## Causal Inference

*15 May 2021 12:15*

Spun off from Causality. Graphical causal models are, I think very strongly, the best way to approach this, and so they get their own notebook.

Things I need to learn more about: non-linear and non-parametric instrumental variables estimators.

*Something that puzzles me*: Can we estimate the causal effects of
common institutions? To give the concrete example that made this strike me:
suppose we want to know whether offering new Ph.D.s "good" post-doctoral
fellowships helps their later career. Any one post-doc program could try to
estimate its effect in any of several well-established ways. (For instance, it
might compare those who accept their fellowships to those just below the
cut-off, or those to whom it made offers which were declined.) However, those
control cases are very likely individuals who are going to get such
fellowships, or similar treatment, anyway. The program is at most getting at
its differential effect, compared to going into a different but similar
program, in an institutional context where such programs are common (for the
relevant population). It is entirely possible that each program has no
differential effect, but that if they were all shut down, everyone would be
much worse off. Is there any way to identify the effect of a pervasive
institution, short of doing the experiment of, say, arbitrarily excluding half
the relevant population? (This is obviously related to all sorts of questions,
like paradoxes of composition, interference, etc.)

See also: Computational Mechanics; Experiments on Social Networks; Graphical Models; Homophily and Influence in Social Networks; Machine Learning, Statistical Inference, and Induction

- Recommended (current big picture):
- Clark Glymour
- The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology [Mini-review]
- "What Went Wrong? Reflections on Science by Observation
and The Bell Curve", Philosophy of Science
**65**(1998): 1--32 [PDF reprint via Prof. Glymour]

- Sander Greenland, Judea Pearl and James M. Robins,
"Causal Diagrams for Epidemiologic Research", Epidemiology
**10**(1999): 37--48 [PDF via Prof. Pearl. Very much*not*just for epidemiologists.] - Stephen L. Morgan and Christopher Winship, Counterfactuals and Causal Inference: Methods and Principles for Social Research [Mini-review]
- Judea Pearl
- "Causal Inference in Statistics: An Overview",
Statistics Surveys
**3**(2009): 96--146 - Causality: Models, Reasoning and Inference

- "Causal Inference in Statistics: An Overview",
Statistics Surveys
- Donald B. Rubin and Richard P. Waterman, "Estimating the Causal
Effects of Marketing Interventions Using Propensity Score
Methodology", math.ST/0609201
= Statistical Science
**21**(2006): 206--222 [A good description of Rubin et al.'s methods for causal inference, adapted to the meanest understanding. I list this here rather than under "more specialized" because Rubin and Waterman do a very good job of explaining, in a clear and concrete problem, just how and why the newer techniques of causal inference are valuable, with just enough technical detail that it doesn't seem like magic. Rubin's paper-collection, Matched Sampling for Causal Effects, has much, much more if this appeals to you, though it is just a paper collection and not a proper book, so there's a lot of redundancy.] - Peter Spirtes, Clark Glymour and Richard Scheines, Causation, Prediction and Search [Comments]

