Causal Dantzig: Fast inference in linear structural equation models with hidden variables under additive interventions

By Dominik Rothenhausler, Peter Buhlmann, Nicolai Meinshausen. 2017

45 citations recorded by the source corpus.

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number of causal predictors. It was recently shown in Peters et al. [2016] that causal inference for the full model is possible when data from distinct observational environments are available, exploiting that the conditional distribution of a response variable is invariant under the correct causal model. Two shortcomings of such an approach are the high computational effort for large-scale data and the assumed absence of hidden confounders. Here we show that these two shortcomings can be addressed if one is willing to make a more restrictive assumption on the type of interventions that generate different environments. Thereby, we look at a different notion of invariance, namely inner-product invariance. By avoiding a computationally cumbersome reverse-engineering approach such as in Peters et al. [2016], it allows for large-scale causal inference in linear structural equation models. We discuss identifiability conditions for the causal parameter and derive asymptotic confidence intervals in the low-dimensional setting. In the case of non-identifiability we show that the solution set of causal Dantzig has predictive guarantees under certain interventions. We derive finite-sample bounds in the high-dimensional setting and investigate its performance on simulated datasets.

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

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Citations in the corpus

An Analysis of the Adaptation Speed of Causal Models (2020, background): “This work has set a fruitful line of research for robust machine learning (Heinze-Deml et al., 2018b,a; Rothenhäusler et al., 2019; Arjovsky et al., 2019).”
CAUSALITY FROM A DISTRIBUTIONAL ROBUSTNESS POINT OF VIEW (2018, background): “The inner-product invariance (8) leads analogously to an estimator that minimizes the `1-norm of a coefficient vector θ, while bounding the difference ‖G(θ) − G(θ)‖∞ of the inner product between predictors and residuals instead of the inner product itself in case of two available distributions, wher”