Differentially-private histogram via the discrete Laplace mechanism

Adds independent discrete Laplace noise, \(P(y) \propto e^{-\epsilon |y|}\), to each bin count. Adding or removing one record changes exactly one bin by 1, so the whole histogram is pure \(\epsilon\)-DP under the add-or-remove-one relation. Noise and sampler as in dplapcnt().

Usage

dplaphist(counts, epsilon, budget = NULL)

Arguments

counts: Vector of non-negative whole-number bin counts.
epsilon: Privacy loss for the whole histogram (positive scalar).
budget: Optional dpbudget() to charge epsilon against.

Value

A numeric vector of whole numbers, the same length as counts (values may be negative; clip for display).

Examples

true <- c(120, 45, 8, 230, 17)
dplaphist(true, epsilon = 0.5)
#> [1] 121  44   3 232  21

# Post-process for display: clip negatives (costs no privacy).
pmax(0, dplaphist(true, epsilon = 1.0))
#> [1] 120  45   4 229  17

# Release a private histogram straight from tabulated data.
counts <- as.integer(table(complaint_sample$year))
dplaphist(counts, epsilon = 1.0)
#> [1] 24999     1