Vertical Federated Learning (VFL) offers a novel paradigm in machine learning, enabling distinct entities to train models cooperatively while maintaining data privacy. This method is particularly pertinent when entities possess datasets with identical sample identifiers but diverse attributes. Recent privacy regulations emphasize an individual'sright to be forgotten, which necessitates the ability for models to unlearn specific training data. The primary challenge is to develop a mechanism to eliminate the influence of a specific client from a model without erasing all relevant data from other clients. Our research investigates the removal of a single client's contribution within the VFL framework. We introduce an innovative modification to traditional VFL by employing a mechanism that inverts the typical learning trajectory with the objective of extracting specific data contributions. This approach seeks to optimize model performance using gradient ascent, guided by a pre-defined constrained model. We also introduce a backdoor mechanism to verify the effectiveness of the unlearning procedure. Our method avoids fully accessing the initial training data and avoids storing parameter updates. Empirical evidence shows that the results align closely with those achieved by retraining from scratch. Utilizing gradient ascent, our unlearning approach addresses key challenges in VFL, laying the groundwork for future advancements in this domain.

Abstract Machine learning is widely deployed in society, unleashing its power in a wide range of applications owing to the advent of big data. One emerging problem faced by machine learning is the discrimination from data, and such discrimination is reflected in the eventual decisions made by the algorithms. Recent study has proved that increasing the size of training (labeled) data will promote the fairness criteria with model performance being maintained. In this work, we aim to explore a more general case where quantities of unlabeled data are provided, indeed leading to a new form of learning paradigm, namely fair semi-supervised learning. Taking the popularity of graph-based approaches in semi-supervised learning, we study this problem both on conventional label propagation method and graph neural networks, where various fairness criteria can be flexibly integrated. Our developed algorithms are proved to be non-trivial extensions to the existing supervised models with fairness constraints. Extensive experiments on real-world datasets exhibit that our methods achieve a better trade-off between classification accuracy and fairness than the compared baselines.

A growing specter in the rise of machine learning is whether the decisions made by machine learning models are fair. While research is already underway to formalize a machine-learning concept of fairness and to design frameworks for building fair models with sacrifice in accuracy, most are geared toward either supervised or unsupervised learning. Yet two observations inspired us to wonder whether semi-supervised learning might be useful to solve discrimination problems. First, previous study showed that increasing the size of the training set may lead to a better trade-off between fairness and accuracy. Second, the most powerful models today require an enormous of data to train which, in practical terms, is likely possible from a combination of labeled and unlabeled data. Hence, in this paper, we present a framework of fair semi-supervised learning in the pre-processing phase, including pseudo labeling to predict labels for unlabeled data, a re-sampling method to obtain multiple fair datasets and lastly, ensemble learning to improve accuracy and decrease discrimination. A theoretical decomposition analysis of bias, variance and noise highlights the different sources of discrimination and the impact they have on fairness in semi-supervised learning. A set of experiments on real-world and synthetic datasets show that our method is able to use unlabeled data to achieve a better trade-off between accuracy and discrimination.