PC, FCI, GES, LINGAM algorithm directly ported from R code and Official Papers
This algorithm is logically translated from the R package: https://www.rdocumentation.org/packages/pcalg/versions/2.6-0 The original algorithm was implemented by Kalisch, M., Mächler, M., Colombo, D., Maathuis, M. H., & Bühlmann, P. (2012). Causal inference using graphical models with the R package pcalg. Journal of Statistical Software, 47(11), 1-26.
Discrete independence tests are also implemented by Keiichi SHIMA / IIJ Innovation Institute Inc. / WIDE project https://github.com/keiichishima/pcalg
Lingam was inspired by https://sites.google.com/site/sshimizu06/lingam, the link from the original LINGAM paper: A Linear Non-Gaussian Acyclic Model for Causal Discovery: https://www.cs.helsinki.fi/u/ahyvarin/papers/JMLR06.pdf
Please note that most of these have not been intensively tested (except for pc). Additionally, directly comparing results from the official R package and a python implementation is difficult due to inherent differences between some math library calls.