Problem 3 (50 Points): Implementing (Centralized) Differential Privacy

Using the same dataset (UCI Machine Learning Adult data) as in Assignment 1 to study differential privacy.

Laplace Mechanism: Query the average age of the records (each record is an individual) with age > 25.

Inject Laplacian noise to the query result (i.e., average age) to ensure -differential privacy with = 0.5, 1.0.

1. 6 Points. In case of = 0.5, generate 1,000 results for the query over the original dataset, and generate

1,000 results for the query over each of three other datasets: removing a record with the oldest age;

removing any record with age = 26; and removing any record with the youngest age.

2. 6 Points. In each of the above 4 groups of 1,000 results, round each number to two decimal places,

define a measure and utilize it to validate that each of the last 3 groups of results and the original

results are 0.5-indistinguishable.

3. 6 Points. Repeat all the above for = 1.0, utilize the above measure to validate that each of the last

3 groups of results and the original results are 1.0-indistinguishable.

4. 7 Points. Define another measure and utilize it to justify that the distortion of the 4,000 results for

= 1.0 is less than that of = 0.5.