Exploratory causal analysis

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Causal analysis is the field of experimental design and statistical analysis pertaining to establishing cause and effect. [1] [2] Exploratory causal analysis (ECA), also known as data causality or causal discovery [3] is the use of statistical algorithms to infer associations in observed data sets that are potentially causal under strict assumptions. ECA is a type of causal inference distinct from causal modeling and treatment effects in randomized controlled trials. [4] It is exploratory research usually preceding more formal causal research in the same way exploratory data analysis often precedes statistical hypothesis testing in data analysis [5] [6]

Contents

Motivation

Data analysis is primarily concerned with causal questions. [3] [4] [7] [8] [9] For example, did the fertilizer cause the crops to grow? [10] Or, can a given sickness be prevented? [11] Or, why is my friend depressed? [12] 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). [13] Causal inference techniques used with experimental data require additional assumptions to produce reasonable inferences with observation data. [14] The difficulty of causal inference under such circumstances is often summed up as "correlation does not imply causation".

Overview

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. [3] 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. [4] Granger causality can also be used to find the causality between two observational variables under different, but similarly strict, assumptions. [15]

The two broad approaches to developing such procedures are using operational definitions of causality [5] 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 [3] ).

Operational definitions of causality

Clive Granger created the first operational definition of causality in 1969. [16] Granger made the definition of probabilistic causality proposed by Norbert Wiener operational as a comparison of variances. [17]

Some authors prefer using ECA techniques developed using operational definitions of causality because they believe it may help in the search for causal mechanisms. [5] [18]

Verification by "truth"

Peter Spirtes, Clark Glymour, and Richard Scheines introduced the idea of explicitly not providing a definition of causality. [3] Spirtes and Glymour introduced the PC algorithm for causal discovery in 1990. [19] Many recent causal discovery algorithms follow the Spirtes-Glymour approach to verification. [20]

Techniques

There are many surveys of causal discovery techniques. [3] [5] [20] [21] [22] [23] This section lists the well-known techniques.

Bivariate (or "pairwise")

Multivariate

Many of these techniques are discussed in the tutorials provided by the Center for Causal Discovery (CCD) .

Use-case examples

Social science

The PC algorithm has been applied to several different social science data sets. [3]

Medicine

The PC algorithm has been applied to medical data. [28] Granger causality has been applied to fMRI data. [29] CCD tested their tools using biomedical data .

Physics

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) [30] and in dynamical systems using pairwise asymmetric inference (a variant of convergent cross mapping). [31]

Criticism

There is debate over whether or not the relationships between data found using causal discovery are actually causal. [3] [25] Judea Pearl has emphasized that causal inference requires a causal model developed by "intelligence" through an iterative process of testing assumptions and fitting data. [7]

Response to the criticism points out that assumptions used for developing ECA techniques may not hold for a given data set [3] [14] [32] [33] [34] and that any causal relationships discovered during ECA are contingent on these assumptions holding true [25] [35]

Software Packages

Comprehensive toolkits

Specific Techniques

Granger causality

convergent cross mapping

LiNGAM

There is also a collection of tools and data maintained by the Causality Workbench team and the CCD team .

Related Research Articles

Causality is an influence by which one event, process, state, or object (acause) contributes to the production of another event, process, state, or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysically prior to notions of time and space.

The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc. This differs from the fallacy known as post hoc ergo propter hoc, in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one.

A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

<span class="mw-page-title-main">Spurious relationship</span> Apparent, but false, correlation between causally-independent variables

In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third, unseen factor.

<span class="mw-page-title-main">Trygve Haavelmo</span> Norwegian economist and econometrician

Trygve Magnus Haavelmo, born in Skedsmo, Norway, was an economist whose research interests centered on econometrics. He received the Nobel Memorial Prize in Economic Sciences in 1989.

<span class="mw-page-title-main">Bernhard Schölkopf</span> German computer scientist

Bernhard Schölkopf is a German computer scientist known for his work in machine learning, especially on kernel methods and causality. He is a director at the Max Planck Institute for Intelligent Systems in Tübingen, Germany, where he heads the Department of Empirical Inference. He is also an affiliated professor at ETH Zürich, honorary professor at the University of Tübingen and the Technical University Berlin, and chairman of the European Laboratory for Learning and Intelligent Systems (ELLIS).

