Abstract
Discovering the causal mechanisms of biological systems is necessary to design new drugs and therapies. Computational Causal Discovery (CD) is a field that offers the potential to discover causal relations and causal models under certain conditions with a limited set of interventions/manipulations. This chapter reviews the basic concepts and principles of CD, the nature of the assumptions to enable it, potential pitfalls in its application, and recent advances and directions. Importantly, several success stories in molecular and systems biology are discussed in detail.
Vincenzo Lagani, Sofia Triantafillou and Gordon Ball have contributed equally to this work.
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Notes
- 1.
Direct causation is defined in the context of all other modeled variables, i.e., a causal relation mediated by none of the observed variables.
- 2.
Linkage disequilibrium, pleiotropic effects and other factors can invalidate the Mendelian Randomization approach; these issues are better explained later in the text.
- 3.
- 4.
Notably, the “Causal Equivalence Theorem” is identical to the LCD procedure presented in [18].
- 5.
Explaining the details of the do-calculus is beyond the scope of this chapter. Interested readers can refer to Pearl’s original publication.
- 6.
An implementation of the IDA algorithm is available in the R package pcalg [46].
References
Akaike, H.: A new look at the statistical model identification. IEEE Trans. Automat. Contr. 19(6), 716–723 (1974)
Akbani, R., Ng, P.K.S., Werner, H.M.J., Shahmoradgoli, M., Zhang, F., Ju, Z., Liu, W., Yang, J.-Y., Yoshihara, K., Li, J., Ling, S., Seviour, E.G., Ram, P.T., Minna, J.D., Diao, L., Tong, P., Heymach, J.V., Hill, S.M., Dondelinger, F., Städler, N., Byers, L., Meric-Bernstam, F., Weinstein, J.N., Broom, B.M., Verhaak, R.G.W., Liang, H., Mukherjee, S., Lu, Y., Mills, G.B.: A pan-cancer proteomic perspective on The Cancer Genome Atlas. Nat. Commun. 5, 3887 (2014)
Aliferis, C.F.: Local causal and Markov blanket induction for causal discovery and feature selection for classification Part I?: algorithms and empirical evaluation. J. Mach. Learn. Res. 11, 171–234 (2010)
Aten, J.E., Fuller, T.F., Lusis, A.J., Horvath, S.: Using genetic markers to orient the edges in quantitative trait networks: the NEO software. BMC Syst. Biol. 2, 34 (2008)
Balding, D.J.: A tutorial on statistical methods for population association studies. Nat. Rev. Genet. 7, 781–791 (2006)
Barrett, T., Wilhite, S.E., Ledoux, P., Evangelista, C., Kim, I.F., Tomashevsky, M., Marshall, K.A., Phillippy, K.H., Sherman, P.M., Holko, M., Yefanov, A., Lee, H., Zhang, N., Robertson, C.L., Serova, N., Davis, S., Soboleva, A.: NCBI GEO: Archive for functional genomics data sets—Update. Nucleic Acids Res. 41 (2013)
Borboudakis, G., Tsamardinos, I.: Bayesian network learning with discrete case-control data. In: Uncertainty in Artificial Intelligence (UAI), 2015
Borboudakis, G., Tsamardinos, I.: Incorporating causal prior knowledge as path-constraints in Bayesian networks and maximal ancestral graphs. In: Proceedings of the 29th International Conference on Machine Learning (ICML-12), 2012, pp. 1799–1806
Burns, M.B., Temiz, N., Harris, R.S.: Evidence for APOBEC3B mutagenesis in multiple human cancers. Nat. Genet. 45(9), 977–983 (2013)
Cai, X., Bazerque, J.A., Giannakis, G.B.: Inference of gene regulatory networks with sparse structural equation models exploiting genetic perturbations. Plos Comput. Biol. 9(5), e1003068 (2013)
Cause and effect. Nat. Methods 7, 243 (2010)
