arXiv subjects

Aleksandra Slavkovic

Publications and source records attributed to Aleksandra Slavkovic.

17 recordsLinked to original sources

arXiv2025

Interpreting Network Differential Privacy

How do we interpret the differential privacy (DP) guarantee for network data? We take a deep dive into a popular form of network DP ($\varepsilon$--edge DP) to find that many of its common interpretations are flawed. Drawing on prior work for privacy with correlated data, we interpret DP through the lens of adversarial hypothesis testing and demonstrate a gap between the pairs of hypotheses actually protected under DP (tests of complete networks) and the sorts of hypotheses implied to be protected by common claims (tests of individual edges). We demonstrate some conditions under which this gap can be bridged, while leaving some questions open. While some discussion is specific to edge DP, we offer selected results in terms of abstract DP definitions and provide discussion of the implications for other forms of network DP.

math.ST↗

arXiv2025

Gaussian Differentially Private Human Faces Under a Face Radial Curve Representation

In this paper we consider the problem of releasing a Gaussian Differentially Private (GDP) 3D human face. The human face is a complex structure with many features and inherently tied to one's identity. Protecting this data, in a formally private way, is important yet challenging given the dimensionality of the problem. We extend approximate DP techniques for functional data to the GDP framework. We further propose a novel representation, face radial curves, of a 3D face as a set of functions and then utilize our proposed GDP functional data mechanism. To preserve the shape of the face while injecting noise we rely on tools from shape analysis for our novel representation of the face. We show that our method preserves the shape of the average face and injects less noise than traditional methods for the same privacy budget. Our mechanism consists of two primary components, the first is generally applicable to function value summaries (as are commonly found in nonparametric statistics or functional data analysis) while the second is general to disk-like surfaces and hence more applicable than just to human faces.

cs.CR↗

arXiv2024

Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms

Differential privacy (DP), provides a framework for provable privacy protection against arbitrary adversaries, while allowing the release of summary statistics and synthetic data. We address the problem of releasing a noisy real-valued statistic vector $T$, a function of sensitive data under DP, via the class of $K$-norm mechanisms with the goal of minimizing the noise added to achieve privacy. First, we introduce the sensitivity space of $T$, which extends the concepts of sensitivity polytope and sensitivity hull to the setting of arbitrary statistics $T$. We then propose a framework consisting of three methods for comparing the $K$-norm mechanisms: 1) a multivariate extension of stochastic dominance, 2) the entropy of the mechanism, and 3) the conditional variance given a direction, to identify the optimal $K$-norm mechanism. In all of these criteria, the optimal $K$-norm mechanism is generated by the convex hull of the sensitivity space. Using our methodology, we extend the objective perturbation and functional mechanisms and apply these tools to logistic and linear regression, allowing for private releases of statistical results. Via simulations and an application to a housing price dataset, we demonstrate that our proposed methodology offers a substantial improvement in utility for the same level of risk.

stat.ME↗

arXiv2022

Formal Privacy for Partially Private Data

Differential privacy (DP) quantifies privacy loss by analyzing noise injected into output statistics. For non-trivial statistics, this noise is necessary to ensure finite privacy loss. However, data curators frequently release collections of statistics where some use DP mechanisms and others are released as-is, i.e., without additional randomized noise. Consequently, DP alone cannot characterize the privacy loss attributable to the entire collection of releases. In this paper, we present a privacy formalism, $(ε, \{ Θ_z\}_{z \in \mathcal{Z}})$-Pufferfish ($ε$-TP for short when $\{ Θ_z\}_{z \in \mathcal{Z}}$ is implied), a collection of Pufferfish mechanisms indexed by realizations of a random variable $Z$ representing public information not protected with DP noise. First, we prove that this definition has similar properties to DP. Next, we introduce mechanisms for releasing partially private data (PPD) satisfying $ε$-TP and prove their desirable properties. We provide algorithms for sampling from the posterior of a parameter given PPD. We then compare this inference approach to the alternative where noisy statistics are deterministically combined with Z. We derive mild conditions under which using our algorithms offers both theoretical and computational improvements over this more common approach. Finally, we demonstrate all the effects above on a case study on COVID-19 data.

