https://journalprivacyconfidentiality.org/index.php/jpc <p>The <em>Journal of Privacy and Confidentiality</em>&nbsp;is an open-access multi-disciplinary journal whose purpose is to facilitate the coalescence of research methodologies and activities in the areas of privacy, confidentiality, and disclosure limitation. The JPC seeks to publish a wide range of research and review papers, not only from academia, but also from government (especially official statistical agencies) and industry, and to serve as a forum for exchange of views, discussion, and news.</p> Society for Privacy and Confidentiality Research, Philadelphia, PA, USA en-US Journal of Privacy and Confidentiality 2575-8527 <p>Copyright is retained by the authors. By submitting to this journal, the author(s) license the article under the <a href="https://creativecommons.org/licenses/by-nc-nd/4.0/">Creative Commons License – Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)</a>, unless choosing a more lenient license (for instance, public domain). For situations not allowed under CC BY-NC-ND, short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.</p> <p>Authors of articles published by the journal grant the journal the right to store the articles in its databases for an unlimited period of time and to distribute and reproduce the articles electronically.</p> https://journalprivacyconfidentiality.org/index.php/jpc/article/view/997 <p>The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Previously known edge differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-valued estimates (not vertex subset solutions) and do not use sublinear space. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge differentially private algorithms use sublinear space with respect to the number of edges in the graph. In addition, for the densest subgraph problem, we output edge differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets.</p> <p>We make novel use of sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space continual release setting. This includes algorithms for densest subgraph, maximum matching, and the first continual release k-core decomposition algorithm. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.</p> Alessandro Epasto Quanquan Liu Tamalika Mukherjee Felix Zhou Copyright (c) 2026 Alessandro Epasto, Quanquan Liu, Tamalika Mukherjee, Felix Zhou https://creativecommons.org/licenses/by-nc-nd/4.0 2026-08-31 2026-08-31 16 2 10.29012/jpc.997 https://journalprivacyconfidentiality.org/index.php/jpc/article/view/1004 <p>The Gaussian distribution is often used to model univariate, numerical data, even in contexts where individuals' data values are bounded, e.g., test scores and biological measurements. We consider Bayesian inference for the parameters of Gaussian models when (i) analysts seek a post-processing algorithm that takes noisy sufficient statistics as inputs and produces a posterior distribution of the parameters as output, and (ii) the privacy mechanism enforces bounds on individual data values as a condition for satisfying pure differential privacy. Our primary contributions focus on the specification of prior distributions for model parameters. Specifically, we illustrate that failing to account for the bounds on data values when using informative prior distributions can result in posterior inferences with undesirable properties. Further, we show theoretically that the usual default priors used in the nonprivate setting do not lead to proper posterior distributions, and we suggest a default prior distribution that does. We also show empirically that one can improve the performance of inferential procedures by incorporating the boundedness assumptions into the specification of prior distributions. We present methods for inferring about the mean and variance of a univariate Gaussian model and the coefficients and variance of a linear regression. As we discuss, the general strategies used for the Gaussian models can be adapted for other models when enforcing bounds on the data values to ensure differential privacy.</p> Zeki Kazan Jerome Reiter Copyright (c) 2026 Zeki Kazan, Jerome Reiter https://creativecommons.org/licenses/by-nc-nd/4.0 2026-08-31 2026-08-31 16 2 10.29012/jpc.1004