Ruminating on Differential Privacy

Differential privacy (DP) is a mathematical paradigm for protecting individuals' privacy in datasets. By allowing data to be analysed without disclosing sensitive information about any individual in the dataset, it can protects the privacy of individuals. Thus, it is a method of protecting the privacy of people in a dataset while maintaining the dataset's overall usefulness.

To protect privacy, the most easy option is anonymization, which removes identifying information. A person's name, for example, may be erased from a medical record. Unfortunately, anonymization is rarely enough to provide privacy because the remaining information might be uniquely identifiable. For example, given a person's gender, postal code, age, ethnicity, and height, it may be able to identify them uniquely even in a massive database.

The concept behind differential privacy is to introduce noise into the data in such a manner that it is hard to verify whether any specific individual's data was included in the dataset. This is accomplished by assigning a random value to each data point, which is chosen in such a manner that it has no effect on the overall statistics of the dataset but makes identifying individual data points more difficult.

The following paper by Apple gives a very good overview of how Apple uses Differential Privacy to gain insight into what many Apple users are doing, while helping to preserve the privacy of individual users - https://www.apple.com/privacy/docs/Differential_Privacy_Overview.pdf

Epsilon (ε) is a parameter in differential privacy that affects the amount of noise introduced to the data. A greater epsilon number adds more noise, which gives more privacy but affects the accuracy of the findings.

Here are some examples of epsilon values that might be used in different applications:

• Healthcare: Epsilon might be set to a small value, such as 0.01, to ensure that the privacy of patients is protected.
• Marketing: Epsilon might be set to a larger value, such as 1.0, to allow for more accurate results.
• Government: Epsilon might be set to a very large value, such as 100.0, to allow for the analysis of large datasets without compromising the privacy of individuals.

Thus, the epsilon value chosen represents a trade-off between privacy and accuracy. The lower the epsilon number, the more private the data will be, but the findings will be less accurate. The greater the epsilon number, the more accurate the findings will be, but the data will be less private.

A deep dive into these techniques is illustrated in this paper - https://www.cis.upenn.edu/~aaroth/Papers/privacybook.pdf