30. IMaGES — Independent Multiple-sample Greedy Equivalence Search

Type: Score-based (multi-dataset)
Output: CPDAG

IMaGES extends GES/FGES to the case where you have multiple datasets measured on the same set of variables, assuming that all datasets share the same causal structure even if their noise distributions differ.

Typical use cases:

• fMRI data from multiple subjects performing the same task

• Multi-site or multi-scanner datasets

• Repeated measurements or multiple sessions

• Any situation with several independent datasets measuring the same variables

IMaGES modifies the scoring step of GES/FGES:

30.1. Key Idea

For each candidate edge addition or removal, compute one BIC score per dataset, then average the scores:

Score_IMaGES = (1/M) * Σ_{m=1}^M BIC_m

This produces:

• More stable structure estimates

• Fewer false positives due to dataset-specific noise

• The ability to use multiple small datasets without concatenating them

The greedy search (forward + backward phases) proceeds just like FGES, but uses this averaged score.

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30.2. Variants

30.2.1. IMaGES

Uses FGES as the greedy engine with the IMaGES averaged score.
Output: CPDAG.

30.2.2. IMaGES-BOSS

Uses BOSS as the search engine but applies the IMaGES score at each step.
Often more scalable and robust than FGES-based IMaGES, especially for mixed data or larger models.

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30.3. When to Use

• You have multiple independent datasets with identical variable sets

• You believe the underlying causal structure is shared

• You want a more stable CPDAG estimate than running searches separately

• Particularly effective for:

  • fMRI studies

  • clinical multi-site data

  • repeated measurements

  • large cohorts with multiple sessions

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30.4. Prior Knowledge Support

IMaGES fully supports background knowledge.

You may connect a Knowledge box to the IMaGES Search box in the GUI, or supply a Knowledge object programmatically (Java, py-tetrad, or rpy-tetrad). IMaGES will enforce:

• Forbidden edges

• Required edges

• Tier/temporal ordering constraints

• Any other structural constraints supported by FGES/BOSS

Because IMaGES performs a score-based CPDAG search (via FGES or BOSS) but aggregates scores across multiple datasets, all knowledge constraints are applied uniformly to each scoring step, ensuring that the pooled/averaged score respects the user’s assumptions across all datasets.

If a constraint is incompatible with any dataset in the collection, IMaGES will still enforce it globally, just as standard FGES/BOSS would.

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30.5. Strengths

• Highly stable compared to single-dataset GES/FGES

• Avoids incorrect concatenation of datasets

• Reduces sampling noise

• Parallelizable (each dataset’s score can be computed independently)

• Still outputs a clean, interpretable CPDAG

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30.6. Limitations

• Requires the assumption of a shared causal structure across datasets

• Not appropriate if datasets differ meaningfully in mechanisms

• Cannot by itself handle latent confounding (use GFCI/BOSS-FCI/FCIT for that)

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30.7. Key Parameters in Tetrad

IMaGES exposes several parameters that control both the FGES/BOSS search step and the multi-dataset scoring behavior. All parameters appear in the Tetrad GUI and scripting interfaces using the camelCase versions shown here.

Parameter (camelCase)	Description
penaltyDiscount	Multiplies the BIC penalty term. Larger values → sparser graphs.
semBicStructurePrior	Prior over graph structures used in SEM-BIC scoring.
semBicRule	Choice of local scoring rule (e.g., “SEM-BIC Score Rule”).
precomputeCovariances	Whether to cache covariances for efficiency across datasets.
singularityLambda	Regularization constant applied when covariance matrices are near-singular.
effectiveSampleSize	Overrides sample size used in scoring (used with weighting or meta-designs).
symmetricFirstStep	Whether the initial forward step uses a symmetric score evaluation.
maxDegree	Maximum allowed degree per node (structural regularization).
numThreads	Number of threads for parallel FGES/BOSS operations.
faithfulnessAssumed	If true, assumes perfect faithfulness during adjacency search.
timeLag	Lag (τ) when IMaGES is applied to time-series or lagged datasets.
timeLagReplicatingGraph	Whether lagged graphs should be structurally replicated across time slices.
randomSelectionSize	Size of random subsets considered during order or edge evaluation.
imagesMetaAlg	Which score-driven meta-algorithm to use for multi-dataset merging.
verbose	Print detailed scoring/decision information during search.

These parameters allow IMaGES to:

• share information across multiple datasets,

• encourage stability and reduce noise in scoring,

• scale to large multi-subject studies (e.g., neuroimaging),

• and enforce structural constraints across datasets or time-slices.

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30.8. Reference

Ramsey, J. D., Hanson, S. J., & Glymour, C. (2011).
Multi-subject search correctly identifies causal connections and most causal directions in the DCM models of the Smith et al. simulation study.
NeuroImage, 58(3), 838–848.

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30.9. Summary

IMaGES = GES/FGES/BOSS + averaged BIC scores across datasets.
A robust and stable multi-sample CPDAG algorithm for repeated-measure or multi-subject data.