Journal of Privacy and Confidentiality

Special Issue on the Theory and Practice of Differential Privacy 2016

2019-10-19T21:03:34-07:00

Make Up Your Mind: The Price of Online Queries in Differential Privacy

2019-10-19T21:03:38-07:00

We consider the problem of answering queries about a sensitive dataset subject to differential privacy. The queries may be chosen adversarially from a larger set $Q$ of allowable queries in one of three ways, which we list in order from easiest to hardest to answer:

Offline: The queries are chosen all at once and the differentially private mechanism answers the queries in a single batch.

Online: The queries are chosen all at once, but the mechanism only receives the queries in a streaming fashion and must answer each query before seeing the next query.

Adaptive: The queries are chosen one at a time and the mechanism must answer each query before the next query is chosen. In particular, each query may depend on the answers given to previous queries.

Many differentially private mechanisms are just as efficient in the adaptive model as they are in the offline model. Meanwhile, most lower bounds for differential privacy hold in the offline setting. This suggests that the three models may be equivalent.

We prove that these models are all, in fact, distinct. Specifically, we show that there is a family of statistical queries such that exponentially more queries from this family can be answered in the offline model than in the online model. We also exhibit a family of search queries such that exponentially more queries from this family can be answered in the online model than in the adaptive model. We also investigate whether such separations might hold for simple queries like threshold queries over the real line.

Concentration Bounds for High Sensitivity Functions Through Differential Privacy

2019-10-19T21:03:36-07:00

A new line of work demonstrates how differential privacy can be used as a mathematical tool for guaranteeing generalization in adaptive data analysis. Specifically, if a differentially private analysis is applied on a sample S of i.i.d. examples to select a low-sensitivity function f, then w.h.p. f(S) is close to its expectation, even though f is being chosen adaptively, i.e., based on the data.

Very recently, Steinke and Ullman observed that these generalization guarantees can be used for proving concentration bounds in the non-adaptive setting, where the low-sensitivity function is fixed beforehand. In particular, they obtain alternative proofs for classical concentration bounds for low-sensitivity functions, such as the Chernoff bound and McDiarmid's Inequality. In this work, we extend this connection between differential privacy and concentration bounds, and show that differential privacy can be used to prove concentration of high-sensitivity functions.

Differentially Private Confidence Intervals for Empirical Risk Minimization

2019-10-19T21:03:36-07:00

The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information. In this paper, we consider the problem of designing confidence intervals for the parameters of a variety of differentially private machine learning models. The algorithms can provide confidence intervals that satisfy differential privacy (as well as the more recently proposed concentrated differential privacy) and can be used with existing differentially private mechanisms that train models using objective perturbation and output perturbation.

Differentially Private Ordinary Least Squares

2019-10-19T21:03:37-07:00

Linear regression is one of the most prevalent techniques in machine learning; however, it is also common to use linear regression for its explanatory capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. gender) and a label (e.g. income) in the presence of other (potentially correlated) features. OLS assumes a particular model that randomly generates the data, and derives t-values - representing the likelihood of each real value to be the true correlation. Using t-values, OLS can release a confidence interval, which is an interval on the reals that is likely to contain the true correlation; and when this interval does not intersect the origin, we can reject the null hypothesis as it is likely that the true correlation is non-zero.
Our work aims at achieving similar guarantees on data under differentially private estimators. First, we show that for well-spread data, the Gaussian Johnson-Lindenstrauss Transform (JLT) gives a very good approximation of t-values; secondly, when JLT approximates Ridge regression (linear regression with l₂-regularization) we derive, under certain conditions, confidence intervals using the projected data; lastly, we derive, under different conditions, confidence intervals for the "Analyze Gauss" algorithm of Dwork et al (STOC 2014).

Per-instance Differential Privacy

2019-10-19T21:03:35-07:00

We consider a refinement of differential privacy --- per instance differential privacy (pDP), which captures the privacy of a specific individual with respect to a fixed data set. We show that this is a strict generalization of the standard DP and inherits all its desirable properties, e.g., composition, invariance to side information and closedness to postprocessing, except that they all hold for every instance separately. We consider a refinement of differential privacy --- per instance differential privacy (pDP), which captures the privacy of a specific individual with respect to a fixed data set. We show that this is a strict generalization of the standard DP and inherits all its desirable properties, e.g., composition, invariance to side information and closedness to postprocessing, except that they all hold for every instance separately. When the data is drawn from a distribution, we show that per-instance DP implies generalization. Moreover, we provide explicit calculations of the per-instance DP for the output perturbation on a class of smooth learning problems. The result reveals an interesting and intuitive fact that an individual has stronger privacy if he/she has small ``leverage score'' with respect to the data set and if he/she can be predicted more accurately using the leave-one-out data set. Simulation shows several orders-of-magnitude more favorable privacy and utility trade-off when we consider the privacy of only the users in the data set. In a case study on differentially private linear regression, provide a novel analysis of the One-Posterior-Sample (OPS) estimator and show that when the data set is well-conditioned it provides $(\epsilon,\delta)$-pDP for any target individuals and matches the exact lower bound up to a $1+\tilde{O}(n^{-1}\epsilon^{-2})$ multiplicative factor. We also demonstrate how we can use a ``pDP to DP conversion'' step to design AdaOPS which uses adaptive regularization to achieve the same results with $(\epsilon,\delta)$-DP.

Program for TPDP 2016

2019-10-19T21:03:37-07:00

The Theory and Practice of Differential Privacy workshop (TPDP 2016) was held in New York City, NY, USA on 23 June 2016 as part of ICML 2016. This is the program.