General Information

---

Project Description

We are gathering more and more digital information about people. As this data becomes more and more detailed, it’s easier and easier to “de-anonymize” or re-identify individuals from their data alone. However, for most applications all we want is population-level statistics.

To ensure individual privacy while at the same time utilize the richness of the data, our approach is to publish “synthetic” data: we learn patterns and correlations in the population and then generate fake individuals/records so that the population statistics are similar. The trick is to learn the patterns and correlations in a privacy-preserving way. The privacy model we will use is differential privacy, a new privacy framework that is rapidly gaining popularity.

The hope is to understand how much privacy is possible through this approach as well as to produce a toolkit that can be used by others to explore synthetic data generation. The work is a blend of probability, randomized algorithms, with some programming/simulation thrown in for good measure.

---

Weekly Log

Week 1:

• Met with Dr. Sarwate and the group.
• Explored literature on differential privacy, probabilistic graphical models and the CLThres algorithm.
• Gave the first presentation.

Week 2:

• Continued literature review from Week 1.
• Worked on the implementation of Chow-Liu algorithm in Python.
• Studied the connection between sensitivity and differential privacy.

Week 3:

• Implemented the simulation of Chow-Liu algorithm based on doubly symmetric binary source.
• Extended the scope of the code to process generic discrete random variables.
• Worked on the sensitivity of mutual information.

Week 4:

• Continued working on the sensitivity of mutual information.
• Selected and pre-processed data from UCI Machine Learning Repository.

Week 5:

• Proved the sensitivity of the entropy function.
• Used the sensitivity of the entropy function to give a loose upper bound for the sensitivity of the plug-in estimate of the mutual information function.
• Worked towards a better upper bound.

Week 6:

• Proved a tight upper bound for the sensitivity of the plug-in estimate of the mutual information function.
• Implemented the simulation of differentially private Chow-Liu algorithm in Python, based on the planted tree model.
• Prepared for the second presentation

Week 7:

• Evaluated our algorithm on the Adult dataset and recovered a robust tree structure.
• Gave the second presentation.

Week 8:

• Worked on the extension of differentially private graphical models to continuous data.
• Gave the sensitivities of sample mean, sample variance and sample covariance of continuous data.

Week 9:

• Worked on the sensitivity of continuous mutual information function based on the results from Week 8.
• Wrote up the final report.

---

Presentations

• First Presentation
• Second Presentation