jax_privacy.matrix_factorization.toeplitz.loss

jax_privacy.matrix_factorization.toeplitz.loss(strategy_coef, n=None, reduction_fn=<function mean>)[source]

Error of C on prefix workload under single participation.

See Scaling up the Amplified Banded Matrix Factorization Mechanism for Differentially Private ML (https://arxiv.org/abs/2405.15913) for details.

Parameters:

strategy_coef (Array) – The nonzero coefficients of the Toeplitz matrix C used in the matrix mechanism with factorization A = B C. That is, coef are the leading nonzero entries of C[:, 0]. C is of size n x n; if len(coef) < n, the remaining coefficients are assumed to be zero. If len(coef) > n, then only the first n coefficients are used.
n (int | None) – Optional, the size of the matrix C (see coef above). If None, the size of the matrix is equal to the number of coefficients.
reduction_fn (Callable[[Array], Array]) – A function that converts per query squared errors to a scalar. Use jnp.mean to optimize mean-squared-error, jnp.max to optimize max squared error (which is equivalent toor lambda v: v[-1] in this case).

Return type:

Array

Returns:

The total squared error times sensitivity of the toeplitz C on the prefix-sum workload under single participation.