In this paper, we tackle structure learning of directed acyclic graphs (DAGs), with the idea of exploiting available prior knowledge of the domain at hand to guide the search of the best structure. In particular, we assume to know the topological ordering of variables in addition to the given data. We study a new algorithm for learning the structure of DAGs, proving its theoretical consistency in the limit of infinite observations. Furthermore, we experimentally compare the proposed algorithm to several popular competitors, to study its behaviour in finite samples. Biological validation of the algorithm is presented through the analysis of non-small cell lung cancer data.
AalenOO, RøyslandK, GranJM, KouyosR and LangeT (2016) Can we believe the dags? A comment on the relationship between causal dags and mechanisms. Statistical Methods in Medical Research, 25(5), 2294–2314.
2.
AllenG and LiuZ (2013) A local Poisson graphical model for inferring networks from sequencing data. NanoBioscience, IEEE Transactions on, 12(3), 189–98.
3.
BühlmannP, PetersJ and ErnestJ (2014) CAM: causal additive models, high-dimensional order search and penalized regression. The Annals of Statistics, 42(6), 2526–56.
4.
CooperGF and HerskovitsE (1992) A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9(4), 309–47.
5.
CsardiG and NepuszT, . (2006) The igraph software package for complex network research. InterJournal, Complex Systems, 1695(5),1–9.
6.
DawidAP (2010) Beware of the dag! In Causality: objectives and assessment, pp. 59–86. PMLR.
7.
DorD and TarsiM (1992) A simple algorithm to construct a consistent extension of a partially oriented graph. Technicial Report R-185, Cognitive Systems Laboratory, UCLA.
8.
FraleyC and RafteryAE (2002) Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–31.
9.
FriedmanN and KollerD (2003) Being Bayesian about network structure: a Bayesian approach to structure discovery in Bayesian networks. Machine Learning, 50, 95–125.
10.
GaleNW, KaplanS, LowensteinEJ, SchlessingerJ and Bar-SagiD (1993) Grb2 mediates the egf-dependent activation of guanine nucleotide exchange on ras. Nature, 363 (6424), 88–92.
11.
GallopinM, RauA and JaffrézicF (2013) A hierarchical poisson log-normal model for network inference from rna sequencing data. PloS One, 8(10), e77503.
12.
HadijiF, MolinaA, NatarajanS and KerstingK (2015) Poisson dependency networks: gradient boosted models for multivariate count data. Machine Learning, 100(2-3), 477–507.
13.
KalischM and BühlmannP (2007) Estimating high-dimensional directed acyclic graphs with the PC-algorithm. Journal of Machine Learning Research, 8(Mar), 613–36.
14.
KanehisaM and GotoS (2000) KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Research, 28(1), 27–30. http://www.ncbi.nlm.nih.gov/pubmed/10592173.
15.
KuipersJ, SuterP and MoffaG (2022) Efficient sampling and structure learning of Bayesian networks. Journal of Computational and Graphical Statistics, 31(3), 639–50.
LemmonMA and SchlessingerJ (2010) Cell signalling by receptor tyrosine kinases. Cell, 141(7), 1117–34.
18.
Y-HLi, ScarlettJ, RavikumarP and CevherV (2015) Sparsistency of -regularized m-estimators. In Artificial intelligence and statistics, pp. 644–52. PMLR.
19.
LiuH, RoederK and WassermanL (2010) Stability approach to regularization selection (stars) for high dimensional graphical models. In Advances in neural information processing systems, pp. 1432–40.
20.
NguyenTKH and ChiognaM (2021) Structure learning of undirected graphical models for count data. Journal of Machine Learning Research, 22(50), 1–53. http://jmlr.org/papers/v22/18-401.html.
21.
PalumboMC, FarinaL, ColosimoA, TunK, DharPK and GiulianiA (2006) Networks everywhere? Some general implications of an emergent metaphor. Current Bioinformatics, 1(2),219–34.
22.
ParkG and RaskuttiG (2015) Learning large-scale Poisson DAG models based on overdispersion scoring. In Advances in neural information processing systems, pp. 631–39.
23.
PearlJ, . (2000) Causality: models, reasoning and inference. Cambridge, UK: Cambridge University Press, Econometric Theory, 19, 675–85.
24.
PetersJ and BühlmannP (2013) Identifiability of Gaussian structural equation models with equal error variances. Biometrika, 101(1), 219–28.
25.
SchmidtM, Niculescu-MizilA and MurphyK (2007) Learning graphical model structure using -regularization paths. In AAAI, volume 7, pp. 1278–83.
26.
SpirtesP, GlymourC and ScheinesR (1993) Causation, prediction, and search. 1993. Lecture Notes in Statistics, 81. New York: Springer.
27.
SuterP, KuipersJ, MoffaG and BeerenwinkelN (2023) Bayesian structure learning and sampling of Bayesian networks with the r package bidag. Journal of Statistical Software, 105, 1–31.
28.
TeyssierM and KollerD (2005) Ordering-based search: A simple and effective algorithm for learning Bayesian networks. In Proceedings of the twenty-first conference on uncertainty in artificial intelligence, UAI'05, pp. 584–90. Arlington, VA: AUAI Press.
29.
TsamardinosI, BrownLE and AliferisCF (2006) The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 65(1), 31–78.
30.
XueJY, ZhaoY, AronowitzJ, MaiTT, VidesA, QeriqiB, KimD, LiC, de StanchinaE, MazutisL, RissoD and LitoP (2020) Rapid non-uniform adaptation to conformation-specific kras (g12c) inhibition. Nature, 577(7790), 421–25.
31.
YangE, AllenG, LiuZ and RavikumarPK (2012) Graphical models via generalized linear models. In Advances in neural information processing systems, pp. 1358–66.
32.
YangE, RavikumarP, AllenGI and LiuZ (2015) Graphical models via univariate exponential family distributions. Journal of Machine Learning Research, 16(1), 3813–47.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
