Exploratory causal analysis

Data analysis is primarily concerned with causal questions.{{cite book |last=Pearl| first = Judea|year = 2018|title = The Book of Why: The New Science of Cause and Effect | publisher = Basic Books| isbn = 978-0465097616}}{{cite book |last=Kleinberg |first=Samantha |author-link=Samantha Kleinberg |title=Why: A Guide to Finding and Using Causes |publisher=O'Reilly Media, Inc. |year=2015 |isbn=978-1491952191}}{{cite book |last1=Illari |first1=P. |last2=Russo |first2=F.|year=2014|title=Causality: Philosophical Theory meets Scientific Practice|publisher=OUP Oxford|isbn=978-0191639685}} For example, did the fertilizer cause the crops to grow?{{cite book | last=Fisher|first=R.|year=1937|title=The design of experiments|publisher=Oliver And Boyd}} Or, can a given sickness be prevented?{{cite book | last=Hill|first=B.|year=1955|title=Principles of Medical Statistics|publisher=Lancet Limited}} Or, why is my friend depressed?{{cite book|last=Halpern|first=J.|year=2016|title=Actual Causality|publisher=MIT Press|isbn=978-0262035026}} The potential outcomes and regression analysis techniques handle such queries when data is collected using designed experiments. Data collected in observational studies require different techniques for causal inference (because, for example, of issues such as confounding).{{cite book|last1=Pearl |first1=J. |last2=Glymour |first2=M. |last3=Jewell |first3=N. P. |year=2016|title=Causal inference in statistics: a primer|publisher=John Wiley & Sons|isbn=978-1119186847}} Causal inference techniques used with experimental data require additional assumptions to produce reasonable inferences with observation data.{{cite journal |title=The Assumptions on Which Causal Inferences Rest |first=R. |last=Stone |journal=Journal of the Royal Statistical Society. Series B (Methodological) |volume=55 |issue=2 |year=1993 |pages=455–466 |doi=10.1111/j.2517-6161.1993.tb01915.x }} The difficulty of causal inference under such circumstances is often summed up as "correlation does not imply causation".

ECA postulates that there exist data analysis procedures performed on specific subsets of variables within a larger set whose outputs might be indicative of causality between those variables. For example, if we assume every relevant covariate in the data is observed, then propensity score matching can be used to find the causal effect between two observational variables. Granger causality can also be used to find the causality between two observational variables under different, but similarly strict, assumptions.{{cite journal|last=Granger|first=C|year=1980|title=Testing for causality: a personal viewpoint|journal=Journal of Economic Dynamics and Control|volume=2|pages=329–352|doi=10.1016/0165-1889(80)90069-X}}

The two broad approaches to developing such procedures are using operational definitions of causality or verification by "truth" (i.e., explicitly ignoring the problem of defining causality and showing that a given algorithm implies a causal relationship in scenarios when causal relationships are known to exist, e.g., using synthetic data).

Clive Granger created the first operational definition of causality in 1969.{{cite journal| last=Granger|first=C. W. J.|year=1969|title=Investigating Causal Relations by Econometric Models and Cross-spectral Methods|journal=Econometrica|volume=37|issue=3|pages=424–438|doi=10.2307/1912791|jstor=1912791}} Granger made the definition of probabilistic causality proposed by Norbert Wiener operational as a comparison of variances.{{cite web |last=Granger|first=Clive|title=Prize Lecture. NobelPrize.org. Nobel Media AB 2018.|url=https://www.nobelprize.org/prizes/economic-sciences/2003/granger/lecture/}}

Some authors prefer using ECA techniques developed using operational definitions of causality because they believe it may help in the search for causal mechanisms.{{cite book|title=Making Things Happen: A Theory of Causal Explanation (Oxford Studies in the Philosophy of Science)|last=Woodward|first=James|publisher=Oxford University Press|year=2004|isbn=978-1435619999}}

Peter Spirtes, Clark Glymour, and Richard Scheines introduced the idea of explicitly not providing a definition of causality. Spirtes and Glymour introduced the PC algorithm for causal discovery in 1990.{{cite journal |author1 =Spirtes, P. |author2=Glymour, C.|s2cid=38398322|year=1991|title=An algorithm for fast recovery of sparse causal graphs|journal=Social Science Computer Review|volume=9|issue=1|pages=62–72|doi=10.1177/089443939100900106}} Many recent causal discovery algorithms follow the Spirtes-Glymour approach to verification.{{cite journal |year=2020|title=A Survey of Learning Causality with Data|arxiv=1809.09337|last1=Guo|first1=Ruocheng|last2=Cheng|first2=Lu|last3=Li|first3=Jundong|last4=Hahn|first4=P. Richard|last5=Liu|first5=Huan|journal=ACM Computing Surveys|volume=53|issue=4|pages=1–37|doi=10.1145/3397269|s2cid=52822969}}

