Nonlinear causal discovery with additive noise models

By Patrik O. Hoyer, Dominik Janzing, Joris M. Mooij, Jan Peters, Bernhard Schölkopf. 2008

1,246 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Causal Inference & Discovery

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”
Discovering Causal Signals in Images (2016, background): “Figure 2 exemplifies a family of such models, the Additive Noise Model (ANM) [10], where the effect variable Y is a nonlinear function f of the cause variable X , plus some independent random noise E.”
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].”
Sample-Efficient Reinforcement Learning via Counterfactual-Based Data Augmentation (2020, background): “, linear relations [13], nonlinear relations with additive noise [14], or the causal model with further post-nonlinear transformations [15].”
On the Binding Problem in Artificial Neural Networks (2020, background): “see Hoyer et al. (2009); Lopez-Paz et al.”
Causality for Machine Learning (2019, background): “se: one can show that given a distribution over 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 Xand Yinterchanged) (Hoyer et al., 2009; Mooij et al., 2009; Peters et al., 2014; Kpotufe et al., 2014; Bauer et al., 201”
Learning Neural Causal Models from Unknown Interventions (2019, methodology): “…based on observational data (Chickering, 2002; Tsamardinos et al., 2006; Goudet et al., 2017; Hauser & Bühlmann, 2012; Spirtes et al., 2000; Sun et al., 2007; Zhang et al., 2012; Shimizu et al., 2006; Hoyer et al., 2009; Daniusis et al., 2012; Budhathoki & Vreeken, 2017; Kalainathan et al., 2018).”
Semi-supervised learning, causality, and the conditional cluster assumption (2019, methodology): “To achieve this, we assume an additive noise model [24] for f0, f1 in eq.”
Causal Discovery from Heterogeneous/Nonstationary Data (2019, methodology): “, 2006), the additive noise model (Hoyer et al., 2009; Zhang and Hyvärinen, 2009a), and the post-nonlinear causal model (Zhang and Chan, 2006; Zhang and Hyvärinen, 2009b).”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, background): “Many extant causal discovery algorithms use conditional independence tests to infer the underlying causal structure over a set of variables from observational data [Pearl, 2000, Spirtes et al., 2000, Hoyer et al., 2009].”
Causal Generative Neural Networks (2017, background): “In observational causal discovery, some authors exploit distributional asymmetries to discover bivariate causal relations [Hoyer et al. , 2009; Zhang and Hyv¨arinen, 2009; Daniusis et al. , 2012; Stegle et al. , 2010; Lopez-Paz et al. , 2015; Fonollosa, 2016], while others rely on conditional…”
Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination (2017, background): “…Moreover, when one ﬁts a ﬁxed functional causal model (e.g., the linear, non-Gaussian model [Shimizu et al. , 2006], the additive noise model [Hoyer et al. , 2009; Zhang and Hyv¨arinen, 2009a], or the post-nonlinear causal model [Zhang and Chan, 2006; Zhang and Hyv¨arinen, 2009b]) to…”
Invariant Causal Prediction for Nonlinear Models (2017, background): “Such assumptions include non-Gaussianity (Shimizu et al., 2006) or equal variances (Peters and B¨uhlmann, 2014) of the errors or non-linearity of the structural equations in additive noise models (Hoyer et al., 2009; Peters et al., 2014).”
Causal inference by using invariant prediction: identification and confidence intervals (2015, background): “…framework of structural equation models, interesting work has been done for fully identiﬁable structures exploiting additional restrictions such as non-Gaussianity [Shimizu et al., 2006], nonlinearity [Hoyer et al., 2009, Peters et al., 2014] or equal error variances [Peters and B¨uhlmann, 2014].”
Consistency of Causal Inference under the Additive Noise Model (2013, methodology): “Various works (Shimizu et al., 2006; Hoyer et al., 2009; Peters et al., 2011a) have successfully validated procedures based on the CAM (outlined in Section 1.”
On causal and anticausal learning (2012, methodology): “In practice, an ANM model can be ﬁt by regressing the effect on the cause while enforcing that the residual noise variable is independent of the cause (Mooij et al., 2009).”
Identifiability of Causal Graphs using Functional Models (2011, methodology): “[2006], Hoyer et al. [2009], Peters et al. [2010] suggest the following procedure to tackle this particularly challenging problem: Whenever the joint distribution P ) allows an additive noise model (ANM) in one direction, i.”