CertIFI: Certifiably Intersectionally Fair & Interpretable models

certifi-learn finds the most biased subgroup in data or in a model's predictions, and trains interpretable classifiers (linear models and rule sets) that are certifiably fair on all intersectional subgroups, for example all combinations of sex, race and age group.

Features

• Bias detection. Find the subgroup with the largest violation of

  • Subgroup Discrepancy / MSD,
  • Statistical Parity Subgroup Fairness (SPSF),
  • False Positive Subgroup Fairness (FPSF).

  Subgroups can be

  • conjunctions of protected attribute values (e.g. SEX = Female AND RAC1P = Black). The exact search is fast, needs no solver, and its result is proven optimal.
  • linear threshold functions of the protected attributes, found by MIO.

• Fair training. Linear classifiers and DNFs (rule sets), trained to optimality under the constraint that every subgroup has bias at most γ. Fairness constraints are generated lazily: only the subgroups that are actually violated are added, so there's no need to enumerate the exponentially many subgroups.

• A scikit-learn-style API that works with pandas DataFrames. Categorical features are encoded automatically.

Installation

pip install "certifi-learn[gurobi]"

Prebuilt wheels are available for Linux, macOS and Windows (Python 3.9+). To install the latest version from GitHub instead, you need a Rust toolchain:

pip install "certifi-learn[gurobi] @ git+https://github.com/Epanemu/CertIFI"

Optional dependencies (extras):

Bias detection on conjunction subgroups needs no extras.

Quickstart

Finding the most biased subgroup

from certifi_learn import find_subgroup
from certifi_learn.encoding import TabularEncoder

# protected: DataFrame of protected attributes, y: binary labels, y_pred: model predictions
enc = TabularEncoder(protected)                 # binarizes into literals like "SEX = Female"
P = enc.binary(protected, negations=False)
names = enc.binary_names(negations=False)

# bias in the data: subgroup whose share differs most between positive and negative labels
sg = find_subgroup(P, y, measure="msd")
print(f"MSD = {sg.value:.3f}, proven optimal: {sg.optimal}")
print(sg.describe(names))
# e.g., on ACS Income (examples/detect_and_train.py):
#   MSD = 0.194, proven optimal: True
#   AGEP between [17, 24.2)

# certify that no subgroup has bias above a threshold
sg = find_subgroup(P, y, measure="msd", gamma=0.25)   # None: no subgroup has MSD > 0.25

# bias of a classifier
sg = find_subgroup(P, y_pred, measure="fpsf", y_true=y)

# also allow negated literals, e.g. "NOT RAC1P = White"
sg = find_subgroup(P, y_pred, measure="spsf", negations=True)

# linear subgroups (MIO, requires a solver)
sg = find_subgroup(P, y_pred, measure="spsf", subgroups="linear", solver="highs", time_limit=300)

find_subgroup returns a DetectedSubgroup with the violation value (of the chosen measure, on the given data), the membership mask, optimal (whether the subgroup is proven to be the most biased), and describe() / contains(X_new). If you pass gamma=..., it returns a subgroup only if one violates the threshold, and None otherwise. That None certifies γ-fairness, unless a warning reports that the search was stopped by the time limit.

Training a fair classifier

from certifi_learn import FairLinearClassifier, FairDNFClassifier

clf = FairLinearClassifier(gamma=0.01, measure="fpsf", time_limit=600)
clf.fit(X, y, X_protected)          # X may include the protected attributes
y_pred = clf.predict(X_test)

print(clf.n_cuts_)                   # number of subgroups constrained during training
print(clf.describe_cut_subgroups())  # which ones

rules = FairDNFClassifier(n_terms=3, gamma=0.01, measure="fpsf").fit(X, y, X_protected)
print(rules.describe())

Common parameters:

Model-specific parameters:

γ-fairness is guaranteed on the training data. On new data, the bias can be somewhat higher. Audit your model on held-out data with find_subgroup.

Bias measures

For a classifier h and a subgroup S:

certifi_learn.measures evaluates these for a given subgroup mask. certifi_learn.exact exposes the Rust search directly (msd, spsf, fpsf), with options such as sample weights, negated literals and grouped one-hot columns. See docs/subgroup_pruning_proof.tex for the algorithm and its proof of correctness.

Example

examples/detect_and_train.py runs end to end on the US Census data (ACS Income, via folktables). It finds the most biased subgroup in the data, trains an unconstrained and a fair linear model, and audits both on test data:

pip install "certifi-learn[gurobi,examples]"
python examples/detect_and_train.py

Development

pip install -e ".[gurobi,highs,test,examples]"   # builds the Rust extension
pytest

Tests that need HiGHS or a Gurobi license are skipped if those are not available.

Citation

@inproceedings{nemecek2026intersectional,
 author = {N\v{e}me\v{c}ek, Ji\v{r}\'{\i} and Kozdoba, Mark and Kryvoviaz, Illia and Pevn\'{y}, Tom\'{a}\v{s} and Mare\v{c}ek, Jakub},
 booktitle = {Advances in Neural Information Processing Systems},
 title = {Intersectional Fairness via Mixed-Integer Optimization},
 volume = {39, Main Conference},
 year = {2026}
}

License

MIT