An Inversion Theorem for Buffered Linear Toeplitz (BLT) Matrices and Applications to Streaming Differential Privacy

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.