Benchmarking Structural Inference Methods for Interacting Dynamical Systems with Synthetic Data
Publication date :
26 September 2024
Event name :
38th Conference on Neural Information Processing Systems
M. Ahmed, S. Karagiorgou, D. Pfoser, and C. Wenk. A comparison and evaluation of map construction algorithms using vehicle tracking data. GeoInformatica, 19:601-632, 2015.
S. Aibar, C. B. González-Blas, T. Moerman, V. A. Huynh-Thu, H. Imrichova, G. Hulselmans, F. Rambow, J.-C. Marine, P. Geurts, J. Aerts, et al. SCENIC: single-cell regulatory network inference and clustering. Nature Methods, 14(11):1083-1086, 2017.
A. A. Alemi, I. Fischer, J. V. Dillon, and K. Murphy. Deep variational information bottleneck. In Proceedings of the 5th International Conference on Learning Representations (ICLR), 2017.
F. Alet, E. Weng, T. Lozano-Pérez, and L. P. Kaelbling. Neural relational inference with fast modular meta-learning. In Advances in Neural Information Processing Systems 32 (NeurIPS), 2019.
A. F. Ansari, K. Benidis, R. Kurle, A. C. Turkmen, H. Soh, A. Smola, B. Wang, and T. Januschowski. Deep explicit duration switching models for time series. In Advances in Neural Information Processing Systems 34 (NeurIPS), 2021.
C. K. Assaad, E. Devijver, and E. Gaussier. Survey and evaluation of causal discovery methods for time series. Journal of Artificial Intelligence Research, 73:767-819, 2022.
A.-L. Barabási. Network science. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1987):20120375, 2013.
B. Barzel, A. Sharma, and A.-L. Barabási. Graph theory properties of cellular networks. Handbook of Systems Biology: Concepts and Insights, pages 177-193, 2012.
P. Bellot, C. Olsen, P. Salembier, A. Oliveras-Vergés, and P. E. Meyer. NetBenchmark: a bioconductor package for reproducible benchmarks of gene regulatory network inference. BMC Bioinformatics, 16:1-15, 2015.
M. Bennasar, Y. Hicks, and R. Setchi. Feature selection using joint mutual information maximisation. Expert Systems with Applications, 42(22):8520-8532, 2015.
M. Bentriou. Statistical Inference and Verification of Chemical Reaction Networks. PhD thesis, Université Paris-Saclay, 2021.
J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah. Julia: A fresh approach to numerical computing. SIAM review, 59(1):65-98, 2017.
R. Bhattacharya, T. Nagarajan, D. Malinsky, and I. Shpitser. Differentiable causal discovery under unmeasured confounding. In Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS), pages 2314-2322. PMLR, 2021.
J. Biagioni and J. Eriksson. Inferring road maps from global positioning system traces: Survey and comparative evaluation. Transportation Research Record, 2291(1):61-71, 2012.
G. Brasó and L. Leal-Taixé. Learning a neural solver for multiple object tracking. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 6247-6257, 2020.
A. Breskin, S. R. Cole, and M. G. Hudgens. A practical example demonstrating the utility of single-world intervention graphs. Epidemiology, 29(3):e20, 2018.
T. E. Chan, M. P. Stumpf, and A. C. Babtie. Gene regulatory network inference from single-cell data using multivariate information measures. Cell Systems, 5(3):251-267, 2017.
P. Chao, W. Hua, R. Mao, J. Xu, and X. Zhou. A survey and quantitative study on map inference algorithms from GPS trajectories. IEEE Transactions on Knowledge and Data Engineering, 34(1):15-28, 2022.
S. Chen, J. Wang, and G. Li. Neural relational inference with efficient message passing mechanisms. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 7055-7063, 2021.
T. Chen and C. Guestrin. XGBoost: A scalable tree boosting system. In Proceedings of the 22nd ACM International Conference on Knowledge Discovery and Data Mining (KDD), pages 785-794. ACM, 2016.
Y. Cheng, R. Yang, T. Xiao, Z. Li, J. Suo, K. He, and Q. Dai. CUTS: neural causal discovery from irregular time-series data. In Proceedings of the 11th International Conference on Learning Representations (ICLR), 2023.
