We present a comprehensive theoretical framework analyzing the relationship between data distributions and fairness guarantees in equitable deep learning. Our work establishes novel theoretical bounds that explicitly account for data distribution heterogeneity across demographic groups, while introducing a formal analysis framework that minimizes expected loss differences across these groups. We derive comprehensive theoretical bounds for fairness errors and convergence rates, and characterize how distributional differences between groups affect the fundamental trade-off between fairness and accuracy. Through extensive experiments on diverse datasets, including FairVision (ophthalmology), CheXpert (chest X-rays), HAM10000 (dermatology), and FairFace (facial recognition), we validate our theoretical findings and demonstrate that differences in feature distributions across demographic groups significantly impact model fairness, with performance disparities particularly pronounced in racial categories. The theoretical bounds we derive crroborate these empirical observations, providing insights into the fundamental limits of achieving fairness in deep learning models when faced with heterogeneous data distributions. This work advances our understanding of fairness in AI-based diagnosis systems and provides a theoretical foundation for developing more equitable algorithms. The code for analysis is publicly available via \url{https://github.com/Harvard-Ophthalmology-AI-Lab/fairness_guarantees}.

Systems thinking provides us with a way to model the algorithmic fairness problem by allowing us to encode prior knowledge and assumptions about where we believe bias might exist in the data generating process. We can then model this using a series of causal graphs, enabling us to link AI/ML systems to politics and the law. By treating the fairness problem as a complex system, we can combine techniques from machine learning, causal inference, and system dynamics. Each of these analytical techniques is designed to capture different emergent aspects of fairness, allowing us to develop a deeper and more holistic view of the problem. This can help policymakers on both sides of the political aisle to understand the complex trade-offs that exist from different types of fairness policies, providing a blueprint for designing AI policy that is aligned to their political agendas.

Fair cake-cutting is a mathematical subfield that studies the problem of fairly dividing a resource among a number of participants. The so-called ``cake,'' as an object, represents any resource that can be distributed among players. This concept is connected to supervised multi-label classification: any dataset can be thought of as a cake that needs to be distributed, where each label is a player that receives its share of the dataset. In particular, any efficient cake-cutting solution for the dataset is equivalent to an optimal decision function. Although we are not the first to demonstrate this connection, the important ramifications of this parallel seem to have been partially forgotten. We revisit these classical results and demonstrate how this connection can be prolifically used for fairness in machine learning problems. Understanding the set of achievable fair decisions is a fundamental step in finding optimal fair solutions and satisfying fairness requirements. By employing the tools of cake-cutting theory, we have been able to describe the behavior of optimal fair decisions, which, counterintuitively, often exhibit quite unfair properties. Specifically, in order to satisfy fairness constraints, it is sometimes preferable, in the name of optimality, to purposefully make mistakes and deny giving the positive label to deserving individuals in a community in favor of less worthy individuals within the same community. This practice is known in the literature as cherry-picking and has been described as ``blatantly unfair.''

Benefiting from the digitization of healthcare data and the development of computing power, machine learning methods are increasingly used in the healthcare domain. Fairness problems have been identified in machine learning for healthcare, resulting in an unfair allocation of limited healthcare resources or excessive health risks for certain groups. Therefore, addressing the fairness problems has recently attracted increasing attention from the healthcare community. However, the intersection of machine learning for healthcare and fairness in machine learning remains understudied. In this review, we build the bridge by exposing fairness problems, summarizing possible biases, sorting out mitigation methods and pointing out challenges along with opportunities for the future.

"ML optimization somehow finds a way and mitigation of bias is not always possible." The debate around fairness and explainability within the AI community has never been hotter. The works of Timnit Gebru and the likes have brought ethical AI to the spotlight. Machine learning has a reputation for being a black box, i.e one does not know what it learns and why it learns so. This makes validating results tricky.

--There has been a growing concern about the fairness of decision-making systems based on machine learning. The shortage of labeled data has been always a challenging problem facing machine learning based systems. In such scenarios, semi-supervised learning has shown to be an effective way of exploiting unlabeled data to improve upon the performance of model. Notably, unlabeled data do not contain label information which itself can be a significant source of bias in training machine learning systems. This inspired us to tackle the challenge of fairness by formulating the problem in a semi-supervised framework. In this paper, we propose a semi-supervised algorithm using neural networks benefiting from unlabeled data to not just improve the performance but also improve the fairness of the decision-making process. The proposed model, called SSFair, exploits the information in the unlabeled data to mitigate the bias in the training data.

The flourishing assessments of fairness measure in machine learning algorithms have shown that dimension reduction methods such as PCA treat data from different sensitive groups unfairly. In particular, by aggregating data of different groups, the reconstruction error of the learned subspace becomes biased towards some populations that might hurt or benefit those groups inherently, leading to an unfair representation. On the other hand, alleviating the bias to protect sensitive groups in learning the optimal projection, would lead to a higher reconstruction error overall. This introduces a trade-off between sensitive groups' sacrifices and benefits, and the overall reconstruction error. In this paper, in pursuit of achieving fairness criteria in PCA, we introduce a more efficient notion of Pareto fairness, cast the Pareto fair dimensionality reduction as a multi-objective optimization problem, and propose an adaptive gradient-based algorithm to solve it. Using the notion of Pareto optimality, we can guarantee that the solution of our proposed algorithm belongs to the Pareto frontier for all groups, which achieves the optimal trade-off between those aforementioned conflicting objectives. This framework can be efficiently generalized to multiple group sensitive features, as well. We provide convergence analysis of our algorithm for both convex and non-convex objectives and show its efficacy through empirical studies on different datasets, in comparison with the state-of-the-art algorithm.