1. Space for things we might want to put at the bottom of each slide. Part 6: Open Problems 1 Marianne Winslett 1,3, Xiaokui Xiao 2, Yin Yang 3, Zhenjie Zhang 3, Gerome Miklau 4 1 University of Illinois at Urbana Champaign, USA 2 Nanyang Technological University, Singapore 3 Advanced Digital Sciences Center, Singapore 4 University of Massachusetts, Amherst, USA

2. Space for things we might want to put at the bottom of each slide. Practical usability & deployment Privacy parameters How should the data owner set privacy parameters to comply with regulation or internal policies? Efficiency & Scalability Executing some mechanisms is still expensive. Some adaptive mechanisms require an optimization step prior to execution. Dependence on the domain of the data is problematic. Automated mechanisms for novice users Allow novice users get the best utility for their task. 2

3. Space for things we might want to put at the bottom of each slide. Error bounds & optimal mechanisms For a given task T, what is the most accurate method of performing T under epsilon-DP? Current answers to this question only for limited T. When is a task or query set “hard”? Note: sensitivity is not a sufficient answer! For data-independent mechanisms: How can we measure the “hardness” of a task T or a set of queries, in terms of the accuracy achievable? For data-dependent mechanisms: How can we measure the “hardness” of a task T on a dataset D. 3

4. Space for things we might want to put at the bottom of each slide. Complex data models Classical DP is defined for a database consisting of a single relation. Naïve extensions to more complex data models do not always provide desirable privacy properties. E.g. for graph data: node DP vs. edge DP Extensions to complex schemas with key/foreign-key relationships not clear. 4

5. Space for things we might want to put at the bottom of each slide. Measuring utility Are we designing differentially private methods with the right utility measures in mind? A typical approach: Given target task T, decompose in query set Q. Develop method to compute Q with low “error” where “error” is max or avg squared error. For complex tasks, does this approach lead to the best utility? 5

6. Space for things we might want to put at the bottom of each slide. Inconsistency Perturbed DP output often violates constraints known to hold on the true data. Coping with inconsistency: Analysts often cannot use data that violates constraints known to hold on the true data. Remove inconsistency: find closest consistent output. Use exponential mechanism to select consistent output. Exploiting inconsistency When/why does removing inconsistency from noisy output improve utility? 6