<span class="mw-page-title-main">Granger causality</span> Statistical hypothesis test for forecasting

The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series. Since the question of "true causality" is deeply philosophical, and because of the post hoc ergo propter hoc fallacy of assuming that one thing preceding another can be used as a proof of causation, econometricians assert that the Granger test finds only "predictive causality". Using the term "causality" alone is a misnomer, as Granger-causality is better described as "precedence", or, as Granger himself later claimed in 1977, "temporally related". Rather than testing whether Xcauses Y, the Granger causality tests whether X forecastsY.

<span class="mw-page-title-main">Causal model</span> Conceptual model in philosophy of science

In the philosophy of science, a causal model is a conceptual model that describes the causal mechanisms of a system. Several types of causal notation may be used in the development of a causal model. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for.

<span class="mw-page-title-main">Mendelian randomization</span> Statistical method in genetic epidemiology

In epidemiology, Mendelian randomization is a method using measured variation in genes to examine the causal effect of an exposure on an outcome. Under key assumptions, the design reduces both reverse causation and confounding, which often substantially impede or mislead the interpretation of results from epidemiological studies.

The average treatment effect (ATE) is a measure used to compare treatments in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control. In a randomized trial, the average treatment effect can be estimated from a sample using a comparison in mean outcomes for treated and untreated units. However, the ATE is generally understood as a causal parameter that a researcher desires to know, defined without reference to the study design or estimation procedure. Both observational studies and experimental study designs with random assignment may enable one to estimate an ATE in a variety of ways.

Causal reasoning is the process of identifying causality: the relationship between a cause and its effect. The study of causality extends from ancient philosophy to contemporary neuropsychology; assumptions about the nature of causality may be shown to be functions of a previous event preceding a later one. The first known protoscientific study of cause and effect occurred in Aristotle's Physics. Causal inference is an example of causal reasoning.

Causal analysis is the field of experimental design and statistics pertaining to establishing cause and effect. Typically it involves establishing four elements: correlation, sequence in time, a plausible physical or information-theoretical mechanism for an observed effect to follow from a possible cause, and eliminating the possibility of common and alternative ("special") causes. Such analysis usually involves one or more artificial or natural experiments.

The Bradford Hill criteria, otherwise known as Hill's criteria for causation, are a group of nine principles that can be useful in establishing epidemiologic evidence of a causal relationship between a presumed cause and an observed effect and have been widely used in public health research. They were established in 1965 by the English epidemiologist Sir Austin Bradford Hill.

Clark N. Glymour is the Alumni University Professor Emeritus in the Department of Philosophy at Carnegie Mellon University. He is also a senior research scientist at the Florida Institute for Human and Machine Cognition.

<span class="mw-page-title-main">Collider (statistics)</span> Variable that is causally influenced by two or more variables

In statistics and causal graphs, a variable is a collider when it is causally influenced by two or more variables. The name "collider" reflects the fact that in graphical models, the arrow heads from variables that lead into the collider appear to "collide" on the node that is the collider. They are sometimes also referred to as inverted forks.

Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed. The study of why things occur is called etiology, and can be described using the language of scientific causal notation. Causal inference is said to provide the evidence of causality theorized by causal reasoning.

Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y. More specifically, if and for denote two random processes and the amount of information is measured using Shannon's entropy, the transfer entropy can be written as:

In statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs are probabilistic graphical models used to encode assumptions about the data-generating process.

<i>Causality</i> (book)

Causality: Models, Reasoning, and Inference is a book by Judea Pearl. It is an exposition and analysis of causality. It is considered to have been instrumental in laying the foundations of the modern debate on causal inference in several fields including statistics, computer science and epidemiology. In this book, Pearl espouses the Structural Causal Model (SCM) that uses structural equation modeling. This model is a competing viewpoint to the Rubin causal model. Some of the material from the book was reintroduced in the more general-audience targeting The Book of Why.

