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Causal discovery and inference: concepts and recent methodological advances
Open accessAbstract
This paper aims to give a broad coverage of central concepts and principles involved in automated causal inference and emerging approaches to causal discovery from i.i.d data and from time series. After reviewing concepts including manipulations, causal models, sample predictive modeling, causal predictive modeling, and structural equation models, we present the constraint-based approach to causal discovery, which relies on the conditional independence relationships in the data, and discuss the assumptions underlying its validity. We then focus on causal discovery based on structural equations models, in which a key issue is the identifiability of the causal structure implied by appropriately defined structural equation models: in the two-variable case, under what conditions (and why) is the causal direction between the two variables identifiable? We show that the independence between the error term and causes, together with appropriate structural constraints on the structural equation, makes it possible. Next, we report some recent advances in causal discovery from time series. Assuming that the causal relations are linear with nonGaussian noise, we mention two problems which are traditionally difficult to solve, namely causal discovery from subsampled data and that in the presence of confounding time series. Finally, we list a number of open questions in the field of causal discovery and inference.
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Metadata
- Authors
- Spirtes, P., & Zhang, K.
- Affiliations
- Carnegie Mellon University (US)
- Max Planck Institute for Intelligent Systems (DE)
- Corresponding author
- Zhang, Kun
- Venue
- Applied Informatics
- Published
- 2016-02-18
- Volume
- 3
- Issue
- 1
- Pages
- 3-3
- ISSN
- 2196-0089 (ISSN-L)
- PMC
- PMC4841209
- OpenAlex
- W2297288734
- Cited by
- 304
- References
- 80
- Citations by year
- 2026: 19 · 2025: 37 · 2024: 32 · 2023: 40 · 2022: 24 · 2021: 42 · 2020: 40 · 2019: 24 · 2018: 25 · 2017: 17 · 2016: 4
- FWCI
- 3.92
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Applied Informatics (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- National Science Foundation (1317428)
- National Institutes of Health
- National Human Genome Research Institute (U54HG008540)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- causal discovery, causal inference, constraint-based causal discovery, conditional independence, causal models, structural equation modeling, confounding, non-Gaussian noise
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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