M. Ö. Cingiz, G. Biricik, and B. Diri. The performance comparison of gene co-expression networks of breast and prostate cancer using different selection criteria. Interdisciplinary Sciences: Computational Life Sciences, 13(3):500-510, 2021.
A. Cini, D. Zambon, and C. Alippi. Sparse graph learning from spatiotemporal time series. Journal of Machine Learning Research, 24(242):1-36, 2023.
R. Ciric, D. H. Wolf, J. D. Power, D. R. Roalf, G. L. Baum, K. Ruparel, R. T. Shinohara, M. A. Elliott, S. B. Eickhoff, C. Davatzikos, et al. Benchmarking of participant-level confound regression strategies for the control of motion artifact in studies of functional connectivity. Neuroimage, 154:174-187, 2017.
D. Colombo, M. H. Maathuis, et al. Order-independent constraint-based causal structure learning. Journal of Machine Learning Research, 15(1):3741-3782, 2014.
D. P. Cook and B. C. Vanderhyden. Context specificity of the EMT transcriptional response. Nature Communications, 11(1):2142, 2020.
B. Cummins, T. Gedeon, and K. Spendlove. On the efficacy of state space reconstruction methods in determining causality. SIAM Journal on Applied Dynamical Systems, 14(1): 335-381, 2015.
A. Das and I. R. Fiete. Systematic errors in connectivity inferred from activity in strongly recurrent networks. Nature Neuroscience, 23(10):1286-1296, Oct 2020.
W. de Nooy. Social Network Analysis, Graph Theoretical Approaches to, page 8231-8245. Springer, 2009.
A. Deshpande, L.-F. Chu, R. Stewart, and A. Gitter. Network inference with granger causality ensembles on single-cell transcriptomics. Cell Reports, 38(6):110333, 2022.
A. Dionisio, R. Menezes, and D. A. Mendes. Mutual information: a measure of dependency for nonlinear time series. Physica A: Statistical Mechanics and its Applications, 344(1-2): 326-329, 2004.
E. Estrada. The Structure of Complex Networks: Theory and Applications. Oxford University Press, 10 2011. ISBN 9780199591756.
J. J. Faith, B. Hayete, J. T. Thaden, I. Mogno, J. Wierzbowski, G. Cottarel, S. Kasif, J. J. Collins, and T. S. Gardner. Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles. PLoS Biology, 5(1):e8, 2007.
Y. Freund and R. E. Schapire. A desicion-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55:119-139, 1997.
K. J. Friston, L. Harrison, and W. Penny. Dynamic causal modelling. Neuroimage, 19(4): 1273-1302, 2003.
F. N. Fritsch and J. Butland. A method for constructing local monotone piecewise cubic interpolants. SIAM Journal on Scientific Computing, 5(2):300-304, 1984.
T. Gebru, J. Morgenstern, B. Vecchione, J. W. Vaughan, H. Wallach, H. D. Iii, and K. Crawford. Datasheets for datasets. Communications of the ACM, 64(12):86-92, 2021.
P. Geurts, D. Ernst, and L. Wehenkel. Extremely randomized trees. Machine Learning, 63: 3-42, 2006.
Y. Gong, G. Liu, Y. Xue, R. Li, and L. Meng. A survey on dataset quality in machine learning. Inf. Softw. Technol., 162:107268, 2023.
J. Gu, F. Fu, and Q. Zhou. Penalized estimation of directed acyclic graphs from discrete data. Statistics and Computing, 29(1):161-176, 2019.
Z. Guo, W. Shiao, S. Zhang, Y. Liu, N. V. Chawla, N. Shah, and T. Zhao. Linkless link prediction via relational distillation. In Proceedings of the 40th International Conference on Machine Learning (ICML), pages 12012-12033. PMLR, 2023.
S. Ha and H. Jeong. Unraveling hidden interactions in complex systems with deep learning. Scientific Reports, 11(1):1-13, 2021.
A. A. Hagberg, D. A. Schult, and P. J. Swart. Exploring network structure, dynamics, and function using NetworkX. In Proceedings of the 7th Python in Science Conference, pages 11-15, 2008.
