Foundations of structural causal models with cycles and latent variables

Bongers, Stephan; Forré, Patrick; Peters, Jonas; Mooij, Joris M.

doi:10.1214/21-aos2064

Cited by 68 publications

(49 citation statements)

References 33 publications

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“…This assumption allows us to relax existing identifiability conditions: it is, for example, possible to identify β * even if there are much less instruments than covariates. Our results are proved in the context of linear structural causal models (SCMs) [Pearl, 2009, Bongers et al, 2021, that is, we also assume linearity among the X variables. We prove sufficient conditions for identifiability of β * that are based on rank conditions of the matrix of causal effects from I on the parents of Y .…”

Section: Introductionmentioning

confidence: 88%

Identifiability of Sparse Causal Effects using Instrumental Variables

Pfister¹,

Peters²

2022

Preprint

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Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in which the causal effect from covariates X on a response Y is sparse. We provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and Y is childless. As an estimator, we propose spaceIV and prove that it consistently estimates the causal effect if the model is identifiable and evaluate its performance on simulated data. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.

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Section: Introductionmentioning

confidence: 88%

Identifiability of Sparse Causal Effects using Instrumental Variables

Pfister¹,

Peters²

2022

Preprint

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“…Definition 11 (Solution). Given an ISCM D = C, I, p I , the solution function s : E → Z is the unique function such that for all i ∈ [n], the following diagram commutes (Bongers et al, 2021)…”

Section: This Lets Us Define Isomorphisms Between Scmsmentioning

confidence: 99%

Weakly supervised causal representation learning

Brehmer¹,

Haan²,

Lippe³

et al. 2022

Preprint

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Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is identifiable in a weakly supervised setting. This requires a dataset with paired samples before and after random, unknown interventions, but no further labels. Finally, we show that we can infer the representation and causal graph reliably in a simple synthetic domain using a variational autoencoder with a structural causal model as prior.

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“…We consider a setting where data are sampled from a structural causal model (SCM) Pearl (2009); Bongers et al (2021) Z j := f j (PA j , j ), for some functions f j , parent sets PA j and noise distributions j . Following Peters et al (2016); Heinze-Deml et al (2018), we consider an SCM over variables Z := (E, X, Y ) where E is an exogenous environment variable (i.e., PA E = ∅), Y is a response variable and X = (X 1 , .…”

Section: Structural Causal Models and Graphsmentioning

confidence: 99%

Invariant Ancestry Search

Mogensen¹,

Thams²,

Peters³

2022

Preprint

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Recently, methods have been proposed that exploit the invariance of prediction models with respect to changing environments to infer subsets of the causal parents of a response variable. If the environments influence only few of the underlying mechanisms, the subset identified by invariant causal prediction, for example, may be small, or even empty. We introduce the concept of minimal invariance and propose invariant ancestry search (IAS). In its population version, IAS outputs a set which contains only ancestors of the response and is a superset of the output of ICP. When applied to data, corresponding guarantees hold asymptotically if the underlying test for invariance has asymptotic level and power. We develop scalable algorithms and perform experiments on simulated and real data.

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Foundations of structural causal models with cycles and latent variables

Cited by 68 publications

References 33 publications

Identifiability of Sparse Causal Effects using Instrumental Variables

Identifiability of Sparse Causal Effects using Instrumental Variables

Weakly supervised causal representation learning

Invariant Ancestry Search

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