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name: linear_datamodel_fit description: Fit target-specific linear datamodel surrogates from subset membership vectors to observed target outcomes.

Linear Datamodel Fit

Use this skill after subset-output pairs are available for a fixed target example. It preserves the paper mechanism of predicting f_A(x; S') from the binary characteristic vector of S'.

Inputs

• Binary membership matrix X with one row per sampled subset.
• Outcome vector y with one value per subset.
• Optional ridge value for stable underdetermined fits.

Outputs

• Datamodel weights theta.
• Intercept.
• Predictions and diagnostics: Pearson correlation, MSE, and optional weight correlation.

Workflow

1. Validate row counts and binary membership values.
2. Add an intercept column.
3. Solve least squares or ridge-regularized normal equations.
4. Evaluate on held-out subsets, not only the fitted rows.
5. Use learned weights as datamodel embeddings or pass them to counterfactual scoring.

Validation

Run:

python scripts/fit_datamodel.py --demo
python tests/test_fit_datamodel.py

Limitations

This skill fits the surrogate only; it does not create the base training subsets or train the original task model.