# IHP “Nexus” Workshop on Privacy and Security: Day 3

I’m doggedly completing these notes because in a fit of ambition I actually started posts for each of the workshop days and now I feel like I need to finish it up. Day 3 was a day of differential privacy: Adam Smith, Cynthia Dwork, and Kamalika Chaudhuri.

Adam gave a tutorial on differential privacy that had a bit of a different flavor from tutorials I have seen before (and given). He started out by highlighting a taxonomy of potential attacks on released data to make a distinction between re-identification, reconstruction, membership, and correlation inferences before going into the definitions, composition theory, Bayesian interpretation, and so on. With the attacks, he focused a bit more on the reconstruction story. The algorithms view of things (as I get it) is to think of, say, an LP relaxation of a combinatorial problem: you solve the LP and round the solution to integers and prove that it’s either correct or close to correct. This has more connections to things we think about in information theory (e.g. compressed sensing) but the way of stating the problem was a bit different. He also described the Homer et al. attack on GWAS. The last part of his talk was on multiplicative weights and algorithms for learning distributions over the data domain, which I think got a bit hairy for the IT folks who hadn’t seen MW before. This made me wonder if these connections between mirror descent on the simplex, information projections, and other topics can be taught in a “first principles” way that doesn’t require you to have a lot of familiarity with one interpretation of the method before bridging to another.

Cynthia gave a talk on false discovery control and how to use differential privacy ideas in a version of the Benjamini-Hochberg BHq procedure for controlling the false discovery rate. A key primitive is the the report noisy argmax procedure, which gives the index of the argmax but not its value (which would entail a further privacy loss). Since most people are not familiar with FDR control, she spent a lot of her talk on that and so the full details of the private version were deferred to the paper. I covered FDR in my detection and estimation class partly from some of the extra attention it has received in the privacy workshops over the last few years.

Kamalika’s talk was on a model for privacy when data may be correlated between individuals. This involves using the Pufferfish model for privacy in which there is an explicit class of probability distribution on parameters and a set of explicit secrets which the algorithm wants to obfuscate: the differential privacy guarantee should hold for the output distribution of the mechanism conditioned on any valid data distribution and any pair of secrets. Since the class of data distributions is arbitrary, we can also consider joint distributions on individuals’ data — if the distribution class has some structure, then there might be a hope to efficiently produce an output of a function. She talked about using the $\ell_{\infty}$ Wasserstein distance to measure the sensitivity of a function, and that adding noise that scales with this sensitivity would guarantee privacy in the Pufferfish model. She then gave an example for Bayesian networks and Markov chains. As we discussed, it seems like for each dependence structure you need to come up with a sort of covering of the dependencies to add noise appropriately. This seems pretty challenging in general now, but maybe after a bit more work there will be a clearer “general” strategy to handle dependence along these lines.

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