Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the @math -differential privacy definition due to (2006). First we apply the output perturbation ideas of (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.
 In this paper, we propose the first formal privacy analysis of a data anonymization process known as the synthetic data generation, a technique becoming popular in the statistics community. The target application for this work is a mapping program that shows the commuting patterns of the population of the United States. The source data for this application were collected by the U.S. Census Bureau, but due to privacy constraints, they cannot be used directly by the mapping program. Instead, we generate synthetic data that statistically mimic the original data while providing privacy guarantees. We use these synthetic data as a surrogate for the original data. We find that while some existing definitions of privacy are inapplicable to our target application, others are too conservative and render the synthetic data useless since they guard against privacy breaches that are very unlikely. Moreover, the data in our target application is sparse, and none of the existing solutions are tailored to anonymize sparse data. In this paper, we propose solutions to address the above issues. We introduce a new, generic framework for private data analysis.The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains.Our framework allows one to release functions f of the data withinstance-based additive noise. That is, the noise magnitude is determined not only by the function we want to release, but also bythe database itself. One of the challenges is to ensure that the noise magnitude does not leak information about the database. To address that, we calibrate the noise magnitude to the smoothsensitivity of f on the database x --- a measure of variabilityof f in the neighborhood of the instance x. The new frameworkgreatly expands the applicability of output perturbation, a technique for protecting individuals' privacy by adding a smallamount of random noise to the released statistics. To our knowledge, this is the first formal analysis of the effect of instance-basednoise in the context of data privacy. Our framework raises many interesting algorithmic questions. Namely,to apply the framework one must compute or approximate the smoothsensitivity of f on x. We show how to do this efficiently for several different functions, including the median and the cost ofthe minimum spanning tree. We also give a generic procedure based on sampling that allows one to release f(x) accurately on manydatabases x. This procedure is applicable even when no efficient algorithm for approximating smooth sensitivity of f is known orwhen f is given as a black box. We illustrate the procedure by applying it to k-SED (k-means) clustering and learning mixtures of Gaussians. We introduce the smoothed analysis of algorithms, which continuously interpolates between the worst-case and average-case analyses of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex algorithm has smoothed complexity polynomial in the input size and the standard deviation of Gaussian perturbations.  The contingency table is a work horse of official statistics, the format of reported data for the US Census, Bureau of Labor Statistics, and the Internal Revenue Service. In many settings such as these privacy is not only ethically mandated, but frequently legally as well. Consequently there is an extensive and diverse literature dedicated to the problems of statistical disclosure control in contingency table release. However, all current techniques for reporting contingency tables fall short on at leas one of privacy, accuracy, and consistency (among multiple released tables). We propose a solution that provides strong guarantees for all three desiderata simultaneously. Our approach can be viewed as a special case of a more general approach for producing synthetic data: Any privacy-preserving mechanism for contingency table release begins with raw data and produces a (possibly inconsistent) privacy-preserving set of marginals. From these tables alone-and hence without weakening privacy--we will find and output the "nearest" consistent set of marginals. Interestingly, this set is no farther than the tables of the raw data, and consequently the additional error introduced by the imposition of consistency is no more than the error introduced by the privacy mechanism itself. The privacy mechanism of [20] gives the strongest known privacy guarantees, with very little error. Combined with the techniques of the current paper, we therefore obtain excellent privacy, accuracy, and consistency among the tables. Moreover, our techniques are surprisingly efficient. Our techniques apply equally well to the logical cousin of the contingency table, the OLAP cube.