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  1. Regularized sparse learning with the ℓ0-norm is important in many areas, including statistical learning and signal processing. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex-constrained sparse learning due to their capability of recovering true support and scalability with large datasets. The current theoretical analysis of IHT assumes the use of centralized IID data. In realistic large-scale scenarios, however, data are distributed, seldom IID, and private to edge computing devices at the local level. Consequently, it is required to study the property of IHT in a federated environment, where local devices update the sparse model individually and communicate with a central server for aggregation infrequently without sharing local data. In this paper, we propose the first group of federated IHT methods: Federated Hard Thresholding (Fed-HT) and Federated Iterative Hard Thresholding (FedIter-HT) with theoretical guarantees. We prove that both algorithms have a linear convergence rate and guarantee for recovering the optimal sparse estimator, which is comparable to classic IHT methods, but with decentralized, non-IID, and unbalanced data. Empirical results demonstrate that the Fed-HT and FedIter-HT outperform their competitor—a distributed IHT, in terms of reducing objective values with fewer communication rounds and bandwidth requirements. 
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    Deep learning holds a great promise of revolutionizing healthcare and medicine. Unfortunately, various inference attack models demonstrated that deep learning puts sensitive patient information at risk. The high capacity of deep neural networks is the main reason behind the privacy loss. In particular, patient information in the training data can be unintentionally memorized by a deep network. Adversarial parties can extract that information given the ability to access or query the network. In this paper, we propose a novel privacy-preserving mechanism for training deep neural networks. Our approach adds decaying Gaussian noise to the gradients at every training iteration. This is in contrast to the mainstream approach adopted by Google's TensorFlow Privacy, which employs the same noise scale in each step of the whole training process. Compared to existing methods, our proposed approach provides an explicit closed-form mathematical expression to approximately estimate the privacy loss. It is easy to compute and can be useful when the users would like to decide proper training time, noise scale, and sampling ratio during the planning phase. We provide extensive experimental results using one real-world medical dataset (chest radiographs from the CheXpert dataset) to validate the effectiveness of the proposed approach. The proposed differential privacy based deep learning model achieves significantly higher classification accuracy over the existing methods with the same privacy budget. 
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  5. While embracing various machine learning techniques to make effective decisions in the big data era, preserving the privacy of sensitive data poses significant challenges. In this paper, we develop a privacy-preserving distributed machine learning algorithm to address this issue. Given the assumption that each data provider owns a dataset with different sample size, our goal is to learn a common classifier over the union of all the local datasets in a distributed way without leaking any sensitive information of the data samples. Such an algorithm needs to jointly consider efficient distributed learning and effective privacy preservation. In the proposed algorithm, we extend stochastic alternating direction method of multipliers (ADMM) in a distributed setting to do distributed learning. For preserving privacy during the iterative process, we combine differential privacy and stochastic ADMM together. In particular, we propose a novel stochastic ADMM based privacy-preserving distributed machine learning (PS-ADMM) algorithm by perturbing the updating gradients, that provide differential privacy guarantee and have a low computational cost. We theoretically demonstrate the convergence rate and utility bound of our proposed PS-ADMM under strongly convex objective. Through our experiments performed on real-world datasets, we show that PS-ADMM outperforms other differentially private ADMM algorithms under the same differential privacy guarantee. 
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