There are many surveys of causal discovery techniques.{{cite journal |year=2018|title=Causal discovery algorithms: A practical guide|journal=Philosophy Compass|volume=13|issue=1|pages=e12470|doi=10.1111/phc3.12470|last1=Malinsky|first1=Daniel|last2=Danks|first2=David|doi-access=free}}{{cite journal |title=Causal discovery and inference: concepts and recent methodological advances|journal=Appl Inform (Berl)|volume=3|pages=3|year=2016|doi=10.1186/s40535-016-0018-x|pmid=27195202|pmc=4841209|last1=Spirtes|first1=P.|last2=Zhang|first2=K. |doi-access=free }}{{cite arXiv |year=2016|title=A review on algorithms for constraint-based causal discovery|eprint=1611.03977|class=cs.AI|last1=Yu|first1=Kui|last2=Li|first2=Jiuyong|last3=Liu|first3=Lin|last4=Richard Hahn|first4=P.|last5=Liu|first5=Huan}} This section lists the well-known techniques.

• Granger causality (there is also the Scholarpedia entry [http://www.scholarpedia.org/article/Granger_causality])
• transfer entropy
• convergent cross mapping

• causation entropy{{cite journal |title=Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings|year=2014|journal=Physica D: Nonlinear Phenomena|volume=267|pages=49–57|bibcode=2014PhyD..267...49S|arxiv=1504.03769|doi=10.1016/j.physd.2013.07.001|last1=Sun|first1=Jie|last2=Bollt|first2=Erik M.|last3=Li|first3=Jundong|last4=Richard Hahn|first4=P.|last5=Liu|first5=Huan|s2cid=14422483}}
• PC algorithm{{cite journal |year=1999|title=Are there algorithms that discover causal structure?|journal=Synthese|volume=121|issue=1–2|pages=29–54|doi=10.1023/A:1005277613752|last1=Freedman|first1=David|last2=Humphreys|first2=Paul|s2cid=6826436}}
• FCI algorithm{{cite journal |title=Comparison of strategies for scalable causal discovery of latent variable models from mixed data|journal=International Journal of Data Science and Analytics|year=2018|volume=6|issue=33|pages=33–45|doi=10.1007/s41060-018-0104-3|pmid=30148202|pmc=6096780|last1=Raghu|first1=V. K.|last2=Ramsey|first2=J. D.|last3=Morris|first3=A.|last4=Manatakis|first4=D. V.|last5=Sprites|first5=P.|last6=Chrysanthis|first6=P. K.|last7=Glymour|first7=C.|last8=Benos|first8=P. V.}}
• LiNGAM{{cite journal|last=Shimizu|first=S|s2cid=49238101|year=2014|title=LiNGAM: non-Gaussian methods for estimating causal structures|journal=Behaviormetrika|volume=41|issue=1|pages=65–98|doi=10.2333/bhmk.41.65}} [https://sites.google.com/site/sshimizu06/lingam/]

Many of these techniques are discussed in the tutorials provided by the Center for Causal Discovery (CCD) [https://www.ccd.pitt.edu/video-tutorials/].

The PC algorithm has been applied to several different social science data sets.

The PC algorithm has been applied to medical data.{{cite journal |title=Application of a Causal Discovery Algorithm to the Analysis of Arthroplasty Registry Data|journal=Biomedical Engineering and Computational Biology|volume=9|pages=117959721875689|year=2018|doi=10.1177/1179597218756896|pmid=29511363|pmc=5826097|last1=Cheek|first1=C.|last2=Zheng|first2=H.|last3=Hallstrom|first3=B. R.|last4=Hughes|first4=R. E.}} Granger causality has been applied to fMRI data.{{cite journal |title=Is Granger Causality a Viable Technique for Analyzing fMRI Data?|year=2013|journal=PLOS ONE|volume=8|issue=7|pages=e67428|doi=10.1371/journal.pone.0067428|pmid=23861763|pmc=3701552|bibcode=2013PLoSO...867428W|last1=Wen|first1=X.|last2=Rangarajan|first2=G.|last3=Ding|first3=M.|doi-access=free}} CCD tested their tools using biomedical data [https://www.ccd.pitt.edu/biomedical-science/].

