RDP curve of composed sampled Gaussians, optionally converted to DP

Mirrors Python morie.fn.rdpcomp.

Usage

morie_rdpcomp(q, sigma, alpha = NULL, steps = 1, delta = NULL)

Arguments

q: Sampling rate.
sigma: Noise multiplier.
alpha: Integer orders; defaults to 2:64.
steps: Number of composed steps.
delta: When supplied, also convert via Mironov (2017) Proposition 3 and minimise over the orders.

Value

A list with the composed curve and, with delta, the converted epsilon and the best_alpha.

References

Mironov, Talwar & Zhang (2019), arXiv:1908.10530.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_rdpcomp(V, V)
#> $estimate
#> [1] 1
#> 
#> $rdp_epsilons
#>  [1]  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0  7.5  8.0
#> [16]  8.5  9.0  9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5
#> [61] 31.0 31.5 32.0
#> 
#> $alphas
#>  [1]  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
#> [26] 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
#> [51] 52 53 54 55 56 57 58 59 60 61 62 63 64
#> 
#> $q
#> [1] 1
#> 
#> $sigma
#> [1] 1
#> 
#> $steps
#> [1] 1
#> 
#> $method
#> [1] "RDP of the Sampled Gaussian Mechanism (Mironov, Talwar & Zhang 2019, Thm 4 / Case I); composition by Mironov (2017) Prop 1"
#>