F. K. Hamey, S. Nestorowa, S. J. Kinston, D. G. Kent, N. K. Wilson, and B. Göttgens. Reconstructing blood stem cell regulatory network models from single-cell molecular profiles. Proceedings of the National Academy of Sciences, 114(23):5822-5829, 2017.
C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. E. Oliphant. Array programming with NumPy. Nature, 585(7825):357-362, 2020.
A.-C. Haury, F. Mordelet, P. Vera-Licona, and J.-P. Vert. TIGRESS: trustful inference of gene regulation using stability selection. BMC Systems Biology, 6(1):1-17, 2012.
T. K. Ho. Random decision forests. In Proceedings of 3rd International Conference on Document Analysis and Recognition (ICDAR), pages 278-282. IEEE, 1995.
W. Huang, G. Wan, M. Ye, and B. Du. Federated graph semantic and structural learning. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI), pages 3830-3838, 2023.
W. Huber, V. J. Carey, R. Gentleman, S. Anders, M. Carlson, B. S. Carvalho, H. C. Bravo, S. Davis, L. Gatto, T. Girke, R. Gottardo, F. Hahne, K. D. Hansen, R. A. Irizarry, M. Lawrence, M. I. Love, J. MacDonald, V. Obenchain, A. K. Ole's, H. Pag'es, A. Reyes, P. Shannon, G. K. Smyth, D. Tenenbaum, L. Waldron, and M. Morgan. Orchestrating high-throughput genomic analysis with Bioconductor. Nature Methods, 12(2):115-121, 2015.
V. A. Huynh-Thu and P. Geurts. dynGENIE3: dynamical GENIE3 for the inference of gene networks from time series expression data. Scientific Reports, 8(1):3384, 2018.
V. A. Huynh-Thu and G. Sanguinetti. Combining tree-based and dynamical systems for the inference of gene regulatory networks. Bioinformatics, 31(10):1614-1622, 2015.
V. A. Huynh-Thu, A. Irrthum, L. Wehenkel, and P. Geurts. Inferring regulatory networks from expression data using tree-based methods. PloS One, 5(9):e12776, 2010.
A. Jaber, M. Kocaoglu, K. Shanmugam, and E. Bareinboim. Causal discovery from soft interventions with unknown targets: Characterization and learning. In Advances in Neural Information Processing Systems 33 (NeurIPS), 2020.
C. Jansen, R. N. Ramirez, N. C. El-Ali, D. Gomez-Cabrero, J. Tegner, M. Merkenschlager, A. Conesa, and A. Mortazavi. Building gene regulatory networks from scATAC-seq and scRNA-seq using linked self organizing maps. PLoS computational biology, 15(11):e1006555, 2019.
J. Jeong, J. C. Gore, and B. S. Peterson. Mutual information analysis of the EEG in patients with Alzheimer's disease. Clinical Neurophysiology, 112(5):827-835, 2001.
G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, and T.-Y. Liu. LightGBM: A highly efficient gradient boosting decision tree. In Advances in Neural Information Processing Systems 30 (NIPS), 2017.
S. Kim. ppcor: an R package for a fast calculation to semi-partial correlation coefficients. Communications for Statistical Applications and Methods, 22(6):665, 2015.
T. Kipf, E. Fetaya, K.-C. Wang, M. Welling, and R. Zemel. Neural relational inference for interacting systems. In Proceedings of the 35th International Conference on Machine Learning (ICML), pages 2688-2697. PMLR, 2018.
M. Kofinas, N. S. Nagaraja, and E. Gavves. Roto-translated local coordinate frames for interacting dynamical systems. In Advances in Neural Information Processing Systems 34 (NeurIPS), 2021.
M. Kofinas, E. J. Bekkers, N. S. Nagaraja, and E. Gavves. Latent Field Discovery in Interacting Dynamical Systems with Neural Fields. In Advances in Neural Information Processing Systems 36 (NeurIPS), 2023.
J. Kwapień and S. Drozdz. Physical approach to complex systems. Physics Reports, 515(3): 115-226, 2012.
J. Li, H. Ma, Z. Zhang, J. Li, and M. Tomizuka. Spatio-temporal graph dual-attention network for multi-agent prediction and tracking. IEEE Transactions on Intelligent Transportation Systems, 23(8):10556-10569, 2022.
