Randomness, Geometry, and Privacy
Each day your actions generate data, and that data is being used at some cost to your privacy. “Differentially private” algorithms seek to protect the privacy of individual data, often by injecting some randomness. Such mechanisms have been used by Apple, Google, Uber, and the US Census Bureau. I’ll describe how such algorithms work, and discuss recent efforts to quantify how much randomness is needed to guarantee privacy but still give accurate answers. Surprisingly, this analysis involves discrete geometry, and sets positioned in space in clever ways.