## 5 Fair Training
### Regularization-based Fairness  
Regularization-based fairness methods are emerging as a promising approach to mitigate biases in machine learning models. Regularization techniques aim to enforce fairness constraints during the model training process, ensuring that the model's predictions are less influenced by sensitive attributes and promote equitable outcomes. Table 9 summarizes and compares different regularization methodologies for AI fairness, including adversarial regularization [205, 206, 207, 208], demographic parity regularization [201, 209, 210, 211], equalized odds regularization [212, 213, 214], covariate leveling regularization [215, 214], and mixture density network regularization [216, 217, 218]. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Post-Processing Fairness Method** & **Features** & **Pros** & **Cons** & **References** \\ \hline Equalized Odds & Adjust model predictions to ensure equalized odds & Ensures equalized false positive and true positive rates across groups & May lead to suboptimal trade-offs between fairness and model performance & [114, 177, 180] \\ \hline Calibration & Calibrates model’s predicted probabilities & Improves fairness by aligning confidence scores with true likelihood & Calibration may not entirely remove bias from the model & [187, 188, 189, 190] \\ \hline Reject Option & Introduces a “reject” option in classification (ROC) & Allows the model to abstain decisions & May lead to lower accuracy due to abstaining from fairness concern cases & [191, 192, 193, 194] \\ \hline Preferential Sampling & Modifies the training data distribution by resampling instances & Improves fairness by adjusting the representation of different groups & May not address the root causes of bias in the model & [194, 195, 196] \\ \hline Threshold Optimization & Adjusts decision thresholds for fairness and accuracy trade-off & Allows fine-tuning of fairness and performance balance & May not fully eliminate all biases in the model & [197, 198, 199, 200] \\ \hline Regularization & Applies fairness constraints during model training & Encourages fairness during the optimization process & Fairness constraints might impact model performance & [201, 202, 203, 204] \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Post-processing fairness comparison. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Regularization-Based Fairness Method** & **Features** & **Pros** & **Cons** & **References** \\ \hline Adversarial & Introduces adversarial & Encourages disentanglement of sensitive attributes & Computationally expensive & [205, 206, 207, 208] \\ \hline Demographic Parity & Enforces similar distributions across groups & Addresses group fairness & May lead to accuracy trade-offs & [201, 209, 210, 211, 204] \\ \hline Equalized Odds & Ensures similar false/true positive rates & Emphasizes fairness in both rates & May lead to accuracy trade-offs & [212, 213, 214] \\ \hline Covariate Shift & Reduces impact of biased/underrepresented subgroups & Addresses bias due to distributional differences & Sensitive to noise in the data & [214, 215] \\ \hline Mixture Density Network & Models uncertainty in predictions & Provides probabilistic approach to fairness regularization & Requires larger amount of data to estimate probability distributions & [216, 217, 218] \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Regularization-based fairness comparison. Regularization-based fairness methods introduce additional components to the model training process to mitigate bias in AI predictions. Adversarial regularization aims to minimize model dependence on sensitive attributes by introducing an adversarial component. Demographic parity regularization enforces similar prediction distributions across sensitive attribute groups. Equalized odds regularization maintains consistent false alarm and true alarm rates among these groups. Covariate leveling regularization adapts predictions to diverse data distributions.