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Learning Linear Causal Representations from Interventions under General Nonlinear Mixing
Simon Buchholz · Goutham Rajendran · Elan Rosenfeld · Bryon Aragam · Bernhard Schölkopf · Pradeep Ravikumar

We study the problem of learning causal representations from unknown, latent interventions in a general setting, where the latent distribution is Gaussian but the mixing function is completely general. We prove strong identifiability results given unknown single-node interventions, i.e., without having access to the intervention targets. This generalizes prior works which have focused on weaker classes, such as linear maps or paired counterfactual data. This is also the first instance of causal identifiability from non-paired interventions for deep neural network embeddings. Our proof relies on carefully uncovering the high-dimensional geometric structure present in the data distribution after a non-linear density transformation, which we capture by analyzing quadratic forms of precision matrices of the latent distributions. Finally, we propose a contrastive algorithm to identify the latent variables in practice and evaluate its performance on various tasks.

Author Information

Simon Buchholz (Max Planck Institute for Intelligent Systems)
Goutham Rajendran (Carnegie Mellon University)
Elan Rosenfeld (CMU)
Bryon Aragam (University of Chicago)
Bernhard Schölkopf (MPI for Intelligent Systems Tübingen, Germany)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

Pradeep Ravikumar (Carnegie Mellon University)

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