提出可高效求逆的流式差分隐私矩阵，支持自动微分优化。
An Inversion Theorem for Buffered Linear Toeplitz (BLT) Matrices and Applications to Streaming Differential Privacy
- 证明BLT矩阵逆仍是BLT，参数可显式计算。
- 给出O(d³)的可微算法，d通常小于10。
- 适用于需参数优化的流式差分隐私系统。
缓冲线性托普利茨（Buffered Linear Toeplitz, BLT）矩阵是一类参数化的下三角矩阵，在具有相关噪声的流式差分隐私中起关键作用。本文核心成果为BLT反演定理：BLT矩阵的逆仍为BLT矩阵，但参数不同。我们进一步提出一种高效的、可微的O(d³)算法来计算逆矩阵的参数，其中d为原BLT矩阵的阶数（通常d < 10）。该表征使得可通过自动微分直接优化BLT参数以设计更优的隐私机制。
原文摘要 · Abstract (English)
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.
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