- Recommended (more specialized):
- Kevin Arceneaux, Alan S. Gerber, Donald P. Green,
"A Cautionary Note on the Use of Matching to Estimate Causal Effects: An Empirical Example Comparing Matching Estimates to an Experimental Benchmark",
Sociological Methods and
Research
**39**(2010): 256--282 ["Cautionary" is not really strong enough.] - Peter M. Aronow and Cyrus Samii, "Does Regression Produce Representative Estimates of Causal Effects?", ssrn/2224964
- Bryant Chen and Judea Pearl, "Regression and Causation: A Critical Examination of Econometrics Textbooks" [PDF preprint via Prof. Pearl]
- Tianjiao Chu and Clark Glymour, "Search for Additive Nonlinear Time Series Causal Models", Journal of Machine Learning Research
**9**(2008): 967--991 - Diego Colombo, Marloes H. Maathuis, Markus Kalisch, Thomas S. Richardson, "Learning high-dimensional directed acyclic graphs with latent and selection variables", arxiv:1104.5617
- Allan Dafoe, "First Do No Harm: The Risks of Modeling Temporal Dependence" [PDF preprint]
- Angus Deaton, "Instruments, Randomization, and Learning about
Development", Journal
of Economic Literature
**48**(2010): 424--455 [PDF reprint via Prof. Deaton] - Vanessa Didelez, "Causal Reasoning for Events in Continuous Time: A Decision–Theoretic Approach", UAI 2015
- Vanessa Didelez, Sha Meng, Nuala A. Sheehan, "Assumptions of IV Methods for Observational Epidemiology", Statistical Science
**25**(2010): 22--40, arxiv:1011.0595 - Felix Elwert and Nicholas A. Christakis,
"Wives and Ex-Wives: A New Test for Homogamy Bias in the Widowhood Effect",
Demography
**45**(2008): 851--873 [PDF preprint courtesy of Prof. Elwert] - Robin J. Evans and Vanessa Didelez, "Recovering from Selection Bias using Marginal Structure in Discrete Models", UAI 2015
- Franklin M. Fisher, "A Correspondence Principle for Simultaneous
Equation
Models", Econometrica
**38**(1970): 73--92 [When are simultaneous systems of equations legitimate limits of models of time-evolution? And when does it make sense to calculate causal effects in simultaneous-equation models by "surgery"?] - Clive Granger, "Investigating Causal Relations by Econometric
Models and Cross Spectral
Methods", Econometrica
**37**(1969): 424--439 [His original paper on what has come to be called "Granger causality". It's actually very interesting — I hadn't realized he got the idea from reading Norbert Wiener, but in retrospect that makes sense and explains why he formulated his test in the frequency domain — but I feel it's very much a dead end for actual causal inference.] - Kevin D. Hoover, Causality in Macroeconomics
- Edward H. Kennedy, "Optimal doubly robust estimation of heterogeneous causal effects", arxiv:2004.14497
- Gary King and Richard Nielsen, "Why Propensity Scores Should Not Be Used for Matching" [Preprint via Prof. King. The point about trying to mimic an fully randomized rather than a blocked experiment is an interesting and I think correct one...]
- Samantha Kleinberg, An Algorithmic Enquiry Concerning Causality [Ph.D. thesis, NYU, 2010; PDF]
- Gustavo Lacerda, Peter Spirtes, Joseph Ramsey and Patrik O. Hoyer, "Discovering Cyclic Causal Models by using Independent Components Analysis" [PDF draft via Gustavo]
- Jan Lemeire, Dominik Janzing, "Replacing Causal Faithfulness with Algorithmic Independence of Conditionals", Minds and Machines
**23**(2013): 227--249 - Judith Lok, Statistical Modeling of Causal Effects in Time (Ph.D. thesis, Vrije Universiteit Amsterdam, 2001)
- Marloes H. Maathuis, Markus Kalisch, Peter Bühlmann, "Estimating high-dimensional intervention effects from observational data", Annals
of Statistics
**37**(2009): 3133--31654, arxiv:0810.4214 - Milan Palus and Aneta
Stefanovska, "Direction of coupling from phases of interacting oscillators: An
information-theoretic approach", Physical Review
E
**67**(2003): 055201 [Thanks to Prof. Palus for a reprint. This is a kind of information-theoretic generalization of Granger causality.] - Judea Pearl, "Linear Models: A Useful ``Microscope'' for Causal Analysis", Journal of Causal Inference
**1**(2013): 155--170 - Tom Pepinsky, "OMFG Exogenous Variation! Or, Can You Find Good Nails When You Find an Indonesian Politics Hammer?" [Admittedly, less formal in presentation than many of the rest of these links]
- Maxim Raginsky, "Directed information and Pearl's causal calculus", arxiv:1110.0718
- J. D. Ramsey, S. J. Hanson, C. Hanson, Y. O. Halchenko,
R. A. Poldrack and C. Glymour, "Six Problems for Causal Inference from
fMRI", NeuroImage
**49**(2010): 1545--1558 [PDF via Prof. Hanson; thanks to Prof. Glymour for having shared a preprint with me] - James M. Robins, Richard Scheines, Peter Spirtes and Larry
Wasserman, "Uniform Consistency in Causal Inference",
Biometrika
**90**(2003): 491--515 [CMU Statistics Tech Report 725, 2000] - Mark R. Rosenzweig and Kenneth I. Wolpin, "Natural "Natural Experiments" in Economics", Journal of Economic Literature
**38**(2000): 827--874 - Heather Sarsons, "Rainfall and Conflict" [From the Annals of Invalid Instruments... PDF preprint]
- Amit Sharma, Jake M. Hofman and Duncan J. Watts, "Estimating the Causal Impact of Recommendation Systems from Observational Data", pp. 453--470 in Michal Feldman, Michael Schwarz and Tim Roughgarden (eds.), Proceedings of the Sixteenth ACM Conference on Economics and Computation [EC '15], arxiv:1510.05569 [Recommendable in this context as a nice case study]
- Herbert Simon
- "Causal Ordering and Identifiability", in Studies in Econometric Method, 1953; reprinted as chapter 1 in Simon's Models of Man [PDF of the 1950 preprint version, as "The Causal Principle and the Identification Problem"]
- "Spurious Correlation: A Causal Interpretation",
Journal of the American Statistical
Association
**49**(1954): 467-479 [PDF reprint]

