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Register a new userAccuracy First: Selecting a Differential Privacy Level for Accuracy-Constrained ERM
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Bo Waggoner
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Traditional approaches to differential privacy assume a fixed privacy requirement $epsilon$ for a computation, and attempt to maximize the accuracy of the computation subject to the privacy constraint. As differential privacy is increasingly deployed in practical settings, it may often be that there is instead a fixed accuracy requirement for a given computation and the data analyst would like to maximize the privacy of the computation subject to the accuracy constraint. This raises the question of how to find and run a maximally private empirical risk minimizer subject to a given accuracy requirement. We propose a general noise reduction framework that can apply to a variety of private empirical risk minimization (ERM) algorithms, using them to search the space of privacy levels to find the empirically strongest one that meets the accuracy constraint, incurring only logarithmic overhead in the number of privacy levels searched. The privacy analysis of our algorithm leads naturally to a version of differential privacy where the privacy parameters are dependent on the data, which we term ex-post privacy, and which is related to the recently introduced notion of privacy odometers. We also give an ex-post privacy analysis of the classical AboveThreshold privacy tool, modifying it to allow for queries chosen depending on the database. Finally, we apply our approach to two common objectives, regularized linear and logistic regression, and empirically compare our noise reduction methods to (i) inverting the theoretical utility guarantees of standard private ERM algorithms and (ii) a stronger, empirical baseline based on binary search.
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We show that adding differential privacy to Explainable Boosting Machines (EBMs), a recent method for training interpretable ML models, yields state-of-the-art accuracy while protecting privacy. Our experiments on multiple classification and regression datasets show that DP-EBM models suffer surprisingly little accuracy loss even with strong differential privacy guarantees. In addition to high accuracy, two other benefits of applying DP to EBMs are: a) trained models provide exact global and local interpretability, which is often important in settings where differential privacy is needed; and b) the models can be edited after training without loss of privacy to correct errors which DP noise may have introduced.
Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing emph{ad hoc} definitions and introduce an alternative notion of accuracy parametrized by, what we call, {distance} -- the {distance} of an input $x$ w.r.t., a deterministic computation $f$ and a distance $d$, is the minimal distance $d(x,y)$ over all $y$ such that $f(y) eq f(x)$. We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuels conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature.
Recent research in differential privacy demonstrated that (sub)sampling can amplify the level of protection. For example, for $epsilon$-differential privacy and simple random sampling with sampling rate $r$, the actual privacy guarantee is approximately $repsilon$, if a value of $epsilon$ is used to protect the output from the sample. In this paper, we study whether this amplification effect can be exploited systematically to improve the accuracy of the privatized estimate. Specifically, assuming the agency has information for the full population, we ask under which circumstances accuracy gains could be expected, if the privatized estimate would be computed on a random sample instead of the full population. We find that accuracy gains can be achieved for certain regimes. However, gains can typically only be expected, if the sensitivity of the output with respect to small changes in the database does not depend too strongly on the size of the database. We only focus on algorithms that achieve differential privacy by adding noise to the final output and illustrate the accuracy implications for two commonly used statistics: the mean and the median. We see our research as a first step towards understanding the conditions required for accuracy gains in practice and we hope that these findings will stimulate further research broadening the scope of differential privacy algorithms and outputs considered.
Differential privacy offers a formal framework for reasoning about privacy and accuracy of computations on private data. It also offers a rich set of building blocks for constructing data analyses. When carefully calibrated, these analyses simultaneously guarantee privacy of the individuals contributing their data, and accuracy of their results for inferring useful properties about the population. The compositional nature of differential privacy has motivated the design and implementation of several programming languages aimed at helping a data analyst in programming differentially private analyses. However, most of the programming languages for differential privacy proposed so far provide support for reasoning about privacy but not for reasoning about the accuracy of data analyses. To overcome this limitation, in this work we present DPella, a programming framework providing data analysts with support for reasoning about privacy, accuracy and their trade-offs. The distinguishing feature of DPella is a novel component which statically tracks the accuracy of different data analyses. In order to make tighter accuracy estimations, this component leverages taint analysis for automatically inferring statistical independence of the different noise quantities added for guaranteeing privacy. We show the flexibility of our approach by not only implementing classical counting queries (e.g., CDFs) but also by analyzing hierarchical counting queries (like those done by Census Bureaus), where accuracy have different constraints per level and data analysts should figure out the best manner to calibrate privacy to meet the accuracy requirements.
Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching reconstruction and membership inference attacks. To defend such privacy attacks, many noises perturbation methods (like differential privacy or CountSketch matrix) have been widely designed. However, the strong defence ability and high learning accuracy of these schemes cannot be ensured at the same time, which will impede the wide application of FL in practice (especially for medical or financial institutions that require both high accuracy and strong privacy guarantee). To overcome this issue, in this paper, we propose emph{an efficient model perturbation method for federated learning} to defend reconstruction and membership inference attacks launched by curious clients. On the one hand, similar to the differential privacy, our method also selects random numbers as perturbed noises added to the global model parameters, and thus it is very efficient and easy to be integrated in practice. Meanwhile, the random selected noises are positive real numbers and the corresponding value can be arbitrarily large, and thus the strong defence ability can be ensured. On the other hand, unlike differential privacy or other perturbation methods that cannot eliminate the added noises, our method allows the server to recover the true gradients by eliminating the added noises. Therefore, our method does not hinder learning accuracy at all.
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