ϵ-Fair: Unifying Algorithmic Fairness via Information Budgets

ϵ-Fair is an information-theoretic framework that turns fairness desiderata into explicit budgets on statistical dependence (mutual information). Those budgets are simple to design with, monitor, and audit, and they translate mechanically into certified bounds on common fairness metrics such as Demographic Parity (DP), Equalized Odds (EO), and Calibration (CAL).

• Applied paper (companion to this repo):
  ϵ-Fair: Unifying Algorithmic Fairness via Information Budgets
  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5403916

• Theory paper (derivations & bounds):
  Theoretical Foundations of Algorithmic Fairness: A Unified Framework Through Pinsker’s Inequality
  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5402916

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Why ϵ-Fair?

• One language for many notions. DP/EO/CAL are unified by bounding the mutual information (MI) between the protected attribute $$A$$ and the model’s prediction $$\hat Y$$, score $$S$$, or representation $$Z$$.
• Budgets → targets. If you enforce $$I(A;\hat Y)\le \epsilon$$, you immediately get certified bounds (with prior-aware constants), e.g.

$$\mathrm{DP} \le \sqrt{\frac{I(A;\hat{Y})}{2\pi_0\pi_1}}$$

$$\mathrm{EO} \le \sqrt{\frac{I(A;\hat{Y} \mid Y = 1)}{2\pi_0^+\pi_1^+}}$$

• Model-agnostic and practitioner-ready. Works with logistic regression, GBDT, calibrated scores, neural nets—anything that produces a score or decision.

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What’s in this repository?

• run_demo.py – Reproduces all figures/CSVs:
  • Utility–Fairness Pareto frontier (observed & certified DP)
  • Representation budget propagation $$I(A;Z)\ \rightarrow$$ DP/EO
  • Drift monitoring with MI time-series + bootstrap CIs
  • Estimator study (InfoNCE lower / plug-in / CLUB upper)
• outputs/ – Auto-generated PNGs/CSVs (created when you run the script).
• requirements.txt – Minimal dependencies.

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Quick start

Setup

git clone https://github.com/asudjianto-xml/e-Fair
cd e-Fair

python -m venv .venv
source .venv/bin/activate    # Windows: .venv\Scripts\activate
pip install -r requirements.txt

# If PyTorch isn't installed:
pip install torch --index-url https://download.pytorch.org/whl/cpu

Reproduce the figures

python run_demo.py

This writes to outputs/:

• pareto_frontier_auc_vs_dp.png
• pareto_frontier_auc_vs_certified_dp.png
• rep_budget_dp_eo.png
• drift_monitoring.png
• estimator_scatter.png

Run individual experiments (Jupyter/Python)

import importlib, run_demo
importlib.reload(run_demo)

run_demo.experiment_pareto()
run_demo.experiment_rep_budget_two_phase()
run_demo.experiment_drift()
run_demo.experiment_estimators()

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The core idea (2 minutes)

• Controlled dependence. Fairness violations are upper-bounded by how much information about $$A$$ the system leaks through $$\hat Y$$ or (S).
• Budgets in MI, targets in metrics. Pick $$\epsilon$$ in MI-space; convert to certified DP/EO/CAL bounds via sharp, prior-aware inequalities.
• Representation budgets propagate. If $$\hat Y=g(Z)$$, then $$I(A;\hat Y)\le I(A;Z)$$. A budget on $$I(A;Z)$$ is a budget on prediction-level gaps.

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What the demos show

Sweep a fairness knob; plot AUC vs observed DP and AUC vs certified DP upper. The certified curve upper-envelopes the observed—governance-ready.

2. Representation budget propagation
   Tighten $$I(A;Z)$$ (CLUB upper) → monotone decreases in DP/EO; AUC stays steady; certified bounds track and upper-envelope observed gaps.

3. Bias drift monitoring
   Track $$\widehat I_t(A;\hat Y)$$ with bootstrap CIs; convert to a certified DP bound; alert when the CI upper exceeds budget.

4. Estimator study (diagnostics)
   InfoNCE (lower) / CLUB (upper) bracket $$I(A;Z)$$; plug-in MI on $$(A,\hat Y)$$ is exact for 2×2 tables. Certification uses uppers or exact estimators.

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Templates for practitioners

Logistic Regression (LR)

• Granularity control: supervised binning caps $$H(S)$$ and leakage capacity.
• Budgeted thresholding: on validation, scan thresholds and keep only those with
  $$\widehat I(A;\hat Y_t)\le \epsilon_{\mathrm{DP}}$$ (and $$\widehat I(A;\hat Y_t\mid Y{=}1)\le \epsilon_{\mathrm{EO}}$$); choose the best utility within the feasible set.
• Certify & monitor: plug-in MI on test + bootstrap CIs → certified DP/EO bounds.

Gradient-Boosted Decision Trees (GBDT)

• Granularity control: depth, min leaf, and rounds cap partition complexity and leakage capacity.
• Budget-aware early stopping: after each round, run the same budgeted threshold scan; keep the best feasible round.
• Certify & monitor: as above.

Example using Neural Networks

In all cases, “budget selection” is just choosing $$\epsilon$$ from a policy target via
$$\epsilon_{\mathrm{DP}}=2,\pi_0\pi_1,\tau_{\mathrm{DP}}^2$$ (and analogously for EO).

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Troubleshooting

• ModuleNotFoundError: torch → install CPU build (see setup).
• AttributeError: missing experiment → available functions: experiment_pareto, experiment_rep_budget_two_phase, experiment_drift, experiment_estimators.
• CLUB/InfoNCE look inverted → short training can narrow/invert the bracket; extend CLUB training. Certification still uses upper (CLUB) and exact plug-in.

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Papers

• Applied (companion to this repo):
  Sudjianto, A. (2025). ϵ-Fair: Unifying Algorithmic Fairness via Information Budgets. SSRN.
  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5403882

• Theory (derivations & bounds):
  Sudjianto, A. (2025). Theoretical Foundations of Algorithmic Fairness: A Unified Framework Through Pinsker’s Inequality. SSRN.
  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5402916

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How to cite

If you use the code or applied workflow, please cite the Applied paper (and optionally the Theory paper when referencing derivations/bounds).

BibTeX

@misc{Sudjianto2025EpsilonFairApplied,
  title        = {ϵ-Fair: Unifying Algorithmic Fairness via Information Budgets},
  author       = {Agus Sudjianto},
  year         = {2025},
  howpublished = {\url{https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5403882}},
  note         = {Companion code: \url{https://github.com/asudjianto-xml/e-Fair}}
}

@misc{Sudjianto2025FairnessTheoryPinsker,
  title        = {Theoretical Foundations of Algorithmic Fairness: A Unified Framework Through Pinsker's Inequality},
  author       = {Agus Sudjianto},
  year         = {2025},
  howpublished = {\url{https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5402916}}
}

@misc{Sudjianto2025EfairCode,
  title        = {e-Fair: Information-Budget Fairness Framework (code)},
  author       = {Agus Sudjianto},
  year         = {2025},
  howpublished = {\url{https://github.com/asudjianto-xml/e-Fair}}
}

Plaintext

Sudjianto, A. (2025). ϵ-Fair: Unifying Algorithmic Fairness via Information Budgets. SSRN.
Sudjianto, A. (2025). Theoretical Foundations of Algorithmic Fairness: A Unified Framework Through Pinsker’s Inequality. SSRN.
Code: https://github.com/asudjianto-xml/e-Fair

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License

See LICENSE in this repository.

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Acknowledgments

If ϵ-Fair helps your work, please ⭐ the repo and cite the papers.