Rows are clipped to L2 norm C, the second-moment matrix formed, and
symmetric Gaussian noise added with sigma calibrated to
\(C^2/n\).
Usage
morie_dp_covariance(
X,
C = 1,
epsilon = 1,
delta = 1e-05,
seed = NULL,
project_psd = TRUE
)
Arguments
- X
data matrix, one row per record.
- C
L2 clipping norm for a row.
- epsilon, delta
privacy budget.
- seed
optional integer seed.
- project_psd
project the result onto the PSD cone.
Value
list with release, raw (pre-projection),
sigma, clipped_fraction,
n_negative_eigenvalues.
Details
Noise breaks positive semi-definiteness, which matters because a
covariance with negative eigenvalues is not a covariance and breaks
anything downstream. Projecting onto the PSD cone is pure
post-processing and therefore FREE – it costs no privacy at all.
Many negative eigenvalues is the diagnostic worth watching: it means
the budget is too small for this dimension, not that the projection
failed.
References
Dwork, C. et al. (2014). Analyze Gauss: optimal bounds
for privacy-preserving PCA. STOC, 11-20.
Examples
set.seed(1)
r <- morie_dp_covariance(matrix(rnorm(200), ncol = 2), C = 3, epsilon = 2)
dim(r$release)
#> [1] 2 2
