---
res:
  bibo_abstract:
  - "We study the problem of maintaining a differentially private decaying sum under
    continual observation. We give a unifying framework and an efficient algorithm
    for this problem for any sufficiently smooth function. Our algorithm is the first
    differentially private algorithm that does not have a multiplicative error for
    polynomially decaying weights. Our algorithm improves on all prior works on differentially
    private decaying sums under continual observation and recovers exactly the additive
    error for the special case of continual counting from Henzinger et al. (SODA 2023)
    as a corollary.\r\nOur algorithm is a variant of the matrix mechanism whose error
    depends on the γ2 and γF norm of the underlying matrix. We give a constructive
    proof for an almost exact upper bound on the γ2 and γF norm and an almost tight
    lower bound on the γ2 norm for a large class of lower-triangular matrices. This
    is the first non-trivial lower bound for lower-triangular matrices whose non-zero
    entries are not all the same. It includes matrices for all continual decaying
    sums problems, resulting in an upper bound on the additive error of any differentially
    private decaying sums algorithm under continual observation.\r\nWe also explore
    some implications of our result in discrepancy theory and operator algebra. Given
    the importance of the γ2 norm in computer science and the extensive work in mathematics,
    we believe our result will have further applications.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Monika H
      foaf_name: Henzinger, Monika H
      foaf_surname: Henzinger
      foaf_workInfoHomepage: http://www.librecat.org/personId=540c9bbd-f2de-11ec-812d-d04a5be85630
    orcid: 0000-0002-5008-6530
  - foaf_Person:
      foaf_givenName: Jalaj
      foaf_name: Upadhyay, Jalaj
      foaf_surname: Upadhyay
  - foaf_Person:
      foaf_givenName: Sarvagya
      foaf_name: Upadhyay, Sarvagya
      foaf_surname: Upadhyay
  bibo_doi: 10.1137/1.9781611977912.38
  bibo_volume: 2024
  dct_date: 2024^xs_gYear
  dct_language: eng
  dct_publisher: Society for Industrial and Applied Mathematics@
  dct_title: A unifying framework for differentially private sums under continual
    observation@
...