- Michael E. Sobel
- "Does Marriage Boost Men's Wages? Identification of Treatment Effects in Fixed Effects Regression Models for Panel Data", Journal of the American Statistical Association
**107**(2012): 521--529 - "What Do Randomized Studies of Housing Mobility Demonstrate? Causal Inference in the Face of Interference", Journal of the American Statistical Association
**101**(2006): 1398--1407

- "Does Marriage Boost Men's Wages? Identification of Treatment Effects in Fixed Effects Regression Models for Panel Data", Journal of the American Statistical Association
- Peter Spirtes, "Limits on Causal Inference from Observational Data" [PostScript preprint; PDF]
- Bastian Steudel and Nihat Ay, "Information-theoretic inference of common ancestors", arxiv:1010.5720
- Elizabeth A. Stuart, "Matching Methods for Causal Inference: A Review and a Look Forward", Statistical Science
**25**(2010): 1--21, arxiv:1010.5586 - C. Uhler, G. Raskutti, B. Yu, Peter Bühlmann, "Geometry of faithfulness assumption in causal inference", arxiv:1207.0547
- Halbert White and Karim Chalak, "Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning",
Journal of Machine Learning Research
**10**(2009): 1759--1799 [Thanks to Doug White for a preprint] - Christopher Winship
- Counterfactual Causal Analysis [Repository page with papers aimed at sociological applications]
- and Stephen L. Morgan, "Estimation of Causal Effects from
Observational Data," Annual Review of
Sociology
**25**(1999): 659--706 [PDF reprint, large] - and Michael Sobel, "Causal Inference in Sociological Studies" [PDF preprint]

- Recommended (historical):
- Hubert M. Blalock, Causal Inferences in Nonexperimental Research [Comments]
- Jerzy Neyman, "On the Application of Probability Theory to
Agricultural Experiments: Essay on Principles, Section
9", Statistical
Science
**5**(1990): 465--472 [Translation of part of Neyman's 1923 dissertation]

- Not altogether recommended:
- Guido W. Imbens and Donald B. Rubin, Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction [for reasons given in my review for the Journal of the American Statistical Association]
- Yuta Saito, Shota Yasui, "Counterfactual Cross-Validation: Stable
Model Selection Procedure for Causal Inference
Models", arxiv:1909.05299 [My
notes after reading were as follows: Their goal is a good one, but the
fundamental issue is that we don't
*have*observations of individual-level causal effects to cross-validate against. So they proxy that by a very standard doubly-robust estimator of said effects; at which point, why not just use that estimator? In any case, I want to see comparisons to the Naive Statistician's approach of just cross-validating for outcomes (rather than differences in potential outcomes). I should add that I've only read version 1 of the paper, from September 2019, and as I add this, in July 2020, they're up to version 5...]

- Modesty forbids me to recommend:
- CRS, Advanced Data Analysis from an Elementary Point of View, Part III (chapters on causal inference for statistics students)
- CRS and Andrew C. Thomas, "Homophily and Contagion Are Generically Confounded in Observational Social Network Studies", arxiv:1004.4704 [Less-technical weblog version]