cs.CR↗

arXiv2022

Shape And Structure Preserving Differential Privacy

It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold. The utility of a mechanism to produce sanitized differentially private estimates from such data is intimately linked to how compatible it is with the underlying structure and geometry of the space. In particular, as recently shown, utility of the Laplace mechanism on a positively curved manifold, such as Kendall's 2D shape space, is significantly influences by the curvature. Focusing on the problem of sanitizing the Fréchet mean of a sample of points on a manifold, we exploit the characterisation of the mean as the minimizer of an objective function comprised of the sum of squared distances and develop a K-norm gradient mechanism on Riemannian manifolds that favors values that produce gradients close to the the zero of the objective function. For the case of positively curved manifolds, we describe how using the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism, and demonstrate this numerically on a dataset of shapes of corpus callosa. Further illustrations of the mechanism's utility on a sphere and the manifold of symmetric positive definite matrices are also presented.

stat.ML↗

arXiv2022

Perfect Spectral Clustering with Discrete Covariates

Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to the algorithm. Here we consider the problem of performing community detection in the presence of discrete node covariates, where network structure is determined by a combination of a latent block model structure and homophily on the observed covariates. We propose a spectral algorithm that we prove achieves perfect clustering with high probability on a class of large, sparse networks with discrete covariates, effectively separating latent network structure from homophily on observed covariates. To our knowledge, our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering in the setting where edge formation is dependent on both latent and observed factors.

stat.ML↗

arXiv2022

Statistical Data Privacy: A Song of Privacy and Utility

To quantify trade-offs between increasing demand for open data sharing and concerns about sensitive information disclosure, statistical data privacy (SDP) methodology analyzes data release mechanisms which sanitize outputs based on confidential data. Two dominant frameworks exist: statistical disclosure control (SDC), and more recent, differential privacy (DP). Despite framing differences, both SDC and DP share the same statistical problems at its core. For inference problems, we may either design optimal release mechanisms and associated estimators that satisfy bounds on disclosure risk, or we may adjust existing sanitized output to create new optimal estimators. Both problems rely on uncertainty quantification in evaluating risk and utility. In this review, we discuss the statistical foundations common to both SDC and DP, highlight major developments in SDP, and present exciting open research problems in private inference.

cs.CR↗

arXiv2022

Exact Privacy Guarantees for Markov Chain Implementations of the Exponential Mechanism with Artificial Atoms

Implementations of the exponential mechanism in differential privacy often require sampling from intractable distributions. When approximate procedures like Markov chain Monte Carlo (MCMC) are used, the end result incurs costs to both privacy and accuracy. Existing work has examined these effects asymptotically, but implementable finite sample results are needed in practice so that users can specify privacy budgets in advance and implement samplers with exact privacy guarantees. In this paper, we use tools from ergodic theory and perfect simulation to design exact finite runtime sampling algorithms for the exponential mechanism by introducing an intermediate modified target distribution using artificial atoms. We propose an additional modification of this sampling algorithm that maintains its $ε$-DP guarantee and has improved runtime at the cost of some utility. We then compare these methods in scenarios where we can explicitly calculate a $δ$ cost (as in $(ε, δ)$-DP) incurred when using standard MCMC techniques. Much as there is a well known trade-off between privacy and utility, we demonstrate that there is also a trade-off between privacy guarantees and runtime.

cs.CR↗

arXiv2021

Consistent Spectral Clustering of Network Block Models under Local Differential Privacy

The stochastic block model (SBM) and degree-corrected block model (DCBM) are network models often selected as the fundamental setting in which to analyze the theoretical properties of community detection methods. We consider the problem of spectral clustering of SBM and DCBM networks under a local form of edge differential privacy. Using a randomized response privacy mechanism called the edge-flip mechanism, we develop theoretical guarantees for differentially private community detection, demonstrating conditions under which this strong privacy guarantee can be upheld while achieving spectral clustering convergence rates that match the known rates without privacy. We prove the strongest theoretical results are achievable for dense networks (those with node degree linear in the number of nodes), while weak consistency is achievable under mild sparsity (node degree greater than $\sqrt{n}$). We empirically demonstrate our results on a number of network examples.

math.ST↗

arXiv2021

Perturbed M-Estimation: A Further Investigation of Robust Statistics for Differential Privacy

Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP procedure should be similar in terms of their probability distribution. While DP mechanisms are provably effective in protecting privacy, they often negatively impact the utility of the query responses, statistics and/or analyses that come as outputs from these mechanisms. To address this problem, we use ideas from the area of robust statistics which aims at reducing the influence of outlying observations on statistical inference. Based on the preliminary known links between differential privacy and robust statistics, we modify the objective perturbation mechanism by making use of a new bounded function and define a bounded M-Estimator with adequate statistical properties. The resulting privacy mechanism, named "Perturbed M-Estimation", shows important potential in terms of improved statistical utility of its outputs as suggested by some preliminary results. These results consequently support the need to further investigate the use of robust statistical tools for differential privacy.

