{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-differential-privacy-mechanism-design-under","title":"A Differential Privacy Mechanism Design Under Matrix-Valued Query","arxiv_id":"1802.10077","date":"2018-02-26","proceeding":null,"authors":["Thee Chanyaswad","Alex Dytso","H. Vincent Poor","Prateek Mittal"],"abstract":"Traditionally, differential privacy mechanism design has been tailored for a\nscalar-valued query function. Although many mechanisms such as the Laplace and\nGaussian mechanisms can be extended to a matrix-valued query function by adding\ni.i.d. noise to each element of the matrix, this method is often sub-optimal as\nit forfeits an opportunity to exploit the structural characteristics typically\nassociated with matrix analysis. In this work, we consider the design of\ndifferential privacy mechanism specifically for a matrix-valued query function.\nThe proposed solution is to utilize a matrix-variate noise, as opposed to the\ntraditional scalar-valued noise. Particularly, we propose a novel differential\nprivacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which\nadds a matrix-valued noise drawn from a matrix-variate Gaussian distribution.\nWe prove that the MVG mechanism preserves $(\\epsilon,\\delta)$-differential\nprivacy, and show that it allows the structural characteristics of the\nmatrix-valued query function to naturally be exploited. Furthermore, due to the\nmulti-dimensional nature of the MVG mechanism and the matrix-valued query, we\nintroduce the concept of directional noise, which can be utilized to mitigate\nthe impact the noise has on the utility of the query. Finally, we demonstrate\nthe performance of the MVG mechanism and the advantages of directional noise\nusing three matrix-valued queries on three privacy-sensitive datasets. We find\nthat the MVG mechanism notably outperforms four previous state-of-the-art\napproaches, and provides comparable utility to the non-private baseline. Our\nwork thus presents a promising prospect for both future research and\nimplementation of differential privacy for matrix-valued query functions.","url_abs":"http://arxiv.org/abs/1802.10077v1","url_pdf":"http://arxiv.org/pdf/1802.10077v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-differential-privacy-mechanism-design-under","repo_url":"https://github.com/inspire-group/MVG-Mechansim","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}