Control options for synthetic score sampling — sampling

Creates a control list for generating synthetic score points from a score histogram. Sampling from a released private histogram is post-processing under the conditions below; it does not alter the histogram mechanism. plot.dp_pca() can also use these controls to sample an empirical reference histogram, which does not make that reference private.

Usage

sampling_control(
  method = "uniform",
  sample_size = NULL,
  bandwidth_scale = NULL
)

Arguments

method: Character vector specifying the sampling construction. "center" selects a histogram bin according to its histogram probability and samples around that bin center using Gaussian jitter. "uniform" selects a histogram bin according to its histogram probability, samples uniformly inside the selected bin, and then adds Gaussian jitter. The default is "uniform". Both methods can be requested with c("center", "uniform") in plot.dp_score(); plot.dp_pca() requires exactly one sampling method.
sample_size: Optional positive integer giving the synthetic sample size for each requested sampling construction. For plot.dp_score(), this is the number of synthetic score points, or the total across all groups for a grouped fit. For plot.dp_pca(), it is the size shared by score and biplot samples within each version; an explicit value also samples non-private reference histograms when comparison panels are requested. With NULL, private samples use the number of input observations and integrated non-private panels use observed scores. The default private sample size assumes that the input sample size is public. See dp_score() and dp_pca() for grouped sampling weights and the applicable privacy conditions.
bandwidth_scale: Gaussian smoothing scale. If NULL, method-specific defaults are used: 0.5 for "center" and 0.25 for "uniform". A single nonnegative number applies the same scale to all requested sampling methods. A named numeric vector can specify method-specific values, for example c(center = 0.5, uniform = 0.2); it must include every requested method. A scale of zero disables Gaussian jitter.

Value

A dppca_sampling_control list with components method, sample_size, and bandwidth_scale. The bandwidth values are resolved to a named numeric vector, while sample_size = NULL is resolved later by the plotting function.

Details

For released histogram probabilities p_k and cells B_k, first draw $$J \sim \mathrm{Categorical}(p_1,\ldots,p_m).$$ With method = "center", sample S^* = c_J + Z, where c_J is the selected cell center. With method = "uniform", sample U uniformly in B_J and use S^* = U + Z. In both cases Gaussian jitter has covariance $$\mathrm{Cov}(Z)=c^2\,\mathrm{diag}(\Delta_x^2,\Delta_y^2),$$ where c is bandwidth_scale and the deltas are bin widths.

Sampling uses only released histogram probabilities and bin geometry. With publicly chosen settings it is post-processing and requires no new privacy budget. Jitter can place points outside the frame; an all-zero histogram yields no sampled points and a warning.

Examples

sampling_control()
#> $method
#> [1] "uniform"
#> 
#> $sample_size
#> NULL
#> 
#> $bandwidth_scale
#> uniform 
#>    0.25 
#> 
#> attr(,"class")
#> [1] "dppca_sampling_control" "list"                  

sampling_control(
  method = c("center", "uniform"),
  sample_size = 1000,
  bandwidth_scale = c(center = 0.5, uniform = 0.2)
)
#> $method
#> [1] "center"  "uniform"
#> 
#> $sample_size
#> [1] 1000
#> 
#> $bandwidth_scale
#>  center uniform 
#>     0.5     0.2 
#> 
#> attr(,"class")
#> [1] "dppca_sampling_control" "list"