18. FCIT — FCI with Targeted Testing

Type: Hybrid (score-guided constraint method)
Output: PAG (guaranteed legal at all intermediate stages)
Knowledge: Fully supported (all Tetrad knowledge types)

FCIT (FCI with Targeted Testing) is one of the mixed-strategy latent-variable algorithms introduced in
Ramsey, Andrews & Spirtes (2025). It enhances FCI by using score information, typically from BOSS, to prioritize which conditional independence tests to perform, drastically reducing spurious independences and search instability.

It preserves full PAG correctness, and importantly, every intermediate orientation is enforced to be legal, preventing the common “illegal PAG” errors observed in FCI/GFCI under finite samples.

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18.1. Key Idea

FCIT modifies FCI in two fundamental ways:

18.1.1. 1. Score-guided targeted testing

Instead of performing CI tests in all possible orders or sizes, FCIT uses:

• A scoring engine (usually BOSS, optionally GRaSP or FGES)

• A ranked list of edges or conditioning sets

to prioritize tests that are likely to be informative.
Low-value or low-priority independence tests are performed later or not at all, reducing the chance of spurious edge removals.

18.1.2. 2. Legality-enforced refinement

At each orientation step, FCIT applies a legality check:

• Reject any orientation that would create a directed cycle,

• Or violate ancestral relations,

• Or create a non-maximal PAG,

• Or violate separation constraints.

Thus, FCIT produces a legal PAG at every intermediate step, not just at the end.

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18.2. When to Use

• Standard FCI or GFCI give unstable or noisy results

• Latent confounding is believed to be present

• The dataset is medium–large (hundreds to thousands of variables)

• You want a clean, readable PAG suitable for scientific interpretation

• You prefer high precision in adjacencies and orientations

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18.3. Strengths

• High stability: fewer spurious independences

• High precision in both adjacencies and orientations

• Produces a legal PAG at every step

• Handles latent confounders and selection bias

• Fully knowledge-aware

• Often faster than FCI/GFCI for moderate-to-large datasets

• Excellent accuracy for medium–high dimensional models

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18.4. Limitations

• Requires a score engine (default: BOSS) — adds computation

• Slightly slower than GFCI on very small models

• Still depends on CI tests in refinement, so extremely small samples may be difficult

• Uses heuristics (targeted testing): still empirically strong, not yet theoretically proven to be complete

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18.5. How It Differs From Related Algorithms

18.5.1. vs. FCI

• FCI performs many CI tests (may be noisy); FCIT prioritizes and reduces them.

• FCI can produce intermediate illegal PAGs; FCIT never does.

18.5.2. vs. GFCI

• GFCI uses FGES for skeletons; FCIT uses score-guided test prioritization instead.

• FCIT tends to produce cleaner PAGs with fewer false positives.

18.5.3. vs. BOSS-FCI / GRaSP-FCI

• BOSS-FCI and GRaSP-FCI replace the skeleton; FCIT replaces the testing schedule.

• FCIT is often the most stable of the mixed-strategy algorithms.

18.5.4. vs. LV-Heuristic

• LV-Heuristic is a heuristic PAG-from-DAG transformer.

• FCIT is a principled hybrid consistent with FCI logic.

Cross-references: 👉 BOSS-FCI •
👉 GRaSP-FCI •
👉 GFCI •
👉 FCI •
👉 LV-Heuristic

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18.6. Prior Knowledge Support

FCIT is fully knowledge-aware, just like PC, FGES, FCI, GFCI, and BOSS-FCI.

Knowledge constraints affect:

• Edge removals

• Orientation decisions

• Legality checks

• Selection-bias assumptions

• Allowed/forbidden ancestral relations

• Tier constraints

All constraints are respected throughout scoring, prioritization, and refinement.

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18.7. Key Parameters in Tetrad

FCIT exposes parameters from:

18.7.1. Score engine (typically BOSS)

Parameter	Meaning
penaltyDiscount	Strength of BIC penalty; higher → sparser score proposals.
maxDegree	Restrict max parent set size (structural regularization).
numThreads	Parallel scoring/testing.
verbose	Print BOSS scoring decisions and test rankings.

18.7.2. FCI-style refinement

Parameter	Meaning
depth	Maximum size of conditioning sets for CI tests.
stableFas	Order-invariant adjacency pruning.
excludeSelectionBias	Whether to interpret tail–tail edges as selection-induced.
fdrQ	Optional FDR correction level.
verbose	Print CI testing and orientation steps.

18.7.3. FCIT-specific

Parameter	Meaning
useBestTestFirst	Whether to rank tests by BOSS scoring (always true in FCIT).
maxTests	Optional cap on total CI tests (rarely needed).
scoreEngine	Choose BOSS/GRaSP/FGES as the scoring backend.

(Names depend slightly on Tetrad version; these reflect Tetrad 7.6.9.)

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18.8. Reference

Ramsey, J., Andrews, B., & Spirtes, P. (2025).
Efficient Latent Variable Causal Discovery: Combining Score Search and Targeted Testing.
arXiv:2510.04263.

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18.9. Summary

FCIT = FCI + score-guided test prioritization + legality checks.

A high-precision, high-stability PAG algorithm for latent-variable causal discovery that suppresses noisy independence tests and guarantees a legal PAG throughout the search.