# Causal discovery methods based on constrained functional causal models

In this section, we would like to introduce causal discovery methods based on constrained functional causal models. Now we have LiNGAM-based methods (ICA-based LiNGAM 1, DirectLiNGAM 2, RCD 3, and CAM-UV 4), post-nonlinear (PNL 5) causal models, and additive noise models (ANM 6).

Contents:

- LiNGAM-based Methods
  - ICA-based LiNGAM
    - Parameters
    - Returns
  - DirectLiNGAM
    - Parameters
    - Returns
  - RCD
    - Parameters
    - Returns
  - CAM-UV
    - Parameters
    - Returns
- Post-nonlinear causal models
  - Algorithm Introduction
  - Parameters
  - Returns
- Additive noise models
  - Algorithm Introduction
  - Parameters
  - Returns

1

  Shimizu, S., Hoyer, P. O., Hyvärinen, A., Kerminen, A., & Jordan, M. (2006). A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research, 7(10).

2

  Shimizu, S., Inazumi, T., Sogawa, Y., Hyvärinen, A., Kawahara, Y., Washio, T., … & Bollen, K. (2011). DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model. The Journal of Machine Learning Research, 12, 1225-1248.

3

  Maeda, T. N., & Shimizu, S. (2020, June). RCD: Repetitive causal discovery of linear non-Gaussian acyclic models with latent confounders. In International Conference on Artificial Intelligence and Statistics (pp. 735-745). PMLR.

4

  Maeda, T. N., & Shimizu, S. (2021). Causal Additive Models with Unobserved Variables. UAI.

5

  Zhang, K., & Hyvärinen, A. (2009, June). On the Identifiability of the Post-Nonlinear Causal Model. In 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009) (pp. 647-655). AUAI Press.

6

  Hoyer, P. O., Janzing, D., Mooij, J. M., Peters, J., & Schölkopf, B. (2008, December). Nonlinear causal discovery with additive noise models. In NIPS (Vol. 21, pp. 689-696).