Fairness is crucial in machine learning to prevent bias based on sensitive attributes in classifier predictions. However, the pursuit of strict fairness often sacrifices accuracy, particularly when significant prevalence disparities exist among groups, making classifiers less practical. For example, Alzheimer's disease (AD) is more prevalent in women than men, making equal treatment inequitable for females. Accounting for prevalence ratios among groups is essential for fair decision-making. In this paper, we introduce prior knowledge for fairness, which incorporates prevalence ratio information into the fairness constraint within the Empirical Risk Minimization (ERM) framework. We develop the Prior-knowledge-guided Fair ERM (PFERM) framework, aiming to minimize expected risk within a specified function class while adhering to a prior-knowledge-guided fairness constraint. This approach strikes a flexible balance between accuracy and fairness. Empirical results confirm its effectiveness in preserving fairness without compromising accuracy.
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