Differentially Private Topological Data Analysis. (arXiv:2305.03609v1 [stat.ML])

This paper is the first to attempt differentially private (DP) topological
data analysis (TDA), producing near-optimal private persistence diagrams. We
analyze the sensitivity of persistence diagrams in terms of the bottleneck
distance, and we show that the commonly used \v{C}ech complex has sensitivity
that does not decrease as the sample size $n$ increases. This makes it
challenging for the persistence diagrams of \v{C}ech complexes to be
privatized. As an alternative, we show that the persistence diagram obtained by
the $L^1$-distance …

analysis data data analysis ech near persistence private producing size terms