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Learning Bivariate Functional Causal Models

  • Olivier Goudet
  • Diviyan Kalainathan
  • Michèle Sebag
  • Isabelle Guyon
Chapter
Part of the The Springer Series on Challenges in Machine Learning book series (SSCML)

Abstract

Finding the causal direction in the cause-effect pair problem has been addressed in the literature by comparing two alternative generative models X → Y and Y → X. In this chapter, we first define what is meant by generative modeling and what are the main assumptions usually invoked in the literature in this bivariate setting. Then we present the theoretical identifiability problem that arises when considering causal graph with only two variables. It will lead us to present the general ideas used in the literature to perform a model selection based on the evaluation of a complexity/fit trade-off. Three main families of methods can be identified: methods making restrictive assumptions on the class of admissible causal mechanism, methods computing a smooth trade-off between fit and complexity and methods exploiting independence between cause and mechanism.

Keywords

Cause-effect pairs Causal discovery Causal modeling Identifiability Causal mechanisms 

Notes

Acknowledgements

The authors would like to thank Daniel Rolland for proofreading this document, as well as the reviewers for their constructive feedback.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Olivier Goudet
    • 1
  • Diviyan Kalainathan
    • 1
  • Michèle Sebag
    • 1
  • Isabelle Guyon
    • 2
    • 3
  1. 1.Team TAU - CNRS, INRIAUniversité Paris Sud, Université Paris SaclayOrsayFrance
  2. 2.Team TAU - CNRS, INRIA, Université Paris SudUniversité Paris SaclayOrsayFrance
  3. 3.ChaLearnBerkeleyUSA

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