4. Advanced Composition Theorems8:
Advanced composition theorems are mathematical tools that provide more accurate and tighter privacy bounds when combining multiple queries or computations in differential privacy. They are designed to address some of the limitations of basic composition techniques and offer more precise quantification of cumulative privacy loss. Two prominent examples of advanced composition theorems are the Moments Accountant and Rényi Differential Privacy.
1. Moments Accountant: The Moments Accountant is a technique used to analyze the privacy loss that accumulates over a sequence of queries. It takes into account the higher moments of the privacy loss distribution, allowing for tighter and more accurate privacy bounds compared to traditional methods. By considering a broader view of the privacy loss distribution, the Moments Accountant provides a more refined estimation of the cumulative privacy guarantee.
2. Rényi Differential Privacy: Rényi Differential Privacy is an extension of the traditional ε-differential privacy concept. It introduces a parameter α that allows for varying levels of privacy protection. When α approaches infinity, Rényi Differential Privacy converges to pure ε-differential privacy. For smaller values of α, Rényi privacy provides tighter privacy bounds compared to basic composition techniques, particularly in settings with a large number of queries.