error-parity

Work presented as an oral at ICLR 2024, titled "Unprocessing Seven Years of Algorithmic Fairness".

Fast postprocessing of any score-based predictor to meet fairness criteria.

The error-parity package can achieve strict or relaxed fairness constraint fulfillment, which can be useful to compare ML models at equal fairness levels.

Package documentation available here.

Contents:

• Installing
• Getting started
• How it works
• Fairness constraints
  • Equalized odds relaxations
• Citing

Installing

Install package from PyPI:

pip install error-parity

Or, for development, you can clone the repo and install from local sources:

git clone https://github.com/socialfoundations/error-parity.git
pip install ./error-parity

Getting started

See detailed example notebooks under the examples folder and on the package documentation.

from error_parity import RelaxedThresholdOptimizer

# Given any trained model that outputs real-valued scores
fair_clf = RelaxedThresholdOptimizer(
    predictor=lambda X: model.predict_proba(X)[:, -1],   # for sklearn API
    # predictor=model,            # use this for a callable model
    constraint="equalized_odds",  # other constraints are available
    tolerance=0.05,               # fairness constraint tolerance
)

# Fit the fairness adjustment on some data
# This will find the optimal _fair classifier_
fair_clf.fit(X=X, y=y, group=group)

# Now you can use `fair_clf` as any other classifier
# You have to provide group information to compute fair predictions
y_pred_test = fair_clf(X=X_test, group=group_test)

How it works

Given a callable score-based predictor (i.e., y_pred = predictor(X)), and some (X, Y, S) data to fit, RelaxedThresholdOptimizer will:

1. Compute group-specific ROC curves and their convex hulls;
2. Compute the $r$-relaxed optimal solution for the chosen fairness criterion (using cvxpy);
3. Find the set of group-specific binary classifiers that match the optimal solution found.
   • each group-specific classifier is made up of (possibly randomized) group-specific thresholds over the given predictor;
   • if a group's ROC point is in the interior of its ROC curve, partial randomization of its predictions may be necessary.

Fairness constraints

You can choose specific fairness constraints via the constraint key-word argument to the RelaxedThresholdOptimizer constructor. The equation under each constraint details how it is evaluated, where $r$ is the relaxation (or tolerance) and $\mathcal{S}$ is the set of sensitive groups.

Currently implemented fairness constraints:

• equalized odds (Hardt et al., 2016) [default];
  • i.e., equal group-specific TPR and FPR;
  • use constraint="equalized_odds";
  • $\max_{a, b \in \mathcal{S}} \max_{y \in {0, 1}} \left( \mathbb{P}[\hat{Y}=1 | S=a, Y=y] - \mathbb{P}[\hat{Y}=1 | S=b, Y=y] \right) \leq r$
  • other relaxations available by changing the l_p_norm parameter;
• equal opportunity;
  • i.e., equal group-specific TPR;
  • use constraint="true_positive_rate_parity";
  • $\max_{a, b \in \mathcal{S}} \left( \mathbb{P}[\hat{Y}=1 | S=a, Y=1] - \mathbb{P}[\hat{Y}=1 | S=b, Y=1] \right) \leq r$
• predictive equality;
  • i.e., equal group-specific FPR;
  • use constraint="false_positive_rate_parity";
  • $\max_{a, b \in \mathcal{S}} \left( \mathbb{P}[\hat{Y}=1 | S=a, Y=0] - \mathbb{P}[\hat{Y}=1 | S=b, Y=0] \right) \leq r$
• demographic parity;
  • i.e., equal group-specific predicted prevalence;
  • use constraint="demographic_parity";
  • $\max_{a, b \in \mathcal{S}} \left( \mathbb{P}[\hat{Y}=1 | S=a] - \mathbb{P}[\hat{Y}=1 | S=b] \right) \leq r$

We welcome community contributions for cvxpy implementations of other fairness constraints.

Equalized odds relaxations

When using constraint="equalized_odds", different relaxations can be chosen by altering the l_p_norm parameter (which dictates how to compute the distance between group-specific ROC points).

A few useful values:

• l_p_norm=np.inf [default] evaluates equalized-odds as the maximum between group-wise TPR and FPR differences (as shown above);
• l_p_norm=1 evaluates equalized-odds as the sum of absolute difference in group-wise TPR and FPR;
  • corresponds to twice the "average absolute odds" metric;
  • accordingly, use twice the tolerance target to constrain the average_abs_odds_difference;

The actual equalized odds constraint implemented is:

$\max_{a, b \in \mathcal{S}} \left\lVert ROC_a - ROC_b \right\rVert_p \leq r,$ where $ROC_a$ is the ROC point of group $S=a$ and $ROC_b$ is the ROC point of group $S=b$.

Citing

@inproceedings{
  cruz2024unprocessing,
  title={Unprocessing Seven Years of Algorithmic Fairness},
  author={Andr{\'e} Cruz and Moritz Hardt},
  booktitle={The Twelfth International Conference on Learning Representations},
  year={2024},
  url={https://openreview.net/forum?id=jr03SfWsBS}
}