Chen, L.S., Emmert-Streib, F., Storey, J.D.: Harnessing naturally randomized transcription to infer regulatory relationships among genes. Genome Biol. 8(10), R219 (2007)
Chickering, D.M.: Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2, 445–498 (2002)
Chickering, D.M., Heckerman, D., Meek, C.: Large-sample learning of Bayesian networks is NP-hard. J. Mach. Learn. Res. 5, 1287–1330 (2004)
Chu, T., Glymour, C., Scheines, R., Spirtes, P.: A statistical problem for inference to regulatory structure from associations of gene expression measurements with microarrays. Bioinformatics 19(9), 1147–1152 (2003)
Claassen, T., Heskes, T.: Causal discovery in multiple models from different experiments. In: Advances in Neural Information Processing Systems (NIPS 2010), 2010, pp. 1–9
Claassen, T., Heskes,T.: Learning causal network structure from multiple (in) dependence models. In: Proceedings of the Fifth European Workshop on Probabilistic Graphical Models (PGM), pp. 81–88
Cooper, G.F.: A simple constraint-based algorithm for efficiently mining observational databases for causal relationships. Data Min. Knowl. Discov. 1, 203–224 (1997)
Cooper, G., Yoo, C.: Causal discovery from a mixture of experimental and observational data. In: Proceedings of the Fifthteenth Conference on Uncertainty in Artificial Intelligence (UAI’99), 1999, pp. 116–125
Danks, D.: Learning the causal structure of overlapping variable sets. In: Discovery Science: Proceedings of the 5th International Conference, 2002, pp. 178–191
Danks, D., Glymour, C., Tillman, R.E.: Integrating locally learned causal structures with overlapping variables. In: Advances in Neural Information Processing Systems, pp. 1665–1672. MIT Press, Cambridge (2009)
Dash, D., Druzdel, M.: Caveats for causal reasoning with equilibrium models. ECSQUARU 2143, 192–203 (2001)
Davey Smith, G., Ebrahim, S.: Mendelian randomization: can genetic epidemiology contribute to understanding environmental determinants of disease?. Int. J. Epidemiol. 32(1), 1–22 (2003)
D’Orazio, M., Di Zio, M., Scanu, M.: Statistical Matching: Theory and Practice, p. 268. Wiley, New York (2006)
Eaton, D., Murphy, K.: Exact Bayesian structure learning from uncertain interventions. In: AISTATS (2007)
Eberhardt, F.: Sufficient condition for pooling data from different distributions. Error (2006)
Evans, R.J., Richardson, T.S.: Marginal log-linear parameters for graphical Markov models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 75(4), 743–768 (2013)
Fisher, R.A.: The distribution of the partial correlation coefficient. Metron 3(3–4), 329–332 (1923)
Fisher, R.A.: The Design of Experiments. Hafner Publishing, New York (1935)
Friedman, N., Murphy, K., Russell, S.: Learning the structure of dynamic probabilistic networks. In: Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 139–147
Fukuda, R., Kelly, B., Semenza, G.L.: Vascular endothelial growth factor gene expression in colon cancer cells exposed to prostaglandin E2 is mediated by hypoxia-inducible factor 1. Cancer Res. 63(9), 2330–2334 (2003)
Gutierrez-Arcelus, M., Lappalainen, T., Montgomery, S.B., Buil, A., Ongen, H., Yurovsky, A., Bryois, J., Giger, T., Romano, L., Planchon, A., Falconnet, E., Bielser, D., Gagnebin, M., Padioleau, I., Borel, C., Letourneau, A., Makrythanasis, P., Guipponi, M., Gehrig, C., Antonarakis, S.E., Dermitzakis, E.T.: Passive and active DNA methylation and the interplay with genetic variation in gene regulation. Elife 2, e00523 (2013)
Hartemink, A.J., Gifford, D.K., Jaakkola, T.S., Young, R.A.: Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks. In: The Pacific Symposium on Biocomputing, 2001, pp. 422–433