- To read:
- Mickel Aickin, Causal Analysis in Biomedicine and Epidemiology: Based on Minimal Sufficient Causation
- Nicola Ancona, Daniele Marinazzo and Sebastiano Stramaglia, "Extending Granger causality to nonlinear systems", physics/0405009
- Aron Barbey and Phillip Wolff, "Learning Causal Structure from Reasoning", phil-sci/3176
- Michael Baumgartner, "Inferring Causal Complexity", phil-sci/2879 [Identifying causal structures among Boolean variables, handling "both mutually dependent causes, i.e. causal chains, and multiple effects, i.e. epiphenomena"]
- Alexandre Belloni, Victor Chernozhukov, Christian Hansen, "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls", arxiv:1201.0224
- Alexandre Belloni, Victor Chernozhukov, Ivan Fernández-Val, Christian Hansen, "Program Evaluation and Causal Inference with High-Dimensional Data",
Econometrica
**85**(2017): 233--298, arxiv:1311.2645 - Andrew Bennett, "Process Tracing and Causal Inference", phil-sci/8872
- Carlo Berzuini, Luisa Bernardinell and Philip Dawid (eds.), Causality: Statistical Perspectives and Applications
- Aaron P. Blaisdell, Kosuke Sawa, Kenneth J. Leising, and Michael
R. Waldmann, "Causal Reasoning in Rats", Science
**311**(2006): 1020--1022 - Hans-Peter Blossfeld and Gotz Rohwer, Techniques of Event-History Modeling: New Approach to Causal Analysis
- Kenneth A. Bollen and Shawn Bauldry, "Model Identification and Computer Algebra", Sociological Methods and Research
**39**(2010): 127--156 - Michael B. Bracken, Risk, Chance, and Causation: Investigating the Origins and Treatment of Disease
- John G. Bullock and Donald P. Green Shang E. Ha, "Yes, But What’s the Mechanism? (Don’t Expect an Easy Answer)", Journal of Personality and Social Psychology
**98**(2010): 550--558 [PDF reprint via Dr. Bullock] - Zhihong Cai, Manabu Kuroki, "On Identifying Total Effects in the Presence of Latent Variables and Selection Bias", UAI 2008, arxiv:1206.3239
- Yonghong Chen, Steven L. Bressler, and Mingzhou Ding, "Frequency
decomposition of conditional Granger causality and application to multivariate
neural field potential
data", q-bio.NC/0608034
= Journal of Neuroscience Methods
**150**(2006): 228--237 - Timothy G. Conley, Christian B. Hansen and Peter E. Rossi,
"Plausibly
Exogenous", The Review
of Economics and Statistics
**94**(2012): 260--272 - Daniel Commenges, Anne Gegout-Petit, "A general dynamical statistical model with possible causal interpretation", Journal of the Royal Statistical Society B
**71**(2009): 719--736, arxiv:0710.4396 - Alexander D'Amour, "On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives", arxiv:1902.10286
- P. Daniusis, D. Janzing, J. Mooij, J. Zscheischler, B. Steudel, K. Zhang and B. Schölkopf, "Inferring deterministic causal relations", UAI 2010 [Abstract, preprint. I heard the talk, which was very interesting, but want to understand the idea better. If you fed this a seauence from the Arnold cat map, could it get the arrow of time?]
- A. Philip Dawid and Vanessa Didelez, "Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview", Statistics Surveys
**4**(2010): 184--231 - Vanessa Didelez, Svend Kreiner and Niels Keiding, "Graphical Models
for Inference Under Outcome-Dependent
Sampling", Statistical
Science
**25**(2010): 368--387, arxiv:1101.0901 - Mingzhou Ding, Yonghong Chen and Steve L. Bressler, "Granger Causality: Basic Theory and Application to Neuroscience", q-bio.QM/0608035 = pp. 451--474 in B. Schelter, M. Winterhalder, and J. Timmer (eds.), Handbook of Time Series Analysis
- Patrick Doreian, "Causality in Social Network Analysis",
Sociological
Methods and Research
**30**(2001): 81--114 - Thad Dunning, "Improving Causal Inference: Strengths and Limitations
of Natural Experiments", Political
Research Quarterly
**61**(2008): 282--293 [PDF reprint via Prof. Dunning] - Frederick Eberhardt and Richard Scheines, "Interventions and Causal Inference", phil-sci/2944
- Michael Eichler
- "Graphical modelling of multivariate time series", math.ST/0610654
- "Graphical Gaussian modelling of multivariate time series with latent variables", Journal of Machine Learning Research Proceedings
**9**(2010): 193--200

- Elena Erosheva, Emily W. Walton and David T. Takeuchi, "Self-Rated
Health among Foreign- and U.S.-Born Asian Americans: A Test of
Comparability", Medical
Care
**45**(2007): 80--87 [As an application of propensity-score matching to a multi-level response] - David A. Freedman
- "On Specifying Graphical Models for Causation," UCB Stat. Tech. Rep. 601 [abstract, pdf]
- Statistical Models and Causal Inference: A Dialogue with the Social Sciences

