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Register a new userDistributed Differentially-Private Algorithms for Matrix and Tensor Factorization
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In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, differentially private algorithms suffer because they introduce noise to guarantee privacy. This paper designs new and improved distributed and differentially private algorithms for two popular matrix and tensor factorization methods: principal component analysis (PCA) and orthogonal tensor decomposition (OTD). The new algorithms employ a correlated noise design scheme to alleviate the effects of noise and can achieve the same noise level as the centralized scenario. Experiments on synthetic and real data illustrate the regimes in which the correlated noise allows performance matching with the centralized setting, outperforming previous methods and demonstrating that meaningful utility is possible while guaranteeing differential privacy.
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Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which operate on such data should be sensitive to the privacy risks in publishing their outputs. Differential privacy is a framework for developing tradeoffs between privacy and the utility of these outputs. In this paper we investigate the theory and empirical performance of differentially private approximations to PCA and propose a new method which explicitly optimizes the utility of the output. We show that the sample complexity of the proposed method differs from the existing procedure in the scaling with the data dimension, and that our method is nearly optimal in terms of this scaling. We furthermore illustrate our results, showing that on real data there is a large performance gap between the existing method and our method.
Large data collections required for the training of neural networks often contain sensitive information such as the medical histories of patients, and the privacy of the training data must be preserved. In this paper, we introduce a dropout technique that provides an elegant Bayesian interpretation to dropout, and show that the intrinsic noise added, with the primary goal of regularization, can be exploited to obtain a degree of differential privacy. The iterative nature of training neural networks presents a challenge for privacy-preserving estimation since multiple iterations increase the amount of noise added. We overcome this by using a relaxed notion of differential privacy, called concentrated differential privacy, which provides tighter estimates on the overall privacy loss. We demonstrate the accuracy of our privacy-preserving dropout algorithm on benchmark datasets.
A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of Gaussian processes (GPs). We propose a method using GPs to provide differentially private (DP) regression. We then improve this method by crafting the DP noise covariance structure to efficiently protect the training data, while minimising the scale of the added noise. We find that this cloaking method achieves the greatest accuracy, while still providing privacy guarantees, and offers practical DP for regression over multi-dimensional inputs. Together these methods provide a starter toolkit for combining differential privacy and GPs.
Deep neural networks with their large number of parameters are highly flexible learning systems. The high flexibility in such networks brings with some serious problems such as overfitting, and regularization is used to address this problem. A currently popular and effective regularization technique for controlling the overfitting is dropout. Often, large data collections required for neural networks contain sensitive information such as the medical histories of patients, and the privacy of the training data should be protected. In this paper, we modify the recently proposed variational dropout technique which provided an elegant Bayesian interpretation to dropout, and show that the intrinsic noise in the variational dropout can be exploited to obtain a degree of differential privacy. The iterative nature of training neural networks presents a challenge for privacy-preserving estimation since multiple iterations increase the amount of noise added. We overcome this by using a relaxed notion of differential privacy, called concentrated differential privacy, which provides tighter estimates on the overall privacy loss. We demonstrate the accuracy of our privacy-preserving variational dropout algorithm on benchmark datasets.
We report on the potential for using algorithms for non-negative matrix factorization (NMF) to improve parameter estimation in topic models. While several papers have studied connections between NMF and topic models, none have suggested leveraging these connections to develop new algorithms for fitting topic models. Importantly, NMF avoids the sum-to-one constraints on the topic model parameters, resulting in an optimization problem with simpler structure and more efficient computations. Building on recent advances in optimization algorithms for NMF, we show that first solving the NMF problem then recovering the topic model fit can produce remarkably better fits, and in less time, than standard algorithms for topic models. While we focus primarily on maximum likelihood estimation, we show that this approach also has the potential to improve variational inference for topic models. Our methods are implemented in the R package fastTopics.
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