skip to main content

Title: A Privacy Preserving Algorithm to Release Sparse High-dimensional Histograms
Differential privacy has emerged as a popular model to provably limit privacy risks associated with a given data release. However releasing high dimensional synthetic data under differential privacy remains a challenging problem. In this paper, we study the problem of releasing synthetic data in the form of a high dimensional histogram under the constraint of differential privacy.We develop an $(\epsilon, \delta)$-differentially private categorical data synthesizer called \emph{Stability Based Hashed Gibbs Sampler} (SBHG). SBHG works by combining a stability based sparse histogram estimation algorithm with Gibbs sampling and feature selection to approximate the empirical joint distribution of a discrete dataset. SBHG offers a competitive alternative to state-of-the art synthetic data generators while preserving the sparsity structure of the original dataset, which leads to improved statistical utility as illustrated on simulated data. Finally, to study the utility of the resulting synthetic data sets generated by SBHG, we also perform logistic regression using the synthetic datasets and compare the classification accuracy with those from using the original dataset.
Authors:
; ; ;
Award ID(s):
1947919
Publication Date:
NSF-PAR ID:
10125680
Journal Name:
Journal of Privacy and Confidentiality
Volume:
8
Issue:
1
ISSN:
2575-8527
Sponsoring Org:
National Science Foundation
More Like this
  1. We describe customized synthetic datasets for publishing mobility data. Private companies are providing new transportation modalities, and their data is of high value for integrative transportation research, policy enforcement, and public accountability. However, these companies are disincentivized from sharing data not only to protect the privacy of individuals (drivers and/or passengers), but also to protect their own competitive advantage. Moreover, demographic biases arising from how the services are delivered may be amplified if released data is used in other contexts. We describe a model and algorithm for releasing origin-destination histograms that removes selected biases in the data using causality-based methods.more »We compute the origin-destination histogram of the original dataset then adjust the counts to remove undesirable causal relationships that can lead to discrimination or violate contractual obligations with data owners. We evaluate the utility of the algorithm on real data from a dockless bike share program in Seattle and taxi data in New York, and show that these adjusted transportation datasets can retain utility while removing bias in the underlying data.« less
  2. Differential Privacy (DP) formalizes privacy in mathematical terms and provides a robust concept for privacy protection. DIfferentially Private Data Synthesis (DIPS) techniques produce and release synthetic individual-level data in the DP framework. One key challenge to develop DIPS methods is the preservation of the statistical utility of synthetic data, especially in high-dimensional settings. We propose a new DIPS approach, STatistical Election to Partition Sequentially (STEPS) that partitions data by attributes according to their importance ranks according to either a practical or statistical importance measure. STEPS aims to achieve better original information preservation for the attributes with higher importance ranks andmore »produce thus more useful synthetic data overall. We present an algorithm to implement the STEPS procedure and employ the privacy budget composability to ensure the overall privacy cost is controlled at the pre-specified value. We apply the STEPS procedure to both simulated data and the 2000–2012 Current Population Survey youth voter data. The results suggest STEPS can better preserve the population-level information and the original information for some analyses compared to PrivBayes, a modified Uniform histogram approach, and the flat Laplace sanitizer.« less
  3. We consider the problem of designing and analyzing differentially private algorithms that can be implemented on discrete models of computation in strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomial-time algorithms. As a case study, we examine the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X. The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy \& Confidentiality 2017) does not satisfy our requirements, as it is based onmore »real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X|, which can be exponential in the bit length of the input.   In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its ``"per-bin accuracy" (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log|X|, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram; it is based on an (n+1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.« less
  4. Data sets and statistics about groups of individuals are increasingly collected and released, feeding many optimization and learning algorithms. In many cases, the released data contain sensitive information whose privacy is strictly regulated. For example, in the U.S., the census data is regulated under Title 13, which requires that no individual be identified from any data released by the Census Bureau. In Europe, data release is regulated according to the General Data Protection Regulation, which addresses the control and transfer of personal data. Differential privacy has emerged as the de-facto standard to protect data privacy. In a nutshell, differentially privatemore »algorithms protect an individual’s data by injecting random noise into the output of a computation that involves such data. While this process ensures privacy, it also impacts the quality of data analysis, and, when private data sets are used as inputs to complex machine learning or optimization tasks, they may produce results that are fundamentally different from those obtained on the original data and even rise unintended bias and fairness concerns. In this talk, I will first focus on the challenge of releasing privacy-preserving data sets for complex data analysis tasks. I will introduce the notion of Constrained-based Differential Privacy (C-DP), which allows casting the data release problem to an optimization problem whose goal is to preserve the salient features of the original data. I will review several applications of C-DP in the context of very large hierarchical census data, data streams, energy systems, and in the design of federated data-sharing protocols. Next, I will discuss how errors induced by differential privacy algorithms may propagate within a decision problem causing biases and fairness issues. This is particularly important as privacy-preserving data is often used for critical decision processes, including the allocation of funds and benefits to states and jurisdictions, which ideally should be fair and unbiased. Finally, I will conclude with a roadmap to future work and some open questions.« less
  5. Multi-dimensional analytical (MDA) queries are often issued against a fact table with predicates on (categorical or ordinal) dimensions and aggregations on one or more measures. In this paper, we study the problem of answering MDA queries under local differential privacy (LDP). In the absence of a trusted agent, sensitive dimensions are encoded in a privacy preserving (LDP) way locally before being sent to the data collector. The data collector estimates the answers to MDA queries, based on the encoded dimensions. We propose several LDP encoders and estimation algorithms, to handle a large class of MDA queries with different types ofmore »predicates and aggregation functions. Our techniques are able to answer these queries with tight error bounds and scale well in high-dimensional settings (i.e., error is polylogarithmic in dimension sizes). We conduct experiments on real and synthetic data to verify our theoretical results, and compare our solution with marginal-estimation based solutions.« less