Causal Inference by using Invariant Prediction: Identification and Confidence Intervals

Peters, Jonas; Bühlmann, Peter; Meinshausen, Nicolai

doi:10.1111/rssb.12167

Cited by 521 publications

(643 citation statements)

References 118 publications

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“…There exist methods for causal discovery from changes of multiple data sets [Hoover, 1990; Tian and Pearl, 2001; Peters et al ., 2016] by exploiting the property of invariance of causal mechanisms. They used linear models to represent causal mechanism and, as a consequence, the invariance of causal mechanisms can be assessed by checking whether the involved parameters change across data sets or not.…”

Section: Cd-nod Phase 2: Nonstationarity Helps Determine Causal Dirmentioning

confidence: 99%

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Zhang

Huang

Zhang³

et al. 2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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It is commonplace to encounter nonstationary or heterogeneous data, of which the underlying generating process changes over time or across data sets (the data sets may have different experimental conditions or data collection conditions). Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper we develop a principled framework for causal discovery from such data, called Constraint-based causal Discovery from Nonstationary/heterogeneous Data (CD-NOD), which addresses two important questions. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a way to determine causal orientations by making use of independence changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. Experimental results on various synthetic and real-world data sets are presented to demonstrate the efficacy of our methods.

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Section: Cd-nod Phase 2: Nonstationarity Helps Determine Causal Dirmentioning

confidence: 99%

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Zhang

Huang

Zhang³

et al. 2017

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence

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“…We then have that SðEÞ% as E%, [6] meaning that for E 2 ⊇ E 1 we have SðE 2 Þ ⊇ SðE 1 Þ. Sufficient conditions under which SðEÞ = S* , that is the causal variables are uniquely identifiable, have been worked out for linear Gaussian SEMs, requiring that E is sufficiently "rich" and form a certain class of interventions (31). From [6], we conclude that with a larger amount of experimental settings ("more heterogeneity") we have higher degree of identifiability of causal effects.…”

Section: Causal Inference Based On Invariance Across Experimentsmentioning

confidence: 99%

“…To the best of our knowledge, however, the work in ref. 31 is the first of its kind that exploits invariance of conditional distributions for statistical estimation and confidence statements.…”

Section: Causal Inference Based On Invariance Across Experimentsmentioning

confidence: 99%

Methods for causal inference from gene perturbation experiments and validation

Meinshausen

Hauser

Mooij

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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109

111

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Inferring causal effects from observational and interventional data is a highly desirable but ambitious goal. Many of the computational and statistical methods are plagued by fundamental identifiability issues, instability, and unreliable performance, especially for largescale systems with many measured variables. We present software and provide some validation of a recently developed methodology based on an invariance principle, called invariant causal prediction (ICP). The ICP method quantifies confidence probabilities for inferring causal structures and thus leads to more reliable and confirmatory statements for causal relations and predictions of external intervention effects. We validate the ICP method and some other procedures using large-scale genome-wide gene perturbation experiments in Saccharomyces cerevisiae. The results suggest that prediction and prioritization of future experimental interventions, such as gene deletions, can be improved by using our statistical inference techniques.interventional-observational data | invariant causal prediction | genome database validation | graphical models I n this article, we discuss statistical methods for causal inference from perturbation experiments. As this is a rather general topic, we focus on the following problem: based on data from observational and perturbation settings, we want to predict the effect and outcome of an unseen and new intervention or perturbation. Taking applications in genomics as an example, a typical task is as follows: based on observational data from wild-type organisms and interventional data from gene knockout or knockdown experiments, we want to predict the effect of a new gene knockout or knockdown on a phenotype of interest. For example, the organism is the model plant Arabidopsis thaliana, the gene knockouts correspond to mutant plants, and the phenotype of interest is the time it takes until the plant is flowering (1).From a methodological viewpoint, the prediction of unseen future interventions belongs to the area of causal inference where one aims to quantify presence and strength of causal effects among various variables. Loosely speaking, a causal effect is the effect of an external intervention (or say the response to a "What if I do?" question). The corresponding theory, e.g., using Pearl's do-operator (2), provides a link between causal effects and perturbations or randomized experiments. We mostly assume here that all of the variables in the causal model (for inferring causal effects) are observed: the case with hidden variables is mentioned only briefly in a later section, although it is an important theme in causal inference (due to the problem of hidden confounding variables) (cf. refs. 2 and 3).A popular and powerful route for causal modeling is given by structural equation models (SEMs) (2, 4). We consider a set of random variables X 1 , . . . , X p , X p+1 , and we often denote by Y = X 1 , emphasizing that Y is our response variable of interest (e.g., a phenotype of interest). The main building blocks of a SEM...

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“…Other excluded methods that make use of interventional data include Cooper and Yoo (1999); Tian and Pearl (2001) and Eaton and Murphy (2007), where the latter does not require knowledge of the precise location of interventions in a similar spirit to Rothenhäusler et al (2015). Hyttinen et al (2012) also makes use of intervention data to learn feedback models, assuming do-interventions, while Peters et al (2016) permits to build a graph nodewise by estimating the parental set of each node separately.…”

Section: Considered Methodsmentioning

confidence: 99%

Causal Structure Learning

Heinze‐Deml

Maathuis

Meinshausen

2018

Annu. Rev. Stat. Appl.

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122

103

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Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system but also the distributions under external interventions. They hence enable predictions under hypothetical interventions, which is important for decision making. The challenging task of learning causal models from data always relies on some underlying assumptions. We discuss several recently proposed structure learning algorithms and their assumptions, and compare their empirical performance under various scenarios.

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Causal Inference by using Invariant Prediction: Identification and Confidence Intervals

Cited by 521 publications

References 118 publications

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination

Methods for causal inference from gene perturbation experiments and validation

Causal Structure Learning

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