43. RFCI — Really Fast Causal Inference

Type: Constraint-based (latent-capable)
Output: RFCI-PAG (a slightly weaker form of a PAG)

RFCI is a computationally streamlined alternative to FCI for situations where latent confounders and selection bias may be present, but where the full FCI algorithm is too slow.
It uses a reduced set of CI tests and simplified orientation rules to produce a graph that is always sound and compatible with FCI, but may be less oriented.
RFCI is designed for high-dimensional problems where FCI’s Possible-D-SEP phase would be prohibitively expensive.

43.1. Key Idea

RFCI follows the PC/FCI template but avoids the most expensive component of FCI:
the Possible-D-SEP edge-removal phase, which searches for long-range separating sets.

Instead:

  1. Local adjacency search (PC-style)
    Uses conditional independence tests with local conditioning sets.

  2. Reduced edge-removal step
    Performs additional CI tests only on adjacency neighborhoods, not full Possible-D-SEP sets.

  3. Simplified orientation rules
    Applies a subset of the FCI rule set, orienting only what can be soundly inferred without long-range separations.

The result is a PAG-like graph with fewer orientations than full FCI, but obtained at a much lower computational cost.

43.2. When to Use

  • When you need latent-capable causal discovery but FCI is too slow.

  • When the dataset is high-dimensional (hundreds or thousands of variables).

  • When you want a method that is:

    • faster than FCI,

    • more informative than PC/CPC in the presence of latent confounding.

  • When you want a sound method—RFCI never produces an orientation that FCI would not.

Related algorithms:

  • Use FCI when full orientation power is needed.

  • Use GFCI, BOSS-FCI, GRaSP-FCI, or FCIT when hybrid score–test methods are preferred.

43.3. Prior Knowledge Support

Yes. RFCI accepts background knowledge.

Supported types:

  • Required edges (force X → Y or X—Y)

  • Forbidden edges (prohibit adjacency or direction)

  • Tier/temporal constraints (edges must point forward in time/tier)

All constraints are enforced consistently throughout adjacency search and orientation.

43.4. Strengths

  • Much faster than FCI — avoids Possible-D-SEP

  • Latent- and selection-capable

  • Provably sound under an independence oracle

  • Works well in high-dimensional settings

  • Never over-orients compared to FCI

  • Fully knowledge-aware (required/forbidden edges, tiers)

43.5. Limitations

  • Less informative than full FCI
    (some edges remain circle–circle where FCI would orient)

  • Finite-sample sensitivity
    As in PC/FCI, CI-test errors can propagate.

  • Outputs an RFCI-PAG, not a fully general PAG
    (same semantics for edges it does orient, but fewer orientations overall)

43.6. Key Parameters in Tetrad

Parameter (camelCase)

Description

indTest

Choice of CI test (Fisher Z, G-test, KCI/RCIT, etc.)

alpha

Significance level for CI tests

depth

Maximum conditioning-set size

knowledge

Background knowledge object defining constraints

verbose

Controls progress/debug output

numThreads

Parallel CI-test execution (if supported)

43.7. Reference

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.

43.8. Summary

RFCI is a sound, high-dimensional alternative to FCI that handles latent confounders and selection bias while avoiding FCI’s costly long-range separation search. It produces a slightly less oriented PAG but is far more scalable and still fully knowledge-aware.