Hauser, A., Bühlmann, P.: Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs. J. Mach. Learn. Res. 13, 2409–2464 (2012)
He, Y.-B.: Active learning of causal networks with intervention experiments and optimal designs. J. Mach. Learn. Res. 9, 2523–2547 (2008)
Hoyer, P.O., Janzing, D., Joris, M., Peters, J., Schölkopf, B.: Nonlinear causal discovery with additive noise models. In: NIPS, 2008
Hug, S., Schmidl, D., Li, W.B., Greiter, M.B., Theis, F.J.: Bayesian model selection methods and their application to biological ODE systems. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Cham (2016, this volume)
Hyttinen, A.: Discovering Causal Relations in the Presence of Latent Confounders. University of Helsinki, Helsinki (2013)
Hyttinen, A., Eberhardt, F., Hoyer, P.O.: Noisy-OR models with latent confounding. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, Barcelona, 2011
Hyttinen, A., Eberhardt, F., Hoyer, P.O.: Causal discovery of linear cyclic models from multiple experimental data sets with overlapping variables. In: Proceedings of the Uncertainty in Artificial Intelligence, 2012
Hyttinen, A., Eberhardt, F., Hoyer, P.O.: Learning linear cyclic causal models with latent variables. J. Mach. Learn. Res. 2013(3387–3439), 3387–3439 (2012). Jan
Hyttinen, A., Eberhardt, F., Jarvisalo, M.: Constraint-Based Causal Discovery: Conflict Resolution with Answer Set Programming. In: Proceedings of the Uncertainty in Artificial Intelligence, 2014
Hyttinen, A., Hoyer, P.O., Eberhardt, F., Järvisalo, M.: Discovering cyclic causal models with latent variables: a general sat-based procedure. In: Proceedings of the Uncertainty in Artificial Intelligence, 2013
Idaghdour, Y., Czika, W., Shianna, K.V., Lee, S.H., Visscher, P.M., Martin, H.C., Miclaus, K., Jadallah, S.J., Goldstein, D.B., Wolfinger, R.D., Gibson, G.: Geographical genomics of human leukocyte gene expression variation in southern Morocco. Nat. Genet. 42(1), 62–67 (2010)
Kalisch, M., Fellinghauer, B.A.G., Grill, E., Maathuis, M.H., Mansmann, U., Buhlmann, P., Stucki, G.: Understanding human functioning using graphical models. BMC Med. Res. Methodol. 10, 14 (2010)
Kalisch, M., Maechler, M., Colombo, D., Maathuis, M.H., Buehlmann, P.: Causal inference using graphical models with the R package pcalg. J. Stat. Softw. 47(11), 1–26 (2012)
Katan, M.B.: Apolipoprotein E isoforms, serum cholesterol, and cancer. Lancet 1(8479), 507–508 (1986)
Kenfield, S.A., Stampfer, M.J., Chan, J.M., Giovannucci, E.: Smoking and prostate cancer survival and recurrence. JAMA 305(24), 2548–2555 (2011)
Kirk, P., Silk, D., Stumpf, M.P.H.: Reverse engineering under uncertainty. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Cham (2016, this volume)
Labrie, F., Dupont, A., Suburu, R., Cusan, L., Tremblay, M., Gomez, J.L., Emond, J.: Serum prostate specific antigen as pre-screening test for prostate cancer. J. Urol. 147(3 Pt 2), 846–851 (discussion 851–852) (1992)
Lagani, V., Tsamardinos, I., Triantafillou, S.: Learning from mixture of experimental data: a constraint—based approach. In: SETN’12 Proceedings of the 7th Hellenic Conference on Artificial Intelligence: Theories and Applications, 2012, vol. 7297, pp. 124–131
Lazar, C., Meganck, S., Taminau, J., Steenhoff, D., Coletta, A., Molter, C., Weiss-Solís, D.Y., Duque, R., Bersini, H., Nowé, A.: Batch effect removal methods for microarray gene expression data integration: a survey. Brief. Bioinform. 14(4), 469–490 (2013)
Le, T.D., Liu, L., Tsykin, A., Goodall, G.J., Liu, B., Sun, B.-Y., Li, J.: Inferring microRNA-mRNA causal regulatory relationships from expression data. Bioinformatics 29(6), 765–771 (2013)
