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Efficient Constrained $k$-Center Clustering with Background Knowledge
Jan 23, 2024
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.
Practical, Private Assurance of the Value of Collaboration
Oct 04, 2023
Two parties wish to collaborate on their datasets. However, before they reveal their datasets to each other, the parties want to have the guarantee that the collaboration would be fruitful. We look at this problem from the point of view of machine learning, where one party is promised an improvement on its prediction model by incorporating data from the other party. The parties would only wish to collaborate further if the updated model shows an improvement in accuracy. Before this is ascertained, the two parties would not want to disclose their models and datasets. In this work, we construct an interactive protocol for this problem based on the fully homomorphic encryption scheme over the Torus (TFHE) and label differential privacy, where the underlying machine learning model is a neural network. Label differential privacy is used to ensure that computations are not done entirely in the encrypted domain, which is a significant bottleneck for neural network training according to the current state-of-the-art FHE implementations. We prove the security of our scheme in the universal composability framework assuming honest-but-curious parties, but where one party may not have any expertise in labelling its initial dataset. Experiments show that we can obtain the output, i.e., the accuracy of the updated model, with time many orders of magnitude faster than a protocol using entirely FHE operations.
A Differentially Private Framework for Deep Learning with Convexified Loss Functions
Apr 03, 2022
Differential privacy (DP) has been applied in deep learning for preserving privacy of the underlying training sets. Existing DP practice falls into three categories - objective perturbation, gradient perturbation and output perturbation. They suffer from three main problems. First, conditions on objective functions limit objective perturbation in general deep learning tasks. Second, gradient perturbation does not achieve a satisfactory privacy-utility trade-off due to over-injected noise in each epoch. Third, high utility of the output perturbation method is not guaranteed because of the loose upper bound on the global sensitivity of the trained model parameters as the noise scale parameter. To address these problems, we analyse a tighter upper bound on the global sensitivity of the model parameters. Under a black-box setting, based on this global sensitivity, to control the overall noise injection, we propose a novel output perturbation framework by injecting DP noise into a randomly sampled neuron (via the exponential mechanism) at the output layer of a baseline non-private neural network trained with a convexified loss function. We empirically compare the privacy-utility trade-off, measured by accuracy loss to baseline non-private models and the privacy leakage against black-box membership inference (MI) attacks, between our framework and the open-source differentially private stochastic gradient descent (DP-SGD) approaches on six commonly used real-world datasets. The experimental evaluations show that, when the baseline models have observable privacy leakage under MI attacks, our framework achieves a better privacy-utility trade-off than existing DP-SGD implementations, given an overall privacy budget $\epsilon \leq 1$ for a large number of queries.
Differentially Private k-Means Clustering with Guaranteed Convergence
Feb 03, 2020
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the centroids of an arbitrary iteration and the information of n-1 out of n items. To protect individual privacy against such an inference attack, preserving differential privacy (DP) for the iterative clustering algorithms has been extensively studied in the interactive settings. However, existing interactive differentially private clustering algorithms suffer from a non-convergence problem, i.e., these algorithms may not terminate without a predefined number of iterations. This problem severely impacts the clustering quality and the efficiency of a differentially private algorithm. To resolve this problem, in this paper, we propose a novel differentially private clustering framework in the interactive settings which controls the orientation of the movement of the centroids over the iterations to ensure the convergence by injecting DP noise in a selected area. We prove that, in the expected case, algorithm under our framework converges in at most twice the iterations of Lloyd's algorithm. We perform experimental evaluations on real-world datasets to show that our algorithm outperforms the state-of-the-art of the interactive differentially private clustering algorithms with guaranteed convergence and better clustering quality to meet the same DP requirement.