S. W. Linderman*, M. J. Johnson*, A. C. Miller, R. P. Adams, D. M. Blei, and L. Paninski. Bayesian learning and inference in recurrent switching linear dynamical systems. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS), pages 914-922. PMLR, 2017.
Y. Liu, S. Magliacane, M. Kofinas, and E. Gavves. Graph switching dynamical systems. In Proceedings of the 40th International Conference on Machine Learning (ICML), pages 21867-21883. PMLR, 2023.
Y. Liu, S. Magliacane, M. Kofinas, and S. Gavves. Amortized equation discovery in hybrid dynamical systems. In Forty-first International Conference on Machine Learning, ICML 2024. PMLR, 2024.
Z.-Q. Liu, R. F. Betzel, and B. Misic. Benchmarking functional connectivity by the structure and geometry of the human brain. Network Neuroscience, 6(4):937-949, 2022.
P. Loskot, K. Atitey, and L. Mihaylova. Comprehensive review of models and methods for inferences in bio-chemical reaction networks. Frontiers in Genetics, 10, 2019.
S. Löwe, D. Madras, R. Z. Shilling, and M. Welling. Amortized causal discovery: Learning to infer causal graphs from time-series data. In Proceedings of the 1st Conference on Causal Learning and Reasoning (CLeaR), pages 509-525. PMLR, 2022.
B. Ma, M. Fang, and X. Jiao. Inference of gene regulatory networks based on nonlinear ordinary differential equations. Bioinformatics, 36(19):4885-4893, 2020.
D. Margaritis. Learning Bayesian network model structure from data. Technical report, Carnegie-Mellon University, School of Computer Science, 2003.
A. A. Margolin, I. Nemenman, K. Basso, C. Wiggins, G. Stolovitzky, R. D. Favera, and A. Califano. ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics, 7:1-15, 2006.
H. Matsumoto, H. Kiryu, C. Furusawa, M. S. Ko, S. B. Ko, N. Gouda, T. Hayashi, and I. Nikaido. SCODE: an efficient regulatory network inference algorithm from single-cell RNA-seq during differentiation. Bioinformatics, 33(15):2314-2321, 2017.
H. Matsumoto, H. Kiryu, C. Furusawa, M. S. H. Ko, S. B. H. Ko, N. Gouda, T. Hayashi, and I. Nikaido. SCODE: an efficient regulatory network inference algorithm from single-cell RNA-Seq during differentiation. Bioinformatics, 33(15):2314-2321, 2017.
G. Menegozzo, D. Dall'Alba, and P. Fiorini. Cipcad-bench: Continuous industrial process datasets for benchmarking causal discovery methods. In 2022 IEEE 18th International Conference on Automation Science and Engineering (CASE), pages 2124-2131, 2022.
P. E. Meyer, F. Lafitte, and G. Bontempi. minet: A R/Bioconductor package for inferring large transcriptional networks using mutual information. BMC bioinformatics, 9:1-10, 2008.
J. R. Otukei and T. Blaschke. Land cover change assessment using decision trees, support vector machines and maximum likelihood classification algorithms. International Journal of Applied Earth Observation and Geoinformation, 12:S27-S31, 2010.
K. Ovens, B. F. Eames, and I. McQuillan. Comparative analyses of gene co-expression networks: Implementations and applications in the study of evolution. Frontiers in Genetics, 12, 2021. ISSN 1664-8021.
L. Pan, C. Shi, and I. Dokmanic. A graph dynamics prior for relational inference. In Proceedings of the 38th AAAI Conference on Artificial Intelligence (AAAI), volume 38, pages 14508-14516, 2024.
N. Papili Gao, S. M. M. Ud-Dean, O. Gandrillon, and R. Gunawan. SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles. Bioinformatics, 34(2):258-266, 2017.
N. Papili Gao, S. M. Ud-Dean, O. Gandrillon, and R. Gunawan. SINCERITIES: inferring gene regulatory networks from time-stamped single cell transcriptional expression profiles. Bioinformatics, 34(2):258-266, 2018.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32 (NeurIPS), 2019.
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825-2830, 2011.
