Privacy via the Johnson-Lindenstrauss Transform

Suppose that party A collects private information about its users, where each user's data is represented as a bit vector. Suppose that party B has a proprietary data mining algorithm that requires estimating the distance between users, such as clustering or nearest neighbors. We ask if it is possible for party A to publish some information about each user so that B can estimate the distance between users without being able to infer any private bit of a user. Our method involves projecting each user's representation into a random, lower-dimensional space via a sparse Johnson-Lindenstrauss transform and then adding Gaussian noise to each entry of the lower-dimensional representation. We show that the method preserves differential privacy---where the more privacy is desired, the larger the variance of the Gaussian noise. Further, we show how to approximate the true distances between users via only the lower-dimensional, perturbed data. Finally, we consider other perturbation methods such as randomized response and draw comparisons to sketch-based methods. While the goal of releasing user-specific data to third parties is more broad than preserving distances, this work shows that distance computations with privacy is an achievable goal.Comment: 24 page

Random projection to preserve patient privacy

With the availability of accessible and widely used cloud services, it is natural that large components of healthcare systems migrate to them; for example, patient databases can be stored and processed in the cloud. Such cloud services provide enhanced flexibility and additional gains, such as availability, ease of data share, and so on. This trend poses serious threats regarding the privacy of the patients and the trust that an individual must put into the healthcare system itself. Thus, there is a strong need of privacy preservation, achieved through a variety of different approaches. In this paper, we study the application of a random projection-based approach to patient data as a means to achieve two goals: (1) provably mask the identity of users under some adversarial-attack settings, (2) preserve enough information to allow for aggregate data analysis and application of machine-learning techniques. As far as we know, such approaches have not been applied and tested on medical data. We analyze the tradeoff between the loss of accuracy on the outcome of machine-learning algorithms and the resilience against an adversary. We show that random projections proved to be strong against known input/output attacks while offering high quality data, as long as the projected space is smaller than the original space, and as long as the amount of leaked data available to the adversary is limited

Detecting Communities under Differential Privacy

Complex networks usually expose community structure with groups of nodes sharing many links with the other nodes in the same group and relatively few with the nodes of the rest. This feature captures valuable information about the organization and even the evolution of the network. Over the last decade, a great number of algorithms for community detection have been proposed to deal with the increasingly complex networks. However, the problem of doing this in a private manner is rarely considered. In this paper, we solve this problem under differential privacy, a prominent privacy concept for releasing private data. We analyze the major challenges behind the problem and propose several schemes to tackle them from two perspectives: input perturbation and algorithm perturbation. We choose Louvain method as the back-end community detection for input perturbation schemes and propose the method LouvainDP which runs Louvain algorithm on a noisy super-graph. For algorithm perturbation, we design ModDivisive using exponential mechanism with the modularity as the score. We have thoroughly evaluated our techniques on real graphs of different sizes and verified their outperformance over the state-of-the-art

Privacy-Utility Trade-off of Linear Regression under Random Projections and Additive Noise

Data privacy is an important concern in machine learning, and is fundamentally at odds with the task of training useful learning models, which typically require the acquisition of large amounts of private user data. One possible way of fulfilling the machine learning task while preserving user privacy is to train the model on a transformed, noisy version of the data, which does not reveal the data itself directly to the training procedure. In this work, we analyze the privacy-utility trade-off of two such schemes for the problem of linear regression: additive noise, and random projections. In contrast to previous work, we consider a recently proposed notion of differential privacy that is based on conditional mutual information (MI-DP), which is stronger than the conventional $(\epsilon, \delta)$-differential privacy, and use relative objective error as the utility metric. We find that projecting the data to a lower-dimensional subspace before adding noise attains a better trade-off in general. We also make a connection between privacy problem and (non-coherent) SIMO, which has been extensively studied in wireless communication, and use tools from there for the analysis. We present numerical results demonstrating the performance of the schemes.Comment: A short version is published in ISIT 201