Collaborating Authors

Capacity Bounded Differential Privacy Machine Learning

Differential privacy, a notion of algorithmic stability, is a gold standard for measuring the additional risk an algorithm's output poses to the privacy of a single record in the dataset. Differential privacy is defined as the distance between the output distribution of an algorithm on neighboring datasets that differ in one entry. In this work, we present a novel relaxation of differential privacy, capacity bounded differential privacy, where the adversary that distinguishes output distributions is assumed to be capacity-bounded -- i.e. bounded not in computational power, but in terms of the function class from which their attack algorithm is drawn. We model adversaries in terms of restricted f-divergences between probability distributions, and study properties of the definition and algorithms that satisfy them.

Subsampled R\'enyi Differential Privacy and Analytical Moments Accountant Machine Learning

We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the R\'enyi Differential Privacy (RDP) (Mironov, 2017) parameters for algorithms that: (1) subsample the dataset, and then (2) apply a randomized mechanism M to the subsample, in terms of the RDP parameters of M and the subsampling probability parameter. This result generalizes the classic subsampling-based "privacy amplification" property of $(\epsilon,\delta)$-differential privacy that applies to only one fixed pair of $(\epsilon,\delta)$, to a stronger version that exploits properties of each specific randomized algorithm and satisfies an entire family of $(\epsilon(\delta),\delta)$-differential privacy for all $\delta\in [0,1]$. Our experiments confirm the advantage of using our techniques over keeping track of $(\epsilon,\delta)$ directly, especially in the setting where we need to compose many rounds of data access.

A unified view on differential privacy and robustness to adversarial examples Machine Learning

This short note highlights some links between two lines of research within the emerging topic of trustworthy machine learning: differential privacy and robustness to adversarial examples. By abstracting the definitions of both notions, we show that they build upon the same theoretical ground and hence results obtained so far in one domain can be transferred to the other. More precisely, our analysis is based on two key elements: probabilistic mappings (also called randomized algorithms in the differential privacy community), and the Renyi divergence which subsumes a large family of divergences. We first generalize the definition of robustness against adversarial examples to encompass probabilistic mappings. Then we observe that Renyi-differential privacy (a generalization of differential privacy recently proposed in~\cite{Mironov2017RenyiDP}) and our definition of robustness share several similarities. We finally discuss how can both communities benefit from this connection to transfer technical tools from one research field to the other.

Privacy Amplification by Iteration Machine Learning

Many commonly used learning algorithms work by iteratively updating an intermediate solution using one or a few data points in each iteration. Analysis of differential privacy for such algorithms often involves ensuring privacy of each step and then reasoning about the cumulative privacy cost of the algorithm. This is enabled by composition theorems for differential privacy that allow releasing of all the intermediate results. In this work, we demonstrate that for contractive iterations, not releasing the intermediate results strongly amplifies the privacy guarantees. We describe several applications of this new analysis technique to solving convex optimization problems via noisy stochastic gradient descent. For example, we demonstrate that a relatively small number of non-private data points from the same distribution can be used to close the gap between private and non-private convex optimization. In addition, we demonstrate that we can achieve guarantees similar to those obtainable using the privacy-amplification-by-sampling technique in several natural settings where that technique cannot be applied.

Private Stochastic Convex Optimization: Efficient Algorithms for Non-smooth Objectives Machine Learning

Modern machine learning systems often leverage data that are generated ubiquitously and seamlessly through devices such as smartphones, cameras, microphones, or user's weblogs, transaction logs, social media, etc. Much of this data is private, and releasing models trained on such data without serious privacy considerations can reveal sensitive information (Narayanan and Shmatikov, 2008; Sweeney, 1997). Consequently, much emphasis has been placed in recent years on machine learning under the constraints of a robust privacy guarantee. One such notion that has emerged as a de facto standard is that of differential privacy. Informally, differential privacy provides a quantitative assessment of how different are the outputs of a randomized algorithm when fed two very similar inputs. If small changes in the input do not manifest as drastically different outputs, then it is hard to discern much information about the inputs solely based on the outputs of the algorithm. In the context of machine learning, this implies that if the learning algorithm is not overly sensitive to any single datum in the training set, then releasing the trained model should preserve the privacy of the training data. This requirement, apriori, seems compatible with the goal of learning, which is to find a model that generalizes well on the population and does not overfit to the given training sample. It seems reasonable then to argue that privacy is not necessarily at odds with generalization, especially when large training sets are available.