Differential Privacy Background Concepts

Consider a situation where several participants participate in a survey and provide details about themselves for analysis. However, the surveying organization is supposed to protect them by ensuring that their privacy is protected. There can be various ways to achieve that but the only mathematically proven method to do so is differential privacy.

Differential privacy is a mechanism that ensures that the participation of an individual does not make a significant impact on the outcome of the analysis. This means it protects the participation of the individual. So, analysts cannot ascertain whether an individual participated in the survey or not. This is rigor is ensured by the definition of differential privacy.

Definition

“A function f is said to be ε-DP if for all databases D1, D2 which differ by only one tuple and subsets y of Y we have

for ε>0”

  

Hence we can say that the ratio of probabilities will be less than ε.

The value of ε (the privacy parameter) is ideally close to 0 which implies that the ratio of probabilities is very near to 1. This logically means that both probabilities are equal but with some level of confidence.

There are various techniques to achieve differential privacy and they are broadly classified into the following four:

• Perturbation based techniques
• Granularity reduction methods
• Synthetic data generation
• Combination of above
  

 

Perturbation-based privacy protects by adding random noise to the data like Laplace noise and Gaussian noise.

Granularity-based privacy protects PII by decreasing the granularity of the data. Techniques like releasing only histogram, dimensionality reduction, sliding window moving average and micro-aggregation fall into this category.
Synthetic data techniques generate synthetic data by using a distribution function derived from data.

The above techniques have different advantages and drawbacks, so they are suitable for a different types of analysis tasks. So, to achieve multiple advantages many times different techniques are combined leading to a small/large framework for providing privacy.

Concluding Remarks: Due to the rigorous definition of differential privacy, it can be used in various scenarios to guarantee privacy mathematically with some statistical level of confidence.

References

1. Cynthia Dwork, Differential Privacy, Springer Berlin Heidelberg, http://dx.doi.org/10.1007/11787006_1
2. David Leoni, Non-interactive Differential Privacy: A Survey, Proceedings of the First International Workshop on Open Data, http://doi.acm.org/10.1145/2422604.2422611
3. A F Karr et al, A Framework for Evaluating the Utility of Data Altered to Protect Confidentiality, The American Statistician, http://dx.doi.org/10.1198/000313006X124640