E. Pereda, R. Q. Quiroga, and J. Bhattacharya. Nonlinear multivariate analysis of neurophysiological signals. Progress in Neurobiology, 77(1-2):1-37, 2005.
A. Pratapa, A. Jalihal, J. Law, A. Bharadwaj, and T. Murali. Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data. Nature Methods, 17: 1-8, 02 2020.
A. Pratapa, A. P. Jalihal, J. N. Law, A. Bharadwaj, and T. Murali. Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data. Nature Methods, 17(2):147-154, 2020.
X. Qiu, A. Rahimzamani, L. Wang, B. Ren, Q. Mao, T. Durham, J. L. McFaline-Figueroa, L. Saunders, C. Trapnell, and S. Kannan. Inferring causal gene regulatory networks from coupled single-cell expression dynamics using Scribe. Cell Systems, 10(3):265-274, 2020.
A. Rahimzamani and S. Kannan. Network inference using directed information: The deterministic limit. In 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 156-163. IEEE, 2016.
A. Rahimzamani and S. Kannan. Potential conditional mutual information: Estimators and properties. In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1228-1235. IEEE, 2017.
S. J. Russell. Artificial intelligence a modern approach. Pearson Education, Inc., 2010.
M. Sanchez-Castillo, D. Blanco, I. M. Tienda-Luna, M. C. Carrion, and Y. Huang. A Bayesian framework for the inference of gene regulatory networks from time and pseudo-time series data. Bioinformatics, 34(6):964-970, 2017.
G. Schiebinger, J. Shu, M. Tabaka, B. Cleary, V. Subramanian, A. Solomon, J. Gould, S. Liu, S. Lin, P. Berube, L. Lee, J. Chen, J. Brumbaugh, P. Rigollet, K. Hochedlinger, R. Jaenisch, A. Regev, and E. S. Lander. Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming. Cell, 176(4):928-943.e22, 2019.
Y. Sha, Y. Qiu, P. Zhou, and Q. Nie. Reconstructing growth and dynamic trajectories from single-cell transcriptomics data. Nature Machine Intelligence, 6(1):25-39, 2024.
J. Shendure, G. J. Porreca, N. B. Reppas, X. Lin, J. P. McCutcheon, A. M. Rosenbaum, M. D. Wang, K. Zhang, R. D. Mitra, and G. M. Church. Accurate multiplex polony sequencing of an evolved bacterial genome. Science, 309(5741):1728-1732, 2005.
R. Shwartz-Ziv and N. Tishby. Opening the black box of deep neural networks via information. arXiv preprint arXiv:1703.00810, 2017.
S. M. Smith, K. L. Miller, G. Salimi-Khorshidi, M. Webster, C. F. Beckmann, T. E. Nichols, J. D. Ramsey, and M. W. Woolrich. Network modelling methods for FMRI. Neuroimage, 54 (2):875-891, 2011.
J. H. Steele. Food webs. In Encyclopedia of Ocean Sciences, pages 596-603. Academic Press, 2009.
D. Szklarczyk, R. Kirsch, M. Koutrouli, K. Nastou, F. Mehryary, R. Hachilif, A. L. Gable, T. Fang, N. Doncheva, S. Pyysalo, P. Bork, L. J. Jensen, and C. von Mering. The STRING database in 2023: protein-protein association networks and functional enrichment analyses for any sequenced genome of interest. Nucleic Acids Research, 51(D1):D638-D646, 2022.
N. Tishby and N. Zaslavsky. Deep learning and the information bottleneck principle. In Proceedings of 2015 IEEE Information Theory Workshop (ITW), pages 1-5. IEEE, 2015.
N. Tishby, F. Pereira, and W. Biale. The information bottleneck method. In Proceedings of the 37th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 368-377. IEEE, 1999.
I. Tsamardinos, C. F. Aliferis, A. R. Statnikov, and E. Statnikov. Algorithms for large scale Markov Blanket discovery. In Proceedings of the 16th International Florida Artificial Intelligence Research Society Conference (FLAIRS), pages 376-380, 2003.
I. Tsamardinos, L. E. Brown, and C. F. Aliferis. The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 65:31-78, 2006.
M. Tsubaki, K. Tomii, and J. Sese. Compound-protein interaction prediction with end-to-end learning of neural networks for graphs and sequences. Bioinformatics, 35(2):309-318, 2019.
