Hypothesis Testing Interpretations and Renyi Differential Privacy

Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectively test whether a specific individual has contributed her data by observing the output of a private mechanism---any test cannot have both high significance and high power. In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation. These conditions are useful to analyze the distinguishability power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Renyi divergence. This analysis also results in an improved conversion rule between these definitions and differential privacy

Hypothesis testing interpretations and Renyi differential privacy

Differential privacy is a de facto standard in data privacy, with applications in the public and private sectors. A way to explain differential privacy, which is particularly appealing to statistician and social scientists, is by means of its statistical hypothesis testing interpretation. Informally, one cannot effectively test whether a specific individual has contributed her data by observing the output of a private mechanism—any test cannot have both high significance and high power. In this paper, we identify some conditions under which a privacy definition given in terms of a statistical divergence satisfies a similar interpretation. These conditions are useful to analyze the distinguishability power of divergences and we use them to study the hypothesis testing interpretation of some relaxations of differential privacy based on Rényi divergence. This analysis also results in an improved conversion rule between these definitions and differential privacy.https://arxiv.org/pdf/1905.09982.pd

Truncated Laplace and Gaussian mechanisms of RDP

The Laplace mechanism and the Gaussian mechanism are primary mechanisms in differential privacy, widely applicable to many scenarios involving numerical data. However, due to the infinite-range random variables they generate, the Laplace and Gaussian mechanisms may return values that are semantically impossible, such as negative numbers. To address this issue, we have designed the truncated Laplace mechanism and Gaussian mechanism. For a given truncation interval [a, b], the truncated Gaussian mechanism ensures the same Renyi Differential Privacy (RDP) as the untruncated mechanism, regardless of the values chosen for the truncation interval [a, b]. Similarly, the truncated Laplace mechanism, for specified interval [a, b], maintains the same RDP as the untruncated mechanism. We provide the RDP expressions for each of them. We believe that our study can further enhance the utility of differential privacy in specific applications

DPSUR: Accelerating Differentially Private Stochastic Gradient Descent Using Selective Update and Release

Machine learning models are known to memorize private data to reduce their training loss, which can be inadvertently exploited by privacy attacks such as model inversion and membership inference. To protect against these attacks, differential privacy (DP) has become the de facto standard for privacy-preserving machine learning, particularly those popular training algorithms using stochastic gradient descent, such as DPSGD. Nonetheless, DPSGD still suffers from severe utility loss due to its slow convergence. This is partially caused by the random sampling, which brings bias and variance to the gradient, and partially by the Gaussian noise, which leads to fluctuation of gradient updates. Our key idea to address these issues is to apply selective updates to the model training, while discarding those useless or even harmful updates. Motivated by this, this paper proposes DPSUR, a Differentially Private training framework based on Selective Updates and Release, where the gradient from each iteration is evaluated based on a validation test, and only those updates leading to convergence are applied to the model. As such, DPSUR ensures the training in the right direction and thus can achieve faster convergence than DPSGD. The main challenges lie in two aspects -- privacy concerns arising from gradient evaluation, and gradient selection strategy for model update. To address the challenges, DPSUR introduces a clipping strategy for update randomization and a threshold mechanism for gradient selection. Experiments conducted on MNIST, FMNIST, CIFAR-10, and IMDB datasets show that DPSUR significantly outperforms previous works in terms of convergence speed and model utility.Comment: This paper has been accepted by VLDB 202

Unraveling the Connections between Privacy and Certified Robustness in Federated Learning Against Poisoning Attacks

Federated learning (FL) provides an efficient paradigm to jointly train a global model leveraging data from distributed users. As local training data comes from different users who may not be trustworthy, several studies have shown that FL is vulnerable to poisoning attacks. Meanwhile, to protect the privacy of local users, FL is usually trained in a differentially private way (DPFL). Thus, in this paper, we ask: What are the underlying connections between differential privacy and certified robustness in FL against poisoning attacks? Can we leverage the innate privacy property of DPFL to provide certified robustness for FL? Can we further improve the privacy of FL to improve such robustness certification? We first investigate both user-level and instance-level privacy of FL and provide formal privacy analysis to achieve improved instance-level privacy. We then provide two robustness certification criteria: certified prediction and certified attack inefficacy for DPFL on both user and instance levels. Theoretically, we provide the certified robustness of DPFL based on both criteria given a bounded number of adversarial users or instances. Empirically, we conduct extensive experiments to verify our theories under a range of poisoning attacks on different datasets. We find that increasing the level of privacy protection in DPFL results in stronger certified attack inefficacy; however, it does not necessarily lead to a stronger certified prediction. Thus, achieving the optimal certified prediction requires a proper balance between privacy and utility loss.Comment: ACM CCS 202