MUSO: Achieving Exact Machine Unlearning in Over-Parameterized Regimes

Machine unlearning (MU) is to make a well-trained model behave as if it had never been trained on specific data. In today's over-parameterized models, dominated by neural networks, a common approach is to manually relabel data and fine-tune the well-trained model. It can approximate the MU model in the output space, but the question remains whether it can achieve exact MU, i.e., in the parameter space. We answer this question by employing random feature techniques to construct an analytical framework. Under the premise of model optimization via stochastic gradient descent, we theoretically demonstrated that over-parameterized linear models can achieve exact MU through relabeling specific data. We also extend this work to real-world nonlinear networks and propose an alternating optimization algorithm that unifies the tasks of unlearning and relabeling. The algorithm's effectiveness, confirmed through numerical experiments, highlights its superior performance in unlearning across various scenarios compared to current state-of-the-art methods, particularly excelling over similar relabeling-based MU approaches.

Data Imputation by Pursuing Better Classification: A Supervised Kernel-Based Method

Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows that the pursuit of better classification can guide the data imputation process. While some works consider using label information to assist in this task, their simplistic utilization of labels lacks flexibility and may rely on strict assumptions. In this paper, we propose a new framework that effectively leverages supervision information to complete missing data in a manner conducive to classification. Specifically, this framework operates in two stages. Firstly, it leverages labels to supervise the optimization of similarity relationships among data, represented by the kernel matrix, with the goal of enhancing classification accuracy. To mitigate overfitting that may occur during this process, a perturbation variable is introduced to improve the robustness of the framework. Secondly, the learned kernel matrix serves as additional supervision information to guide data imputation through regression, utilizing the block coordinate descent method. The superiority of the proposed method is evaluated on four real-world data sets by comparing it with state-of-the-art imputation methods. Remarkably, our algorithm significantly outperforms other methods when the data is missing more than 60\% of the features

Decentralized Kernel Ridge Regression Based on Data-dependent Random Feature

Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random features on different nodes are identical. However, in many applications, data on different nodes varies significantly on the number or distribution, which calls for adaptive and data-dependent methods that generate different RFs. To tackle the essential difficulty, we propose a new decentralized KRR algorithm that pursues consensus on decision functions, which allows great flexibility and well adapts data on nodes. The convergence is rigorously given and the effectiveness is numerically verified: by capturing the characteristics of the data on each node, while maintaining the same communication costs as other methods, we achieved an average regression accuracy improvement of 25.5\% across six real-world data sets.