jax_privacy.matrix_factorization.buffered_toeplitz.iteration_error
- jax_privacy.matrix_factorization.buffered_toeplitz.iteration_error(inv_blt, i)[source]
Computes the error on iteration i which is also the max error.
That is, for a Buffered Linear Toeplitz matrix, the max error from iteration 0 through i is achieved on iteration i, so this equivalently computes the max error for i+1 iterations.
Here “error” is the squared error introduced in the n-th iterate (partial sum) assuming unit-variance noise. This generally scales as O(n), and so optimization routines might normalize by an additional factor of n.
This implements https://arxiv.org/pdf/2404.16706 Lemma 5.4.
- Parameters:
inv_blt (
BufferedToeplitz) – The Buffered Linear Toeplitz operator where inv_blt.C() represents C^{-1} in the matrix factorization mechanism.i (
Union[Array,ndarray,bool,number]) – The iteration for which to compute error, 0-indexed. To compute the max error for an n iteration mechanism, one should thus pass i = n-1 to this function.
- Return type:
Array- Returns:
The squared-error (variance) on iteration iter.