Lemeire, J., Janzing, D.: Replacing causal faithfulness with algorithmic independence of conditionals. Minds Mach. (2012)
Liu, Y., Aryee, M.J., Padyukov, L., Fallin, M.D., Hesselberg, E., Runarsson, A., Reinius, L., Acevedo, N., Taub, M., Ronninger, M., Shchetynsky, K., Scheynius, A., Kere, J., Alfredsson, L., Klareskog, L., Ekström, T.J., Feinberg, A.P.: Epigenome-wide association data implicate DNA methylation as an intermediary of genetic risk in rheumatoid arthritis. Nat. Biotechnol. 31(2), 142–7 (2013)
Maathuis, M.H., Kalisch, M., Bühlmann, P.: Estimating high-dimensional intervention effects from observational data. Ann. Stat. 37(6A), 3133–3164 (2009)
Maathuis, M.H., Colombo, D., Kalisch, M., Bühlmann, P.: Predicting causal effects in large-scale systems from observational data. Nat. Methods 7(4), 247–248 (2010)
MacKinnon, D.P.: Introduction to Statistical Mediation Analysis (Multivariate Applications Series), p. 488. Routledge, New York (2008)
Mani, S., Cooper, G.F.: Causal discovery using a Bayesian local causal discovery algorithm. Stud. Health Technol. Inform. 107(Pt 1), 731–735 (2004)
Marbach, D., Schaffter, T., Mattiussi, C., Dario, F.: Generating realistic in silico gene networks for performance assessment of reverse engineering methods. J. Comput. Biol. 16(2), 229–239 (2009)
Margaritis, D.: Distribution-free learning of Bayesian network structure in continuous domains. In: AAAI’05 Proceedings of the 20th National Conference on Artificial Intelligence—Volume 2, 2005, pp. 825–830
Margaritis, D., Thrun, S.: Bayesian network induction via local neighborhoods. Adv. Neural Inf. Process. Syst. 12, 505–511 (2000)
McDonald, J.H.: Handbook of Biological Statistics, p. 291. Sparky House Publishing, Baltimore (2009)
Meganck, S., Maes, S., Leray, P., Manderick, B.: Learning semi-markovian models using experiments. In: Third European Workshop on Probabilistic Graphical Models (PGM), 2006
Meinshausen, N., Buhlmann, P.: Stability selection. J. R. Stat. Soc. Ser. B 72(4), 417–473 (2010)
Miles, C., Wayne, M.: Quantitative trait locus (QTL) analysis. Nat. Educ. 1(1) (2008)
Millstein, J., Zhang, B., Zhu, J., Schadt, E.E.: Disentangling molecular relationships with a causal inference test. BMC Genet. 10, 23 (2009)
Monti, S., Cooper, G.F.: A multivariate discretization method for learning Bayesian networks from mixed data. In: UAI’98 Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, 1998, pp. 404–413
Mooij, J., Janzing, D., Peters, J., Schölkopf, B.: Regression by dependence minimization and its application to causal inference in additive noise models. In: Proceedings of the 26th Annual International Conference on Machine Learning—ICML ’09, 2009, pp. 745–752
Näger, P.M.: Causal graphs for EPR experiments. In: Foundations of Physics 2013: The 17th UK and European Meeting on the Foundations of Physics, 2013
Neapolitan, R.E.: Learning Bayesian Networks. Pearson Prentice Hall, New York (2004)
Neto, E.C., Keller, M.P., Attie, A.D., Yandell, B.S.: Causal graphical models in systems genetics: a unified framework for joint inference of causal network and genetic architecture for correlated phenotypes. Ann. Appl. Stat. 4(1), 320–339 (2010). Mar
Nica, A.C., Montgomery, S.B., Dimas, A.S., Stranger, B.E., Beazley, C., Barroso, I., Dermitzakis, E.T.: Candidate causal regulatory effects by integration of expression QTLs with complex trait genetic associations. PLoS Genet. 6(4), e1000895 (2010)
