In this paper, we study the problem of publishing a stream of real-valued data satisfying differential privacy (DP). One major challenge is that the maximal possible value can be quite large; thus it is necessary to estimate a threshold so that numbers above it are truncated to reduce the amount of noise that is required to all the data. The estimation must be done based on the data in a private fashion. We develop such a method that uses the Exponential Mechanism with a quality function that approximates well the utility goal while maintaining a low sensitivity. Given the threshold, we then propose a novel online hierarchical method and several post-processing techniques. Building on these ideas, we formalize the steps into a framework for private publishing of stream data. Our framework consists of three components: a threshold optimizer that privately estimates the threshold, a perturber that adds calibrated noises to the stream, and a smoother that improves the result using post-processing. Within our framework, we design an algorithm satisfying the more stringent setting of DP called local DP (LDP). To our knowledge, this is the first LDP algorithm for publishing streaming data. Using four real-world datasets, we demonstrate that our mechanism outperforms the state-of-the-art by a factor of 6-10 orders of magnitude in terms of utility (measured by the mean squared error of answering a random range query).

Machine learning models are vulnerable to simple model stealing attacks if the adversary can obtain output labels for chosen inputs. To protect against these attacks, it has been proposed to limit the information provided to the adversary by omitting probability scores, significantly impacting the utility of the provided service. In this work, we illustrate how a service provider can still provide useful, albeit misleading, class probability information, while significantly limiting the success of the attack. Our defense forces the adversary to discard the class probabilities, requiring significantly more queries before they can train a model with comparable performance. We evaluate several attack strategies, model architectures, and hyperparameters under varying adversarial models, and evaluate the efficacy of our defense against the strongest adversary. Finally, we quantify the amount of noise injected into the class probabilities to mesure the loss in utility, e.g., adding 1.74 nats per query on CIFAR-10 and 3.27 on MNIST. Our extensive evaluation shows our defense can degrade the accuracy of the stolen model at least 20%, or require 4x more queries while keeping the accuracy of the protected model almost intact.

The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed towards a comprehensive measure of robustness. In this paper, we provide a theoretical justification for converting robustness analysis into a local Lipschitz constant estimation problem, and propose to use the Extreme Value Theory for efficient evaluation. Our analysis yields a novel robustness metric called CLEVER, which is short for Cross Lipschitz Extreme Value for nEtwork Robustness. The proposed CLEVER score is attack-agnostic and computationally feasible for large neural networks. Experimental results on various networks, including ResNet, Inception-v3 and MobileNet, show that (i) CLEVER is aligned with the robustness indication measured by the $\ell_2$ and $\ell_\infty$ norms of adversarial examples from powerful attacks, and (ii) defended networks using defensive distillation or bounded ReLU indeed achieve better CLEVER scores. To the best of our knowledge, CLEVER is the first attack-independent robustness metric that can be applied to any neural network classifier.