An Inversion Theorem for Buffered Linear Toeplitz (BLT) Matrices and Applications to Streaming Differential Privacy
Year: 2025
Type: preprint
Abstract: Buffered Linear Toeplitz (BLT) matrices are a family of parameterized lower-triangular matrices that play an important role in streaming differential privacy with correlated noise. Our main result is a BLT inversion theorem: the inverse of a BLT matrix is itself a BLT matrix with different parameters. We also present an efficient and differentiable $O(d^3)$ algorithm to compute the parameters of the inverse BLT matrix, where $d$ is the degree of the original BLT (typically $d < 10$). Our characterization enables direct optimization of BLT parameters for privacy mechanisms through automatic differentiation.
Source: arXiv (Cornell University)
Authors: McMahan, H. Brendan, Pillutla, Krishna
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417522623
Cites:
Cited by:
Related to: