Differential Privacy as a Causal Property
This work clarifies foundational concepts in differential privacy, potentially impacting its application in statistics and experimental design.
The paper tackles the challenge of characterizing differential privacy's guarantee without assuming data independence by introducing causal and associative views, showing that a simple causal characterization exists and resolves prior confusion.
We present associative and causal views of differential privacy. Under the associative view, the possibility of dependencies between data points precludes a simple statement of differential privacy's guarantee as conditioning upon a single changed data point. However, we show that a simple characterization of differential privacy as limiting the effect of a single data point does exist under the causal view, without independence assumptions about data points. We believe this characterization resolves disagreement and confusion in prior work about the consequences of differential privacy. The associative view needing assumptions boils down to the contrapositive of the maxim that correlation doesn't imply causation: differential privacy ensuring a lack of (strong) causation does not imply a lack of (strong) association. Our characterization also opens up the possibility of applying results from statistics, experimental design, and science about causation while studying differential privacy.