- Anne Gegout-Petit and Daniel Commenges, "A general definition of influence between stochastic processes", arxiv:0905.3619
- Glymour and Cooper (eds.), Computation, Causation and Discovery
- Adam Glynn and Kevin Quinn, "Non-parametric Mechanisms and Causal Modeling" [PDF preprint]
- Jorge Goncalves and Sean Warnick, "Dynamical Structure Functions for the Estimation of LTI Networks with Limited Information", q-bio.MN/0610008 [LTI = "linear, time-invariant"]
- Alison Gopnik and Laura Schulz (eds.), Causal Learning: Psychology, Philosophy and Computation
- James B. Grace, Structural Equation Modeling and Natural Systems [Blurb]
- Stefan Haufe, Guido Nolte, Klaus-Robert Mueller and Nicole Kraemer, "Sparse Causal Discovery in Multivariate Time Series", arxiv:0901.1234 [I am not altogether happy with defining "causes" as "has a non-zero coefficient in a vector autoregression"...]
- Jeffrey Haydu, "Reversals of fortune: path dependency,
problem solving, and temporal cases", Theory and Society
**39**(2010): 25--48 - Yang-Bo He and Zhi Geng, "Active Learning of Causal
Networks with Intervention Experiments and Optimal Designs",
Journal of
Machine Learning Research
**9**(2008): 2523--2547 - Jennifer L. Hill, "Bayesian nonparametric modeling for
causal inference", Journal of Computational and Graphical
Statistics
**20**(2011): 217--240 [Abstract doesn't address issues of identifiability, or the causation/prediction difference] - Kosuke Imai, Quantitative Social Science
- Kosuke Imai, Luke Keele, and Teppei Yamamoto, "Identification,
Inference and Sensitivity Analysis for Causal Mediation
Effects", Statistical
Science
**25**(2010): 51--71 - Kosuke Imai, Gary King and Elizabeth Stuart, "Misunderstandings among Experimentalists and Observationalists about Causal Inference" [PDF pre-print]
- Katsuhiko Ishiguro, Nobuyuki Otsu, Max Lungarella and Yasuo
Kuniyoshi, "Comparison of nonlinear Granger causality extensions for
low-dimensional
systems", Physical
Review E
**77**(2008): 036217 - Michael Jachan, Kathrin Henschel, Jakob Nawrath, Ariane Schad, Jens
Timmer and Bjorn Schelter, "Inferring direct directed-information flow from
multivariate nonlinear time
series", Physical
Review E
**80**(2009): 011138 - Dominik Janzing, Xiaohai Sun and Bernhard Schölkopf, "Distinguishing Cause and Effect via Second Order Exponential Models", arxiv:0910.5561
- David D. Jensen, Andrew S. Fast, Brian J. Taylor, Marc E. Maier, "Automatic Identification of Quasi-Experimental Designs for Discovering Causal Knowledge", SIGKDD 2008 [PDF reprint]
- Changsung Kang, Jin Tian, "Inequality Constraints in Causal Models with Hidden Variables", arxiv:1206.6829
- Jack Katz, "From How to Why: On Luminous Description and
Causal Inference in Ethnography"
- "Part I", Ethnography
**2**(2001): 443--473 [PDF reprint] - "Part II", Ethnography
**3**(2002): 63--90 [PDF reprint]

- "Part I", Ethnography
- Alon Keinan, Ben Sandbank, Claus C. Hilgetag, Isaac Meilijson and
Eytan Ruppin, "Fair Attribution of Functional Contribution in Artificial and
Biological Networks", Neural
Computation
**16**(2004): 1887--1915 - Samantha Kleinberg, Why: A Guide to Finding and Using Causes
- Ioannis Kontoyiannis, Maria Skoularidou, "Estimating the Directed Information and Testing for Causality", arxiv:1507.01234
- Manabu Kuroki, "Bounds on average causal effects in studies with a
latent response variable", Metrika
**61**(2005): 63--71 - Manabu Kuroki, Zhihong Cai, Hiroki Motogaito "The Graphical Identification for Total Effects by using Surrogate Variables", UAI 2005, arxiv:1207.1392
- Vincent Lariviere, Yves Gingras, "The impact factor's Matthew effect: a natural experiment in bibliometrics", arxiv:0908.3177
- Stephen A. Lauer, Nicholas G. Reich, Laura B. Balzer, "The covariate-adjusted residual estimator and its use in both randomized trials and observational settings", arxiv:1910.11397
- Max A. Little, Reham Badawy, "Causal bootstrapping", arxiv:1910.09648
- Judith J. Lok
- "Mimicking counterfactual outcomes for the estimation of causal effects", math.ST/0409045
- "Statistical modelling of causal effects in continuous
time", Annals of Statistics
**36**(2008): 1464--1507, math.ST/0410271

