Identifying confounders using additive noise models

By Dominik Janzing, Jan Peters, Joris M. Mooij, Bernhard Schölkopf. 2009

69 citations recorded by the source corpus.

We propose a method for inferring the existence of a latent common cause ("confounder") of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data.

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

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “[229] for linear functions, and it can be generalized to include nonlinear rescalings [279], loops [174], confounders [123], and multivariable settings [189].”
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): “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).”
Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders (2013, background): “Other results for the linear case are presented in Silva et al. (2006) and for the non-linear case with additive noise in Janzing et al. (2009).”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, background): “Finally, it would be very interesting to extend (sparse) permutation search to (possibly nonidentifiable) models with hidden variables [7, 11, 23, 34] or with graph structures allowing for cycles [19, 20, 30, 33].”
Causal Inference on Discrete Data Using Additive Noise Models (2009, neutral): “[8] make first steps toward identifying”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Other work concentrates on hidden variables in structural equation models (e.g., Hoyer et al., 2008; Janzing et al., 2009; Silva and Ghahramani, 2009).”
Causality : Objectives and Assessment (2010, methodology): “Novel methods for identifying latent confounders use a combination of nonlinear dimensionality reduction and kernel dependence measures (Janzing et al., 2009).”
Identifying Cause and Effect on Discrete Data using Additive Noise Models (2010, methodology): “Sun et al. (2006); Janzing et al. (2009b) fit joint distributions of cause and effect with conditional densities whose logarithm is a second order polynomial (up to the log-partition function) and show that this often makes causal directions identifiable when some or all variables are discrete.”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, background): “As well as evaluating CAN on CelebA [147] image data (including the generation of interventional samples), they also evaluate it on the more traditional CHILD [227] and Alarm [14] datasets showing competitive performance.”
Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables (2015, background): “In recent years, several methods have been suggested that make use not only of conditional independences, but also other properties of the joint statistical distribution between the observed variables [3, 4, 5, 6] (See also the works discussed in Secs.”
Estimating Causal Direction and Confounding of Two Discrete Variables (2016, background): “1, although Hoyer et al. (2008) have extended the linear non-Gaussian methods to the general hypothesis space of Fig, 1 and Janzing et al. (2009) showed that the additive noise assumption can be used to detect pure confounding with some success, i.e. to distinguish hypothesis B from hypotheses C…”