<i>The Book of Why</i> 2018 book by Judea Pearl and Dana Mackenzie

The Book of Why: The New Science of Cause and Effect is a 2018 nonfiction book by computer scientist Judea Pearl and writer Dana Mackenzie. The book explores the subject of causality and causal inference from statistical and philosophical points of view for a general audience.

References

  1. ↑ Rohlfing, Ingo; Schneider, Carsten Q. (2018). "A Unifying Framework for Causal Analysis in Set-Theoretic Multimethod Research" (PDF). Sociological Methods & Research. 47 (1): 37–63. doi:10.1177/0049124115626170. S2CID   124804330. Archived from the original (PDF) on 9 October 2022. Retrieved 29 February 2020.
  2. ↑ Brady, Henry E. (7 July 2011). "Causation and Explanation in Social Science". The Oxford Handbook of Political Science. doi:10.1093/oxfordhb/9780199604456.013.0049 . Retrieved 29 February 2020.
  3. 1 2 3 4 5 6 7 8 9 10 11 Spirtes, P.; Glymour, C.; Scheines, R. (2012). Causation, Prediction, and Search. Springer Science & Business Media. ISBN   978-1461227489.
  4. 1 2 3 Rosenbaum, Paul (2017). Observation and Experiment: An Introduction to Causal Inference. Harvard University Press. ISBN   9780674975576.
  5. 1 2 3 4 McCracken, James (2016). Exploratory Causal Analysis with Time Series Data (Synthesis Lectures on Data Mining and Knowledge Discovery). Morgan & Claypool Publishers. ISBN   978-1627059343.
  6. ↑ Tukey, John W. (1977). Exploratory Data Analysis. Pearson. ISBN   978-0201076165.
  7. 1 2 Pearl, Judea (2018). The Book of Why: The New Science of Cause and Effect. Basic Books. ISBN   978-0465097616.
  8. ↑ Kleinberg, Samantha (2015). Why: A Guide to Finding and Using Causes. O'Reilly Media, Inc. ISBN   978-1491952191.
  9. ↑ Illari, P.; Russo, F. (2014). Causality: Philosophical Theory meets Scientific Practice. OUP Oxford. ISBN   978-0191639685.
  10. ↑ Fisher, R. (1937). The design of experiments. Oliver And Boyd.
  11. ↑ Hill, B. (1955). Principles of Medical Statistics. Lancet Limited.
  12. ↑ Halpern, J. (2016). Actual Causality. MIT Press. ISBN   978-0262035026.
  13. ↑ Pearl, J.; Glymour, M.; Jewell, N. P. (2016). Causal inference in statistics: a primer. John Wiley & Sons. ISBN   978-1119186847.
  14. 1 2 Stone, R. (1993). "The Assumptions on Which Causal Inferences Rest". Journal of the Royal Statistical Society. Series B (Methodological). 55 (2): 455–466. doi:10.1111/j.2517-6161.1993.tb01915.x.
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  16. ↑ Granger, C. W. J. (1969). "Investigating Causal Relations by Econometric Models and Cross-spectral Methods". Econometrica. 37 (3): 424–438. doi:10.2307/1912791. JSTOR   1912791.
  17. ↑ Granger, Clive. "Prize Lecture. NobelPrize.org. Nobel Media AB 2018".
  18. ↑ Woodward, James (2004). Making Things Happen: A Theory of Causal Explanation (Oxford Studies in the Philosophy of Science). Oxford University Press. ISBN   978-1435619999.
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  20. 1 2 Guo, Ruocheng; Cheng, Lu; Li, Jundong; Hahn, P. Richard; Liu, Huan (2020). "A Survey of Learning Causality with Data". ACM Computing Surveys. 53 (4): 1–37. arXiv: 1809.09337 . doi:10.1145/3397269. S2CID   52822969.
  21. ↑ Malinsky, Daniel; Danks, David (2018). "Causal discovery algorithms: A practical guide". Philosophy Compass. 13 (1): e12470. doi: 10.1111/phc3.12470 .
