{"id":20796,"date":"2025-02-03T11:20:42","date_gmt":"2025-02-03T11:20:42","guid":{"rendered":"https:\/\/dataforpublicgood.org.in\/?p=20796"},"modified":"2025-06-27T01:15:19","modified_gmt":"2025-06-27T01:15:19","slug":"optimal-tree-based-mechanisms-for-differentially-private-approximate-cdfs","status":"publish","type":"post","link":"https:\/\/dataforpublicgood.org.in\/cdpg\/data-privacy\/optimal-tree-based-mechanisms-for-differentially-private-approximate-cdfs\/","title":{"rendered":"Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20796\" class=\"elementor elementor-20796\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2dac990 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2dac990\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-51804ec\" data-id=\"51804ec\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5ac4424 elementor-widget elementor-widget-text-editor\" data-id=\"5ac4424\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-438085c elementor-widget elementor-widget-text-editor\" data-id=\"438085c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h1>Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs<\/h1>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ff9263c elementor-widget elementor-widget-text-editor\" data-id=\"ff9263c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"color: blue;\"><strong>Authors<\/strong>: V. A. Rameshwar, A. Tandon, and A. Sharma<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9514863 elementor-widget elementor-widget-text-editor\" data-id=\"9514863\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p>This paper considers the epsilon-differentially private (DP) release of an approximate cumulative distribution function (CDF) of the samples in a dataset. We assume that the true (approximate) CDF is obtained after lumping the data samples into a fixed number K of bins. In this work, we extend the well-known binary tree mechanism to the class of level-uniform tree-based mechanisms and identify epsilon-DP mechanisms that have a small l2-error. We identify optimal or close-to-optimal tree structures when either of the parameters, which are the branching factors or the privacy budgets at each tree level, are given, and when the algorithm designer is free to choose both sets of parameters. Interestingly, when we allow the branching factors to take on real values, under certain mild restrictions, the optimal level-uniform tree-based mechanism is obtained by choosing equal branching factors independent of K, and equal privacy budgets at all levels.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-85f0dee elementor-widget elementor-widget-text-editor\" data-id=\"85f0dee\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><strong>Journal\/Conference<\/strong><\/p><p>2025 International Conference on Communication Systems &amp; NETworkS (COMSNETS) &#8211; Cyber Security and Privacy Workshop<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-979fd33\" data-id=\"979fd33\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4ce5c30 elementor-widget elementor-widget-image\" data-id=\"4ce5c30\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"300\" src=\"https:\/\/dataforpublicgood.org.in\/cdpg\/wp-content\/uploads\/2025\/02\/Optimal-Tree-Based-Mechanisms-img.jpg\" class=\"attachment-full size-full\" alt=\"Optimal-Tree-Based-Mechanisms-img\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c27cce3 elementor-button-success elementor-align-center elementor-widget elementor-widget-button\" data-id=\"c27cce3\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/ieeexplore.ieee.org\/abstract\/document\/10885649\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-sm elementor-animation-shrink\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Know more<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3d308ba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3d308ba\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e1458bc\" data-id=\"e1458bc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5229c9c elementor-widget elementor-widget-html\" data-id=\"5229c9c\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\n    .post-style-3 .entry-header {\n        display: none;\n    }\n    \n    h1 {\n        font-size:28px !important;\n        text-transform: inherit !important;\n    }\n    \n<\/style>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs Authors: V. A. Rameshwar, A. Tandon, and A. Sharma This paper considers the epsilon-differentially private (DP) release of an approximate cumulative distribution function (CDF) of the samples in a dataset. We assume that the true (approximate) CDF is obtained after lumping the data samples into a fixed number K of bins. In &hellip;<\/p>\n","protected":false},"author":2,"featured_media":21060,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[92],"tags":[],"class_list":["post-20796","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-privacy"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs - Data for Public Good<\/title>\n<meta name=\"description\" content=\"This paper considers the epsilon-differentially private (DP) release of an approximate cumulative distribution function (CDF) of the samples in a dataset.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dataforpublicgood.org.in\/cdpg\/data-privacy\/optimal-tree-based-mechanisms-for-differentially-private-approximate-cdfs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs - 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