cbcd

cbcd (constraint-based causal discovery) is a Python library implementing the PC and FCI algorithm families for i.i.d. data and the PCMCI family for time-series data. It targets the research and applied-causal-inference setting: every published algorithm in the package carries a structural-regression test against a d-separation oracle and, where a reference implementation exists, a parity test against it.

Scope

The package implements:

  • PC family — cbcd.pc (Spirtes & Glymour, 1991; Spirtes et al., 2000), returning a CPDAG over an observed variable set under causal sufficiency.

  • FCI family — cbcd.fci, cbcd.rfci, cbcd.anytime_fci (Spirtes et al., 2000; Colombo et al., 2012; Spirtes, 2001), returning a partial ancestral graph (PAG) without assuming causal sufficiency.

  • PCMCI family — cbcd.pcmci (Runge et al., 2019), recovering a time-series CPDAG over lagged variables under stationarity.

Algorithms are wired from a small set of structural Protocols (CITest, SkeletonAlgorithm, ColliderOrienter, CPDAGRules, PAGRules, PAGSkeletonRefinement); composing a new algorithm is mostly plumbing existing pieces. The full Protocol contract is frozen under decision D15 for v0.x and is documented in the Reference.

Architectural commitments

cbcd does not depend on causal-learn, directly or transitively. CI tests plug in through the structural cbcd.CITest Protocol and may originate from cbcd.citest (the bundled linear-Gaussian and χ² tests), from citk (a sister toolkit covering kernel, regression-based, and ML-based tests), or from any user-defined object satisfying the Protocol’s three members (n_vars, __call__, details). The contract is enforced at construction time by Python’s structural duck-typing — no inheritance is required.

A d-separation oracle suitable for structural-regression testing is provided by the sister package dagsampler via its as_ci_oracle() method.

Reading this documentation

The site follows the Diátaxis layout. New users should start with the Tutorial. Practitioners with a specific task should consult the How-to section. The Reference is automatically generated from docstrings on every build. The Explanation section discusses theory, design rationale, and the rationale behind specific implementation choices.

References

  • Colombo, D., Maathuis, M. H., Kalisch, M., & Richardson, T. S. (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, 40(1), 294–321.

  • Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., & Sejdinovic, D. (2019). Detecting and quantifying causal associations in large nonlinear time series datasets. Science Advances, 5(11), eaau4996.

  • Spirtes, P. (2001). An anytime algorithm for causal inference. Proceedings of AISTATS 2001, 213–221.

  • Spirtes, P., & Glymour, C. (1991). An algorithm for fast recovery of sparse causal graphs. Social Science Computer Review, 9(1), 62–72.

  • Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, Prediction, and Search (2nd ed.). MIT Press.