Below is an interactive visualization that exemplifies the problem on 2-dimensional data. The input dataset is shown on the left. It is represented as a 2D histogram of counts over a uniform grid imposed over the domain.
On the right we show a noisy histogram representation of the output of a differentially private algorithm executed on the input. The output is also represented as a histogram of counts over a uniform grid. The number of bins in the output histogram matches that of the input. While the algorithms themselves may not actually generate a histogram, our visualization represents the histogram inferred from the noisy counts generated by the algorithm.
A rectangular range query can be specified on the input dataset by clicking and dragging anywhere on the input plot. The count within the range will be printed below. The range query can be dismissed by clicking anywhere on the input. Range queries on the input are mirrored on the algorithm output. The noisy count and the absolute error are printed below. The error of an algorithm is measured as the average error over a workload (or a set) of range queries.