ECA is used in physics to understand the physical causal mechanisms of the system, e.g., in geophysics using the PC-stable algorithm (a variant of the original PC algorithm){{cite journal |title=Causal discovery in the geosciences—Using synthetic data to learn how to interpret results|journal=Computers & Geosciences|volume=99|year=2017|pages=50–60|doi=10.1016/j.cageo.2016.10.008|bibcode=2017CG.....99...50E|last1=Ebert-Uphoff|first1=Imme|last2=Deng|first2=Yi|doi-access=free}} and in dynamical systems using pairwise asymmetric inference (a variant of convergent cross mapping).{{cite journal |title=Convergent cross-mapping and pairwise asymmetric inference|journal=Phys. Rev. E|volume=90|issue=6|pages=062903|year=2014|doi=10.1103/PhysRevE.90.062903|pmid=25615160|bibcode=2014PhRvE..90f2903M|arxiv=1407.5696|last1=McCracken|first1=J. M.|last2=Weigel|first2=R. S.|last3=Li|first3=Jundong|last4=Richard Hahn|first4=P.|last5=Liu|first5=Huan|s2cid=7506718}}

There is debate over whether or not the relationships between data found using causal discovery are actually causal. Judea Pearl has emphasized that causal inference requires a causal model developed by "intelligence" through an iterative process of testing assumptions and fitting data.

Response to the criticism points out that assumptions used for developing ECA techniques may not hold for a given data set{{cite journal|last=Scheines|first=R.|year=1997|title=An introduction to causal inference|journal=Causality in Crisis|pages=185–199|url=http://mlg.eng.cam.ac.uk/zoubin/SALD/Intro-Causal.pdf}}{{cite journal|last=Holland|first=P. W.|year=1986|title=Statistics and causal inference|journal=Journal of the American Statistical Association|volume=81|issue=396|pages=945–960|doi=10.1080/01621459.1986.10478354|s2cid=14377504 }}{{cite book|last1=Imbens |first1=G. W. |last2=Rubin |first2=D. B.|year=2015|title=Causal inference in statistics, social, and biomedical sciences|publisher=Cambridge University Press|isbn=978-0521885881}} and that any causal relationships discovered during ECA are contingent on these assumptions holding true{{cite book|last1=Morgan |first1=S. L. |last2=Winship |first2=C.|year=2015|title=Counterfactuals and causal inference|publisher=Cambridge University Press|isbn=978-1107065079}}

• [https://cmu-phil.github.io/tetrad/manual/ Tetrad] is an open source GUI-based Java program that provides a collection of causal discovery algorithms.{{cite web |url=http://www.phil.cmu.edu/tetrad/publications.html |title=Causal Models and Statistical Data, The Tetrad Project}} The algorithm library used by Tetrad is also available as a command-line tool, Python API, and R wrapper.{{cite web |url=https://www.ccd.pitt.edu/tools/ |title=Tools, Center for Causal Discovery, University of Pittsburg|date=10 August 2016 }}
• [https://jlizier.github.io/jidt/ Java Information Dynamics Toolkit (JIDT)] is an open source Java library for performing information-theoretic causal discovery (i.e., transfer entropy, conditional transfer entropy, etc.)[https://github.com/jlizier/jidt/wiki/Documentation]. Examples of using the library in MATLAB, GNU Octave, Python, R, Julia and Clojure are provided in the documentation [https://github.com/jlizier/jidt].
• [https://cran.r-project.org/web/packages/pcalg/index.html pcalg] is an R package that provides some of the same causal discovery algorithms provided in Tetrad [https://cran.r-project.org/web/packages/pcalg/vignettes/pcalgDoc.pdf] {{Webarchive|url=https://web.archive.org/web/20170720172611/https://cran.r-project.org/web/packages/pcalg/vignettes/pcalgDoc.pdf |date=2017-07-20 }}.

• R package [https://rdrr.io/cran/lmtest/man/grangertest.html]
• Python package [https://www.statsmodels.org/dev/generated/statsmodels.tsa.stattools.grangercausalitytests.html]

• R package [https://cran.r-project.org/web/packages/rEDM/vignettes/rEDM-tutorial.html] {{Webarchive|url=https://web.archive.org/web/20190925235524/https://cran.r-project.org/web/packages/rEDM/vignettes/rEDM-tutorial.html |date=2019-09-25 }}

• MATLAB/GNU Octave package [https://sites.google.com/site/sshimizu06/lingam/]

There is also a collection of tools and data maintained by the Causality Workbench team [http://www.causality.inf.ethz.ch/resources.php] and the CCD team [https://www.ccd.pitt.edu/tools/].

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