Nitsch, D., Molokhia, M., Smeeth, L., DeStavola, B.L., Whittaker, J.C., Leon, D.A.: Limits to causal inference based on Mendelian randomization: a comparison with randomized controlled trials. Am. J. Epidemiol. 163(5), 397–403 (2006)
Ornatsky, O., Bandura, D., Baranov, V., Nitz, M., Winnik, M.A., Tanner, S.: Highly multiparametric analysis by mass cytometry. J. Immunol. Methods 361(1–2), 1–20 (2010)
O’Rourke, K.: An historical perspective on meta-analysis: dealing quantitatively with varying study results. J. R. Soc. Med. 100(12), 579–82 (2007)
Pan, S.J., Yang, Q.: A survey on transfer learning. IEEE Trans. Knowl. Data Eng. 22, 1345–1359 (2010)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco (1988)
Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press, Cambridge (2009)
Pearl, J.: Interpretation and Identification of Causal Mediation. University of California, Los Angeles (2013)
Peña, J.M., Björkegren, J., Tegnér, J.: Growing Bayesian network models of gene networks from seed genes. Bioinformatics 21(Suppl 2), ii224–i229 (2005)
Peters, J., Mooij, J., Janzing, D., Schoelkopf, B.: Identifiability of Causal Graphs Using Functional Models. arXiv.org (2012)
Petretto, E.: Single cell expression quantitative trait loci and complex traits. Genome Med. 5(8), 72 (2013)
Richardson, T., Spirtes, P.: Automated causal discovery in linear feedback models. In: Glymour, C., Cooper, G. (eds.) Computation, Causation and Discovery, pp. 253–302. AAAI press, Cambridge (1999)
Richardson, T., Spirtes, P.: Ancestral graph Markov models. Ann. Stat. 30(4), 962–1030 (2002)
Richardson, T., Evans, R., Robins, J.: Transparent parametrizations of models for potential outcomes. Bayesian Stat. 9, 569–610 (2011)
Robins, J.M., Wasserman, L.: On the impossibility of inferring causation from association without background knowledge. In: Glymour, C., Cooper, G.F. (eds.) Computation, Causation, and Discovery, pp. 305–321. AAAI Press/The MIT Press, Menlo Park, CA, Cambridge, MA (1999)
Rockman, M.V.: Reverse engineering the genotype-phenotype map with natural genetic variation. Nature 456, 738–744 (2008)
Sachs, K., Perez, O., Pe’er, D., Lauffenburger, D.A., Nolan, G.P.: Causal protein-signaling networks derived from multiparameter single-cell data. Science 308(5721), 523–529 (2005)
Schadt, E.E.: Causal inference and the construction of predictive network models in biology. In: Handbook of Systems Biology Concept and Insights, pp. 499–514. Elsevier Inc. (2013)
Schadt, E.E., Lamb, J., Yang, X., Zhu, J., Edwards, S., Guhathakurta, D., Sieberts, S.K., Monks, S., Reitman, M., Zhang, C., Lum, P.Y., Leonardson, A., Thieringer, R., Metzger, J.M., Yang, L., Castle, J., Zhu, H., Kash, S.F., Drake, T.A., Sachs, A., Lusis, A.J.: An integrative genomics approach to infer causal associations between gene expression and disease. Nat. Genet. 37(7), 710–717 (2005)
Schmidt, M., Murphy, K.: Modeling discrete interventional data using directed cyclic graphical models. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI ’09), 2009, pp. 487–495
Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)
Shang, Z., Zhu, S., Zhang, H., Li, L., Niu, Y.: Germline homeobox B13 (HOXB13) G84E mutation and prostate cancer risk in European descendants: a meta-analysis of 24,213 cases and 73,631 controls. Eur. Urol. 64(1), 173–176 (2013)
Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.: A linear non-Gaussian acyclic model for causal discovery. J. Mach. Learn. Res. 7(2), 2003–2030 (2006)
Sleiman Itani, B.S., Ohannessian, M., Sachs, K., Nolan, G.P., Dahleh, M.A., Guyon, I., Janzing, D.: Structure learning in causal cyclic networks. In: NIPS, 2008, pp. 165–176
