Private Decayed Sum Estimation under Continual Observation

In monitoring applications, recent data is more important than distant data. How does this affect privacy of data analysis? We study a general class of data analyses - computing predicate sums - with privacy. Formally, we study the problem of estimating predicate sums {\em privately}, for sliding windows (and other well-known decay models of data, i.e. exponential and polynomial decay). We extend the recently proposed continual privacy model of Dwork et al. We present algorithms for decayed sum which are \eps-differentially private, and are accurate. For window and exponential decay sums, our algorithms are accurate up to additive 1/\eps and polylog terms in the range of the computed function; for polynomial decay sums which are technically more challenging because partial solutions do not compose easily, our algorithms incur additional relative error. Further, we show lower bounds, tight within polylog factors and tight with respect to the dependence on the probability of error

Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants

PRIVACY PRESERVING DATA MINING FOR NUMERICAL MATRICES, SOCIAL NETWORKS, AND BIG DATA

Motivated by increasing public awareness of possible abuse of confidential information, which is considered as a significant hindrance to the development of e-society, medical and financial markets, a privacy preserving data mining framework is presented so that data owners can carefully process data in order to preserve confidential information and guarantee information functionality within an acceptable boundary. First, among many privacy-preserving methodologies, as a group of popular techniques for achieving a balance between data utility and information privacy, a class of data perturbation methods add a noise signal, following a statistical distribution, to an original numerical matrix. With the help of analysis in eigenspace of perturbed data, the potential privacy vulnerability of a popular data perturbation is analyzed in the presence of very little information leakage in privacy-preserving databases. The vulnerability to very little data leakage is theoretically proved and experimentally illustrated. Second, in addition to numerical matrices, social networks have played a critical role in modern e-society. Security and privacy in social networks receive a lot of attention because of recent security scandals among some popular social network service providers. So, the need to protect confidential information from being disclosed motivates us to develop multiple privacy-preserving techniques for social networks. Affinities (or weights) attached to edges are private and can lead to personal security leakage. To protect privacy of social networks, several algorithms are proposed, including Gaussian perturbation, greedy algorithm, and probability random walking algorithm. They can quickly modify original data in a large-scale situation, to satisfy different privacy requirements. Third, the era of big data is approaching on the horizon in the industrial arena and academia, as the quantity of collected data is increasing in an exponential fashion. Three issues are studied in the age of big data with privacy preservation, obtaining a high confidence about accuracy of any specific differentially private queries, speedily and accurately updating a private summary of a binary stream with I/O-awareness, and launching a mutual private information retrieval for big data. All three issues are handled by two core backbones, differential privacy and the Chernoff Bound