cs.CR↗

arXiv2019

Differentially Private Inference for Binomial Data

We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests can be written in terms of linear constraints, and for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a 'Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. Our tests can also be stated as a post-processing of a random variable, whose distribution we coin ''Truncated-Uniform-Laplace'' (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact $p$-values, which are easily computed in terms of the Tulap random variable. Using the above techniques, we show that our tests can be applied to give uniformly most accurate one-sided confidence intervals and optimal confidence distributions. We also derive uniformly most powerful unbiased (UMPU) two-sided tests, which lead to uniformly most accurate unbiased (UMAU) two-sided confidence intervals. We show that our results can be applied to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that all our tests have exact type I error, and are more powerful than current techniques.

math.ST↗

arXiv2019

Formal Privacy for Functional Data with Gaussian Perturbations

Motivated by the rapid rise in statistical tools in Functional Data Analysis, we consider the Gaussian mechanism for achieving differential privacy with parameter estimates taking values in a, potentially infinite-dimensional, separable Banach space. Using classic results from probability theory, we show how densities over function spaces can be utilized to achieve the desired differential privacy bounds. This extends prior results of Hall et al (2013) to a much broader class of statistical estimates and summaries, including "path level" summaries, nonlinear functionals, and full function releases. By focusing on Banach spaces, we provide a deeper picture of the challenges for privacy with complex data, especially the role regularization plays in balancing utility and privacy. Using an application to penalized smoothing, we explicitly highlight this balance in the context of mean function estimation. Simulations and an application to diffusion tensor imaging are briefly presented, with extensive additions included in a supplement.

math.ST↗

arXiv2018

Differentially Private Uniformly Most Powerful Tests for Binomial Data

We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a `Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. Our tests can also be stated as a post-processing of a random variable, whose distribution we coin "Truncated-Uniform-Laplace" (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact p-values, which are easily computed in terms of the Tulap random variable. We show that our results also apply to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that our tests have exact type I error, and are more powerful than current techniques.

math.ST↗

arXiv2017

Providing Accurate Models across Private Partitioned Data: Secure Maximum Likelihood Estimation

This paper focuses on the privacy paradigm of providing access to researchers to remotely carry out analyses on sensitive data stored behind firewalls. We address the situation where the analysis demands data from multiple physically separate databases which cannot be combined. Motivating this problem are analyses using multiple data sources that currently are only possible through extension work creating a trusted user network. We develop and demonstrate a method for accurate calculation of the multivariate normal likelihood equation, for a set of parameters given the partitioned data, which can then be maximized to obtain estimates. These estimates are achieved without sharing any data or any true intermediate statistics of the data across firewalls. We show that under a certain set of assumptions our method for estimation across these partitions achieves identical results as estimation with the full data. Privacy is maintained by adding noise at each partition. This ensures each party receives noisy statistics, such that the noise cannot be removed until the last step to obtain a single value, the true total log-likelihood. Potential applications include all methods utilizing parameter estimation through maximizing the multivariate normal likelihood equation. We give detailed algorithms, along with available software, and both a real data example and simulations estimating structural equation models (SEMs) with partitioned data.

stat.ME↗

arXiv2017

General and specific utility measures for synthetic data

Data holders can produce synthetic versions of datasets when concerns about potential disclosure restrict the availability of the original records. This paper is concerned with methods to judge whether such synthetic data have a distribution that is comparable to that of the original data, what we will term general utility. We consider how general utility compares with specific utility, the similarity of results of analyses from the synthetic data and the original data. We adapt a previous general measure of data utility, the propensity score mean-squared-error (pMSE), to the specific case of synthetic data and derive its distribution for the case when the correct synthesis model is used to create the synthetic data. Our asymptotic results are confirmed by a simulation study. We also consider two specific utility measures, confidence interval overlap and standardized difference in summary statistics, which we compare with the general utility results. We present two examples examining this comparison of general and specific utility to real data syntheses and make recommendations for their use for evaluating synthetic data.

stat.AP↗

arXiv2016

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples.

stat.ME↗

arXiv2014

10 Simple Rules for the Care and Feeding of Scientific Data

This article offers a short guide to the steps scientists can take to ensure that their data and associated analyses continue to be of value and to be recognized. In just the past few years, hundreds of scholarly papers and reports have been written on questions of data sharing, data provenance, research reproducibility, licensing, attribution, privacy, and more, but our goal here is not to review that literature. Instead, we present a short guide intended for researchers who want to know why it is important to "care for and feed" data, with some practical advice on how to do that.

cs.DL↗