Identiﬁability of Causal Graphs using Functional Models

By Jan Peters, †. JorisM.Mooij, Bernhard Sch¨olkopf

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Citations in the corpus

Toward Causal Representation Learning (2021, positive): “It generalizes results of Shimizu et al. [229] for linear functions, and it can be generalized to include non-linear rescalings [279], loops [174], confounders [123], and multivariable settings [189].”
Causality for Machine Learning (2019, background): “It generalizes results of Shimizu et al. (2006) for linear functions, and it can be generalized to include nonlinear rescalings (Zhang and Hyvärinen, 2009), loops (Mooij et al., 2011), confounders (Janzing et al., 2009), and multi-variable settings (Peters et al., 2011).”
Consistency of Causal Inference under the Additive Noise Model (2013, methodology): “A special case of SCMs is the Causal Additive Noise Model (CAM) (Shimizu et al., 2006; Hoyer et al., 2009; Tillman et al., 2009; Peters et al., 2011a;b) which is given as follows: given two random variables X and Y , X is assumed to cause Y if (i) Y can be obtained as a function of X plus a noise…”
Robust Learning via Cause-Effect Models (2011, background): “…recently been shown [7] that an assumption of nonlinear functions with additive noise renders the two variable case (and thus the multivariate case [8]) identiﬁable, i.e., we can distinguish between the causal structures X → Y and X ← Y , given that one and only one of these two alternatives is…”
Causal Inference on Time Series using Structural Equation Models (2012, methodology): “Peters et al. [2011b] show that identiﬁability in the bivariate case is enough for multiple variables.”
Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs (2013, methodology): “Under additional assumptions, identiﬁability of the whole DAG is guaranteed as with linear structural equation models with non-Gaussian errors (Shimizu et al., 2006) or additive noise models (Hoyer et al., 2009), see also Peters et al. (2011).”
On Causal Discovery with Cyclic Additive Noise Models (2011, background): “…as it only considers two variables, it may be possible to use this two-variable identiﬁability result as a key building block for deriving more general identiﬁability results for many variables, similar as how [12] generalized the (acyclic) identiﬁability result of [11] from two to many variables.”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “This paper builds on the conference papers of Hoyer et al. (2009), Peters et al. (2011b) and Mooij et al. (2009) 1 but extends the material in several aspects.”
Discovery of Causal Models that Contain Latent Variables through Bayesian Scoring of Independence Constraints (2017, background): “Considerable CBN research has focused on constraint-based and Bayesian approaches to learning CBNs, although other approaches are being actively developed and investigated [30].”
Score-based causal learning in additive noise models (2013, methodology): “We also look at two simulation settings suggested in Peters et al. [2011], where the graph consists of 4 nodes and the edge functions are nonlinear but parametrized by 4 and 5 parameters respectively.”
Cyclic Causal Discovery from Continuous Equilibrium Data (2013, background): “Recently, several methods have been proposed for causal discovery from continuous-valued observational data by exploiting independence of the estimated noise with the input (Shimizu et al., 2006; Hoyer et al., 2009; Zhang and Hyv¨arinen, 2009; Peters et al., 2011).”
Quantifying causal influences (2012, methodology): “We here restrict attention to linear structural equations, but interesting generalizations are given by additive noise models [8, 17, 18] and post-nonlinear models [23].”