BARC Talk by Tamalika Mukherjee

How to Make Your Approximation Algorithm Private

We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Our results focus on algorithms A that output an approximation to a function f of the form (1−a)f(x)−k<=A(x)<=(1+a)f(x)+k, where 0<=a <1 is a parameter that can be "tuned" to small-enough values while incurring only a poly blowup in the running time/space. We show that such algorithms can be made DP without sacrificing accuracy, as long as the function f has small global sensitivity. We achieve these results by applying the smooth sensitivity framework developed by Nissim, Raskhodnikova, and Smith (STOC 2007).

Our framework naturally applies to transform non-private FPRAS (resp. FPTAS) algorithms into (ϵ,δ)-DP (resp. ϵ-DP) approximation algorithms. We apply our framework in the context of sublinear-time and sublinear-space algorithms, while preserving the nature of the algorithm in meaningful ranges of the parameters.

Our results include the first (to the best of our knowledge) (ϵ,δ)-edge DP sublinear-time algorithm for estimating the number of triangles, the number of connected components, and the weight of a MST of a graph, as well as a more efficient algorithm (while sacrificing pure DP in contrast to previous results) for estimating the average degree of a graph. In the area of streaming algorithms, our results include (ϵ,δ)-DP algorithms for estimating L_p-norms, distinct elements, and weighted MST for both insertion-only and turnstile streams.

Our transformation also provides a private version of the smooth histogram framework, which is commonly used for converting streaming algorithms into sliding window variants, and achieves a multiplicative approximation to many problems, such as estimating L_p-norms, distinct elements, and the length of the longest increasing subsequence.

Tamalika Mukherjee is a final-year Ph.D. candidate at Purdue University, advised by Jeremiah Blocki and Elena Grigorescu.

Her research interests lie broadly in differential privacy, sublinear algorithms and cryptography. Her dissertation studies the design of differentially private algorithms in resource-constrained settings, where the resource can be time, or space.

During her Ph.D. she has worked as a Research Intern at Analog Devices and a Student Researcher at Google Research. Tamalika's research is supported by the Bilsland Dissertation Fellowship from Purdue University.