[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86090-en":3,"doc-seo-86090-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86090,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Differentially Private Consistent Release of Counting Queries","The work investigates releasing counting-query outputs via a stochastic mechanism that is simultaneously consistent and (ε,δ)-differentially private. Consistency enforces that the released count remains within the feasible range of the query, while utility is evaluated through the worst-case probability of error. A closed-form expression yields the minimum achievable error probability and an explicit optimal mechanism. The analysis then generalizes to cascaded privacy with a fixed stochastic transformation, deriving conditions for zero utility loss and bounds on optimal performance, including a high-privacy result for uncoded M-ary PSK over AWGN.","Differentially Private Consistent Release of  \nCounting Queries  \nBorzoo Rassouli 1 and Morteza Varasteh2  \n1 Nokia Bell Labs, Stuttgart, Germany  \n2 University of Essex, Colchester, UK  \n[borzoo.rassouli@nokia-bell-labs.com](borzoo.rassouli@nokia-bell-labs.com), [m.varasteh@essex.ac.uk](m.varasteh@essex.ac.uk)  \narXiv :2607 . 10952v 1 [ cs .IT] 12 Jul 2026  \nAbstract—We study the problem of releasing counting-query outputs through a stochastic mechanism that is both consistent and (ϵ,δ)-differentially private. Consistency requires the released value to lie within the feasible range of the query, while utility is measured by the worst-case probability of error. We first derive a closed-form expression for the minimum achievable error probability and obtain an explicit optimal mechanism. By exploiting the active differential privacy constraints satisfied by this mechanism, we then characterize the entire class of optimal mechanisms via a propagation argument, identifying the structural properties shared by all optimizers.  \nWe next extend the framework to the setting in which the privacy mechanism is cascaded with an arbitrary fixed stochastic transformation representing a predetermined portion of the communication medium between the source and the destination. We first establish necessary and sufficient conditions under which this partial fixation of the medium incurs no loss in utility. We then derive upper and lower bounds on the optimal achievable performance based on convex mixing and spectral perturbation. Finally, we apply the theory to (M)-ary phase-shift keying (PSK) transmission over an additive white Gaussian noise (AWGN) channel and show that uncoded transmission is effectively optimal in the high-privacy regime.  \nI. INTRODUCTION  \nThe widespread deployment of data-driven services has intensified the need for mechanisms that simultaneously provide strong privacy guarantees and preserve utility. Differential privacy (DP) has emerged as a principled framework for this purpose, offering protection against inference attacks while enabling meaningful data analysis [1]–[3] . Its promise lies in providing strong, quantifiable protection for individuals while still allowing meaningful statistical or algorithmic utility. Over the past decade, differential privacy has been adopted across a broad spectrum of domains, including machine learning [4],[5], signal processing [6], [7], and communication systems and now plays a pivotal role in the design of privacy-preserving mechanisms.  \nA fundamental class of statistical releases consists of counting queries, whose output is an integer-valued statistic, such as the number of users possessing a given attribute [8],[9] . Although such aggregate statistics may appear to reveal little about individual records, numerous de-anonymization and reconstruction attacks have demonstrated that they can nevertheless leak sensitive information [10] .  \nOn another note, in many applications, it is not sufficient to release a private estimate of the count; the released value should also be consistent [11], meaning that it lies within the feasible range of counts. Consistency preserves the semantic  \nvalidity of the released statistic and eliminates the need for additional post-processing to project infeasible outputs back onto the admissible set.  \nThere is an extensive body of literature on the differentially private release of queries. In [12], the authors introduce the exponential mechanism to satisfy pure differential privacy for general query functions. The authors in [13] show that in the context of pure differential privacy, the geometric mechanism, i.e., adding noise with geometric distribution, is universally optimal for a broad class of loss functions in discrete settings. The authors in [14] show how adding Gaussian noise preserves approximate differential privacy for releasing infinite dimensional functions. Based on [13], the authors in [15] derive the optimal noise probability distr","cbCaiqopFKeshV0R","https://ap.wps.com/l/cbCaiqopFKeshV0R","pdf",1332649,3,1,13,"English","en",105,"# Introduction\n## Differential Privacy Motivation\n## Counting Queries and Privacy Risks\n## Consistency Requirement\n## Related Work\n## Problem Formulation and Objective\n## Two Settings and Main Results","[{\"question\":\"What does consistency mean for releasing counting queries in this framework?\",\"answer\":\"Consistency requires the released count to lie within the feasible range of the query, avoiding infeasible outputs and eliminating the need for extra projection post-processing.\"},{\"question\":\"How is utility measured when designing the differentially private mechanism?\",\"answer\":\"Utility is measured by the worst-case probability of error over all possible input values.\"},{\"question\":\"What is the contribution for the single-stage (idealized) mechanism design?\",\"answer\":\"The paper derives a closed-form minimum achievable error probability, provides an explicit canonical optimal mechanism, and characterizes the full class of optimal mechanisms using active differential privacy constraints and a propagation 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does consistency mean for releasing counting queries in this framework?","Question",{"text":75,"@type":76},"Consistency requires the released count to lie within the feasible range of the query, avoiding infeasible outputs and eliminating the need for extra projection post-processing.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is utility measured when designing the differentially private mechanism?",{"text":80,"@type":76},"Utility is measured by the worst-case probability of error over all possible input values.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the contribution for the single-stage (idealized) mechanism design?",{"text":84,"@type":76},"The paper derives a closed-form minimum achievable error probability, provides an explicit canonical optimal mechanism, and characterizes the full class of optimal mechanisms using active differential privacy constraints and a propagation 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