Consistency of Causal Inference under the Additive Noise Model

By Samory Kpotufe, Eleni Sgouritsa, Dominik Janzing, Bernhard Schölkopf. 2013

45 citations recorded by the source corpus.

We analyze a family of methods for statistical causal inference from sample under the socalled Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. We derive general conditions under which the given family of inference methods consistently infers the causal direction in a nonparametric setting.

Subfields: Artificial Intelligence, Statistics and Probability, Causal Inference & Discovery, Signal Processing

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “On the other hand, although methods for learning causal structure from observations exist [18], [37], [83], [113], [123], [139], [161], [174]–[176], [188]–[190], [229], [237], [246], [279], learning causal relations frequently requires collecting data from multiple environments or the ability to per”
Towards Causal Representation Learning (2021, background): “[237, 188, 229, 113, 174, 187, 139, 17, 246, 277, 175, 123, 186, 176, 36, 82, 161], learning causal relations frequently requires collecting data from multiple environments, or the ability to perform interventions [251].”
Causality for Machine Learning (2019, background): “…X,Y generated by an additive noise model, one cannot fit an additive noise model in the opposite direction (i.e., with the roles of X and Y interchanged) (Hoyer et al., 2009; Mooij et al., 2009; Peters et al., 2014; Kpotufe et al., 2014; Bauer et al., 2016), cf. also the work of Sun et al. (2006).”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “Strictly speaking, we need to use separate sub-samples to estimate function and noise terms, respectively, see Kpotufe et al. (2014).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “A low HSIC p-value indicates that we Algorithm 1 General procedure to decide whether p(x, y) satisfies an additive noise model X → Y or Y → X. Input: 1.”
Score-based causal learning in additive noise models (2013, background): “[19] considers a similar problem as ours: however, while they only treat the case with two variables, we allow for more realistic multivariate settings.”
From Dependence to Causation (2016, background): “Additive noise models are consistent (Kpotufe et al., 2014), and there exists extensions to discrete variables (Peters et al., 2011), latent variables (Stegle et al., 2010), cyclic graphs (Mooij et al., 2011; Lacerda et al., 2012), and postnonlinear equations xi = gi(fi(Pa(xi)) + ni), where gi : R→…”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, result): “The algorithm deﬁnitively concludes that German causes English. information or distance correlation [Sz ´ ekely et al. 2009] or to determine whether the consistency results in Kpotufe et al. [2014] hold for our method.”
Non-linear Causal Inference using Gaussianity Measures (2014, background): “Similar results have been obtained in the case of nonlinear relations and the univariate data case (Hyvärinen and Smith, 2013; Kpotufe et al., 2014).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “Kpotufe et al. (2014); Nowzohour and Bühlmann (2015) proposed to use as a score the sum of the estimated differential entropies of inputs and residuals and proved consistency of that procedure.”
Towards a Learning Theory of Cause-Effect Inference (2015, methodology): “This model was later extended into nonlinear additive noise models (Hoyer et al., 2009; Zhang & Hyvärinen, 2009; Stegle et al., 2010; Kpotufe et al., 2013; Peters et al., 2014), which prefer the causal direction under which the alleged cause is independent from the additive residuals of some…”
The Randomized Causation Coefficient (2014, background): “The consistency of causal inference under the additive noise model was established by Kpotufe et al. (2013).”