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Abstract:
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In this presentation I will discuss recent results and challenges in extending data privacy tools to handle complex high-dimensional statistical summaries from functional data analysis. Such data is becoming increasingly common and provides a rich source of information for scientific research. However, this is a double edged sword as there is a substantial risk of privacy disclosures; ensuring that a statistical summary is private in infinite dimensions can be surprisingly delicate. I will present recent work on Gaussian perturbations, elliptical perturbations, and exponential mechanisms with potentially infinite dimensional summaries. On a positive note, these tools represent several options with provable privacy and utility guarantees. However, each has some corresponding negative attributes, which are specific to infinite dimensional summaries.
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