  22. ↑ Spirtes, P.; Zhang, K. (2016). "Causal discovery and inference: concepts and recent methodological advances". Appl Inform (Berl). 3: 3. doi: 10.1186/s40535-016-0018-x . PMC   4841209 . PMID   27195202.
  23. ↑ Yu, Kui; Li, Jiuyong; Liu, Lin; Richard Hahn, P.; Liu, Huan (2016). "A review on algorithms for constraint-based causal discovery". arXiv: 1611.03977 [cs.AI].
  24. ↑ Sun, Jie; Bollt, Erik M.; Li, Jundong; Richard Hahn, P.; Liu, Huan (2014). "Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings". Physica D: Nonlinear Phenomena. 267: 49–57. arXiv: 1504.03769 . Bibcode:2014PhyD..267...49S. doi:10.1016/j.physd.2013.07.001. S2CID   14422483.
  25. 1 2 3 Freedman, David; Humphreys, Paul (1999). "Are there algorithms that discover causal structure?". Synthese. 121 (1–2): 29–54. doi:10.1023/A:1005277613752. S2CID   6826436.
  26. ↑ Raghu, V. K.; Ramsey, J. D.; Morris, A.; Manatakis, D. V.; Sprites, P.; Chrysanthis, P. K.; Glymour, C.; Benos, P. V. (2018). "Comparison of strategies for scalable causal discovery of latent variable models from mixed data". International Journal of Data Science and Analytics. 6 (33): 33–45. doi:10.1007/s41060-018-0104-3. PMC   6096780 . PMID   30148202.
  27. ↑ Shimizu, S (2014). "LiNGAM: non-Gaussian methods for estimating causal structures". Behaviormetrika. 41 (1): 65–98. doi:10.2333/bhmk.41.65. S2CID   49238101.
  28. ↑ Cheek, C.; Zheng, H.; Hallstrom, B. R.; Hughes, R. E. (2018). "Application of a Causal Discovery Algorithm to the Analysis of Arthroplasty Registry Data". Biomed Eng Comput Biol. 9: 117959721875689. doi:10.1177/1179597218756896. PMC   5826097 . PMID   29511363.
  29. ↑ Wen, X.; Rangarajan, G.; Ding, M. (2013). "Is Granger Causality a Viable Technique for Analyzing fMRI Data?". PLOS ONE. 8 (7): e67428. Bibcode:2013PLoSO...867428W. doi: 10.1371/journal.pone.0067428 . PMC   3701552 . PMID   23861763.
  30. ↑ Ebert-Uphoff, Imme; Deng, Yi (2017). "Causal discovery in the geosciences—Using synthetic data to learn how to interpret results". Computers & Geosciences. 99: 50–60. Bibcode:2017CG.....99...50E. doi: 10.1016/j.cageo.2016.10.008 .
  31. ↑ McCracken, J. M.; Weigel, R. S.; Li, Jundong; Richard Hahn, P.; Liu, Huan (2014). "Convergent cross-mapping and pairwise asymmetric inference". Phys. Rev. E. 90 (6): 062903. arXiv: 1407.5696 . Bibcode:2014PhRvE..90f2903M. doi:10.1103/PhysRevE.90.062903. PMID   25615160. S2CID   7506718.
  32. ↑ Scheines, R. (1997). "An introduction to causal inference" (PDF). Causality in Crisis: 185–199.
  33. ↑ Holland, P. W. (1986). "Statistics and causal inference". Journal of the American Statistical Association. 81 (396): 945–960. doi:10.1080/01621459.1986.10478354. S2CID   14377504.
  34. ↑ Imbens, G. W.; Rubin, D. B. (2015). Causal inference in statistics, social, and biomedical sciences. Cambridge University Press. ISBN   978-0521885881.
  35. ↑ Morgan, S. L.; Winship, C. (2015). Counterfactuals and causal inference. Cambridge University Press. ISBN   978-1107065079.
  36. ↑ "Causal Models and Statistical Data, The Tetrad Project".
  37. ↑ "Tools, Center for Causal Discovery, University of Pittsburg". 10 August 2016.
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