jax_privacy.matrix_factorization.toeplitz.optimal_max_error_strategy_coefs

jax_privacy.matrix_factorization.toeplitz.optimal_max_error_strategy_coefs(n)

Returns the coefs of the optimal Toeplitz strategy matrix C for max error.

These coefficients were introduced by Fichtenberger, Henzinger, and Upadhyay in “Constant Matters: Fine-grained Error Bound on Differentially Private Continual Observation” (https://proceedings.mlr.press/v202/fichtenberger23a/fichtenberger23a.pdf, https://arxiv.org/pdf/2202.11205), and proved to be optimal for max error under single participations by Dvijotham, McMahan, Pillutla, Steinke, and Thakurta in “Efficient and Near-Optimal Noise Generation for Streaming Differential Privacy” (https://arxiv.org/abs/2404.16706).

Parameters:

n (int) – The number of coefficients to return.

Return type:

Array

Returns:

The coefficients of the lower-triangular Toeplitz matrix C that factorizes the prefix sum matrix A as A = C @ C.