Many data applications have certain invariant constraints due to practical needs. Data curators who employ differential privacy need to respect such constraints on the sanitized data product as a primary utility requirement. Invariants challenge the formulation, implementation, and interpretation of privacy guarantees. We propose subspace differential privacy, to honestly characterize the dependence of the sanitized output on confidential aspects of the data. We discuss two design frameworks that convert well-known differentially private mechanisms, such as the Gaussian and the Laplace mechanisms, to subspace differentially private ones that respect the invariants specified by the curator. For linear queries, we discuss the design of near-optimal mechanisms that minimize the mean squared error. Subspace differentially private mechanisms rid the need for post-processing due to invariants, preserve transparency and statistical intelligibility of the output, and can be suitable for distributed implementation. We showcase the proposed mechanisms on the 2020 Census Disclosure Avoidance demonstration data, and a spatio-temporal dataset of mobile access point connections on a large university campus.
more »
« less
Integer Subspace Differential Privacy
We propose new differential privacy solutions for when external invariants and integer constraints are simultaneously enforced on the data product. These requirements arise in real world applications of private data curation, including the public release of the 2020 U.S. Decennial Census. They pose a great challenge to the production of provably private data products with adequate statistical usability. We propose integer subspace differential privacy to rigorously articulate the privacy guarantee when data products maintain both the invariants and integer characteristics, and demonstrate the composition and post-processing properties of our proposal. To address the challenge of sampling from a potentially highly restricted discrete space, we devise a pair of unbiased additive mechanisms, the generalized Laplace and the generalized Gaussian mechanisms, by solving the Diophantine equations as defined by the constraints. The proposed mechanisms have good accuracy, with errors exhibiting sub-exponential and sub-Gaussian tail probabilities respectively. To implement our proposal, we design an MCMC algorithm and supply empirical convergence assessment using estimated upper bounds on the total variation distance via L-lag coupling. We demonstrate the efficacy of our proposal with applications to a synthetic problem with intersecting invariants, a sensitive contingency table with known margins, and the 2010 Census county-level demonstration data with mandated fixed state population totals.
more »
« less
- Award ID(s):
- 2118953
- PAR ID:
- 10464766
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 37
- Issue:
- 6
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 7349 to 7357
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, đť‘“-DP and the PLD formalism) via the characteristic function (đťś™-function) of a certain dominating privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and đť‘“-DP, thus providing (đťś–,𝛿)-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the complex logarithm of đťś™-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments.more » « less
-
Post-processing immunity is a fundamental property of differential privacy: it enables arbitrary data-independent transformations to differentially private outputs without affecting their privacy guarantees. Post-processing is routinely applied in data-release applications, including census data, which are then used to make allocations with substantial societal impacts. This paper shows that post-processing causes disparate impacts on individuals or groups and analyzes two critical settings: the release of differentially private datasets and the use of such private datasets for downstream decisions, such as the allocation of funds informed by US Census data. In the first setting, the paper proposes tight bounds on the unfairness of traditional post-processing mechanisms, giving a unique tool to decision-makers to quantify the disparate impacts introduced by their release. In the second setting, this paper proposes a novel post-processing mechanism that is (approximately) optimal under different fairness metrics, either reducing fairness issues substantially or reducing the cost of privacy. The theoretical analysis is complemented with numerical simulations on Census data.more » « less
-
more » « less
Large corporations, government entities and institutions such as hospitals and census bureaus routinely collect our personal and sensitive information for providing services. A key technological challenge is designing algorithms for these services that provide useful results, while simultaneously maintaining the privacy of the individuals whose data are being shared. Differential privacy (DP) is a cryptographically motivated and mathematically rigorous approach for addressing this challenge. Under DP, a randomized algorithm provides privacy guarantees by approximating the desired functionality, leading to a privacy–utility trade-off. Strong (pure DP) privacy guarantees are often costly in terms of utility. Motivated by the need for a more efficient mechanism with better privacy–utility trade-off, we propose Gaussian FM, an improvement to the functional mechanism (FM) that offers higher utility at the expense of a weakened (approximate) DP guarantee. We analytically show that the proposed Gaussian FM algorithm can offer orders of magnitude smaller noise compared to the existing FM algorithms. We further extend our Gaussian FM algorithm to decentralized-data settings by incorporating the CAPE protocol and propose capeFM. Our method can offer the same level of utility as its centralized counterparts for a range of parameter choices. We empirically show that our proposed algorithms outperform existing state-of-the-art approaches on synthetic and real datasets.
-
There has been considerable controversy regarding the accuracy and privacy of de-identification mechanisms used in the U.S. Decennial Census. We theoretically and experimentally analyze two such classes of mechanisms, swapping and differential privacy, especially examining their effects on ethnoracial minority groups. We first prove that the expected error of queries made on swapped demographic datasets is greater in sub-populations whose racial distributions differ more from the racial distribution of the global population. We also prove that the probability that m unique entries exist in a sub-population shrinks exponentially as the sub-population size grows. These properties suggest that swapping, which prioritizes unique entries, will produce poor accuracy for minority groups. We then empirically analyze the impact of swapping and differential privacy on the accuracy and privacy of a de- mographic dataset. We evaluate accuracy in several ways, including methods that stress the effect on minority groups. We evaluate privacy by counting the number of re-identified entries in a simulated linkage attack. Finally, we explore the disproportionate presence of minority groups in identified entries. Our empirical findings corroborate our theoretical results: for minority representation, the utility of differential privacy is comparable to the utility of swapping, while providing a stronger privacy guarantee. Swapping places a disproportionate privacy burden on minority groups, whereas an ϵ- differentially private mechanism is ϵ-differentially private for all subgroups.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/aaai.v37i6.25895