- Daniele Marinazzo, Mario Pellicoro and Sebastiano Stramaglia,
"Nonlinear parametric model for Granger causality of time series",
Physical Review
E
**73**(2006): 066216, cond-mat/0602183 - Conor Mayo-Wilson
- "The Problem of Piecemeal Induction",
Philosophy of Science
**78**(2011): 864--874 - Combining Causal Theories and Dividing Scientific Labor [Ph.D. thesis, CMU Philosophy Dept., 2012; thanks to Dr. Mayo-Wilson for a copy]

- "The Problem of Piecemeal Induction",
Philosophy of Science
- Vaughn R. McKim and Stephen P. Turner (ed.), Causality in Crisis? Statistical Methods and the Search for Causal Knowledge in the Social Sciences
- K. Mengersen, S. A. Moynihan, R. L. Tweedie, "Causality and Association: The Statistical and Legal Approaches", arxiv:0710.4459
- Trang Quynh Nguyen, Elizabeth A. Stuart, "Propensity score analysis with latent covariates: Measurement error bias correction using the covariate's posterior mean, aka the inclusive factor score", arxiv:1907.12709
- Judea Pearl, "On Measurement Bias in Causal Inference", UAI 2010, arxiv:1203.3504
- Jonas Peters, Dominik Janzing and Bernhard Schökopf
- "Causal Inference on Discrete Data using Additive Noise Models", arxiv:0911.0280
- Elements of Causal Inference: Foundations and Learning Algorithms

- Adam Przeworski, "Is the Science of Comparative Politics Possible?" [PDF preprint. On drawing causal conclusions from natural "quasi-experiments".]
- Roland R. Ramsahai,
- "Causal Bounds and Instruments", UAI 2007, arxiv:1206.5262
- "Causal Bounds and Observable Constraints for Non-deterministic Models", Journal of Machine Learning Research
**13**(2012): 829--848

- Paul R. Rosenbaum, Observation and Experiment: An Introduction to Causal Inference
- Federica Russo, "Correlational data, causal hypotheses, and validity", phil-sci/8349
- Federica Russo and Jon Williamson, "Generic versus Single-case Causality: the Case of Autopsy", phil-sci/5148
- Anil K. Seth and Gerald M. Edelman, "Distinguishing Causal
Interactions in Neural Populations", Neural
Computation
**19**(2007): 910--933 - Glenn Shafer, The Art of Causal Conjecture [Bought from an on-line bookstore which gave the title as The Art of Casual Conjecture; a book which should be written. Reviwed by Glymour (PDF)]
- Ilya Shpitser, Judea Pearl, "Complete Identification Methods for
the Causal
Hierarchy", Journal of
Machine Learning Research
**9**(2008): 1941--1979 - Linda Sommerlade, Michael Eichler, Michael Jachan, Kathrin Henschel,
Jens Timmer, and Bjorn Schelter, "Estimating causal dependencies in
networks of nonlinear stochastic dynamical systems", Physical
Review E
**80**(2009): 051128 - Ioannis Tsamardinos, Sofia Triantafillou, Vincenzo Lagani, "Towards Integrative Causal Analysis of Heterogeneous Data Sets and Studies",
Journal
of Machine Learning Research
**13**(2012): 1097--1157 - Mark J. van der Laan, "Causal Inference for Networks", UC Berkeley Biostatistics working paper no. 300 (2012)
- Mark J. van der Laan and Sherri Rose, Targeted Learning: Causal Inference for Observational and Experimental Data
- P. F. Verdes, "Assessing causality from multivariate time series",
Physical Review
E
**72**(2005):v 026222 - Kenneth I. Wolpin, The Limits of Inference without Theory
- S. Yang, L. Wang, P. Ding, "Causal inference with confounders missing not at random", Biometrika
**106**(2019): 875--888