S. Varrette, H. Cartiaux, S. Peter, E. Kieffer, T. Valette, and A. Olloh. Management of an Academic HPC & Research Computing Facility: The ULHPC Experience 2.0. In Proc. of the 6th ACM High Performance Computing and Cluster Technologies Conf. (HPCCT 2022), Fuzhou, China, July 2022. Association for Computing Machinery (ACM). ISBN 978-1-4503-9664-6.
I. Virshup, S. Rybakov, F. J. Theis, P. Angerer, and F. A. Wolf. anndata: Annotated data. BioRxiv, pages 2021-12, 2021.
P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, I. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E. A. Quintero, C. R. Harris, A. M. Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17:261-272, 2020.
A. Wang and J. Pang. Iterative structural inference of directed graphs. In Advances in Neural Information Processing Systems 35 (NeurIPS), 2022.
A. Wang, T. P. Tong, and J. Pang. Effective and efficient structural inference with reservoir computing. In Proceedings of the 40th International Conference on Machine Learning (ICML), volume 202, pages 36391-36410. PMLR, 2023.
E. Webb, B. Day, H. Andres-Terre, and P. Lió. Factorised neural relational inference for multi-interaction systems. arXiv preprints arXiv:1905.08721, 2019.
Wes McKinney. Data Structures for Statistical Computing in Python. In Proceedings of the 9th Python in Science Conference, pages 56-61, 2010.
P. L. Williams and R. D. Beer. Nonnegative decomposition of multivariate information. arXiv preprint arXiv:1004.2515, 2010.
H. Wu, Y. Liang, W. Xiong, Z. Zhou, W. Huang, S. Wang, and K. Wang. Earthfarsser: Versatile spatio-temporal dynamical systems modeling in one model. In Proceedings of the 38th AAAI Conference on Artificial Intelligence (AAAI), pages 15906-15914, 2024.
T. Wu, T. Breuel, M. Skuhersky, and J. Kautz. Discovering nonlinear relations with minimum predictive information regularization. arXiv preprint arXiv:2001.01885, 2020.
M. Yang, F. Liu, Z. Chen, X. Shen, J. Hao, and J. Wang. Causalvae: Disentangled representation learning via neural structural causal models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9593-9602. Computer Vision Foundation/IEEE, 2021.
C. Zhang, B. Chen, and J. Pearl. A simultaneous discover-identify approach to causal inference in linear models. In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), pages 10318-10325, 2020.
M. Zhang and Y. Chen. Link prediction based on graph neural networks. In Advances in Neural Information Processing Systems 31 (NeurIPS), 2018.
X. Zhang, X.-M. Zhao, K. He, L. Lu, Y. Cao, J. Liu, J.-K. Hao, Z.-P. Liu, and L. Chen. Inferring gene regulatory networks from gene expression data by path consistency algorithm based on conditional mutual information. Bioinformatics, 28(1):98-104, 2012.
X. Zhang, M. Zeman, T. Tsiligkaridis, and M. Zitnik. Graph-guided network for irregularly sampled multivariate time series. In Proceedings of the 10th International Conference on Learning Representations (ICLR), 2022.
J. Zhao, Y. Zhou, X. Zhang, and L. Chen. Part mutual information for quantifying direct associations in networks. Proceedings of the National Academy of Sciences, 113(18):5130-5135, 2016.
M. Zhao, W. He, J. Tang, Q. Zou, and F. Guo. A comprehensive overview and critical evaluation of gene regulatory network inference technologies. Briefings in Bioinformatics, 22 (5):bbab009, 2021.
S. Zheng, Z. Li, K. Fujiwara, and G. Tanaka. Diffusion model for relational inference. arXiv preprint arXiv:2401.16755, 2024.
Q. Zhou. Multi-domain sampling with applications to structural inference of Bayesian networks. Journal of the American Statistical Association, 106(496):1317-1330, 2011.
D. Zügner, F.-X. Aubet, V. G. Satorras, T. Januschowski, S. Günnemann, and J. Gasthaus. A study of joint graph inference and forecasting. arXiv preprint arXiv:2109.04979, 2021.