Sobel, M.E.: Asymptotic confidence intervals for indirect effects in structural equation models. Sociol. Methodol. 13(1982), 290–312 (1982)
Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, vol. 81. Springer, New York (1993)
Stekhoven, D.J., Moraes, I., Sveinbjornsson, G., Hennig, L., Maathuis, M.H., Buhlmann, P.: Causal stability ranking. Bioinformatics 28(21), 2819–2823 (2012)
Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S., Gilles, E.D.: Metabolic network structure determines key aspects of functionality and regulation. Nature 420(6912), 190–193 (2002)
Sunnåker, M., Stelling, J.: Model extension and model selection. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Cham (2016, this volume)
Tian, J., Pearl, J.: Causal discovery from changes. In: UAI’01 Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 2001, pp. 512–521
Tian, J., Pearl, J.: On the identication of causal effects. Technical Report R-290-L, 2003
Tillman, R.E., Spirtes, P.: Learning equivalence classes of acyclic models with latent and selection variables from multiple datasets with overlapping variables. J. Mach. Learn. Res. Proc. Track 15, 3–15 (2011)
Triantafillou, S., Tsamardinos, I.: Constraint-Based Causal Discovery from Multiple Interventions over Overlapping Variable Sets. JMLR, to appear
Triantafillou, S., Tsamardinos, I., Tollis, I.G.: Learning causal structure from overlapping variable sets. In: Proceedings of Artificial Intelligence and Statistics, 2010
Tsamardinos, I., Borboudakis, G.: Permutation testing improves Bayesian network learning. In: ECML PKDD’10 Proceedings of the 2010 European Conference on Machine Learning and Knowledge Discovery in Databases: Part III, 2010, pp. 322–337
Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max-min hill-climbing Bayesian network structure learning algorithm. Mach. Learn. 65(1), 31–78 (2006)
Tsamardinos, I., Triantafillou, S., Lagani, V.: Towards integrative causal analysis of heterogeneous data sets and studies. J. Mach. Learn. Res. 13(1), 1097–1157 (2012)
Tsamardinos, I., Aliferis, C.F., Statnikov, A., Brown, L.E.: Scaling-Up Bayesian Network Learning to Thousands of Variables Using Local Learning Techniques
Wills, Q.F., Livak, K.J., Tipping, A.J., Enver, T., Goldson, A.J., Sexton, D.W., Holmes, C.: Single-cell gene expression analysis reveals genetic associations masked in whole-tissue experiments. Nat. Biotechnol. 31(8), 748–752 (2013)
Zhang, J.: On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artif. Intell. 172(16–17), 1873–1896 (2008)
Zhang, K., Hyvärinen, A.: On the identifiability of the post-nonlinear causal model. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, 2009, pp. 647–655
Zhang, W.M., Wong, T.M.: Suppression of cAMP by phosphoinositol/Ca2+ pathway in the cardiac kappa-opioid receptor. Am. J. Physiol. 274(1 Pt 1), C82–C87 (1998)
Zhang, W., Zhu, J., Schadt, E.E., Liu, J.S.: A Bayesian partition method for detecting pleiotropic and epistatic eQTL modules. PLoS Comput. Biol. 6(1), e1000642 (2010)
Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B 67(2), 301–320 (2005)
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This work was partially funded by STATegra EU FP7 project, No 306000 and EPILOGEAS GSRT ARISTEIA II project, No 3446.
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Lagani, V., Triantafillou, S., Ball, G., Tegnér, J., Tsamardinos, I. (2016). Probabilistic Computational Causal Discovery for Systems Biology. In: Geris, L., Gomez-Cabrero, D. (eds) Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_3
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