Papers › Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little...
Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication
Jayadev Acharya, Ziteng Sun, Huanyu Zhang
We study the problem of estimating k-ary distributions under ε-local differential privacy. n samples are distributed across users who send privatized versions of their sample to a central server. All previously known sample optimal algorithms require linear (in k) communication from each user in the high privacy regime (ε=O(1)), and run in time that grows as n·k, which can be prohibitive for large domain size k. We propose Hadamard Response (HR}, a local privatization scheme that requires no shared randomness and is symmetric with respect to the users. Our scheme has order optimal sample complexity for all ε, a communication of at most logk+2 bits per user, and nearly linear running time of Õ(n + k). Our encoding and decoding are based on Hadamard matrices, and are simple to implement. The statistical performance relies on the coding theoretic aspects of Hadamard matrices, ie, the large Hamming distance between the rows. An efficient implementation of the algorithm using the Fast Walsh-Hadamard transform gives the computational gains. We compare our approach with Randomized Response (RR), RAPPOR, and subset-selection mechanisms (SS), both theoretically, and experimentally. For k=10000, our algorithm runs about 100x faster than SS, and RAPPOR.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections