Hadamard response estimator for local differential privacy

Formula: phat(x) = 2(e^eps + 1)/(e^eps - 1) * (phat(C_x) - 1/2)

Usage

Ldphr(counts, epsilon, n = NULL)

Arguments

counts

See Usage.

epsilon

See Usage.

n

See Usage.

Value

List with p, p_set (the empirical p(C_x)), scale, epsilon, n, k.

References

Acharya, Sun and Zhang (2019), Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication, AISTATS, PMLR 89. Equations (8), (9) and (10). Verified against the paper.

Examples

Ldphr(counts = c(1, 2, 3, 4, 5, 6, 7, 8), epsilon = 5L)
#> $p
#> [1] -0.9572580 -0.9009487 -0.8446394 -0.7883301 -0.7320208 -0.6757115 -0.6194022
#> [8] -0.5630929
#> 
#> $p_set
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $scale
#> [1] 2.027135
#> 
#> $epsilon
#> [1] 5
#> 
#> $n
#> [1] 36
#> 
#> $k
#> [1] 8
#> 
#> $method
#> [1] "Hadamard response LDP distribution estimator"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"