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On the Identifiability and Estimation of Causal Location-Scale Noise Models
Alexander Immer · Christoph Schultheiss · Julia Vogt · Bernhard Schölkopf · Peter Bühlmann · Alexander Marx

Thu Jul 27 04:30 PM -- 06:00 PM (PDT) @ Exhibit Hall 1 #118
We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect $Y$ can be written as a function of the cause $X$ and a noise source $N$ independent of $X$, which may be scaled by a positive function $g$ over the cause, i.e., $Y = f(X) + g(X)N$. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of $Y$ given $X$ as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Author Information

Alexander Immer (ETH-Z, MPI-IS)
Christoph Schultheiss (ETHZ - ETH Zurich)
Julia Vogt (Memorial Sloan Kettering Cancer Center)
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.

Peter Bühlmann (ETHZ - ETH Zurich)
Alexander Marx (ETH Zürich)

Postdoc at the ETH AI Center who is interested in Causality and Medical Data Science.

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