TY - GEN
T1 - On Differentially Private Linear Algebra
AU - Kaplan, Haim
AU - Mansour, Yishay
AU - Moran, Shay
AU - Stemmer, Uri
AU - Tur, Nitzan
N1 - Publisher Copyright:
© 2025 Owner/Author.
PY - 2025/6/15
Y1 - 2025/6/15
N2 - We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As an application, we obtain efficient DP algorithms for learning halfspaces and affine subspaces. Our algorithms addressing equalities are strongly polynomial, whereas those addressing inequalities are weakly polynomial. Furthermore, this distinction is inevitable: no DP algorithm for linear programming can be strongly polynomial-time efficient.
AB - We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As an application, we obtain efficient DP algorithms for learning halfspaces and affine subspaces. Our algorithms addressing equalities are strongly polynomial, whereas those addressing inequalities are weakly polynomial. Furthermore, this distinction is inevitable: no DP algorithm for linear programming can be strongly polynomial-time efficient.
KW - differential privacy
KW - linear algebra
UR - https://www.scopus.com/pages/publications/105009832352
U2 - 10.1145/3717823.3718274
DO - 10.1145/3717823.3718274
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AN - SCOPUS:105009832352
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 2362
EP - 2373
BT - STOC 2025 - Proceedings of the 57th Annual ACM Symposium on Theory of Computing
A2 - Koucky, Michal
A2 - Bansal, Nikhil
PB - Association for Computing Machinery
T2 - 57th Annual ACM Symposium on Theory of Computing, STOC 2025
Y2 - 23 June 2025 through 27 June 2025
ER -