Differential Privacy

2.

Mathematical Foundations of Differential Privacy

2.1.

Neighboring Databases

2.1.1.

Unbounded Model

2.1.1.1.

Adding or Removing a Record

2.1.1.2.

Definition and Use Cases

2.1.1.3.

Sensitivity Implications

2.1.2.

2.1.2.1.

Changing a Record

2.1.2.2.

Definition and Use Cases

2.1.2.3.

Sensitivity Implications

2.1.3.

Relationship Between Models

2.1.3.1.

When to Use Each Model

2.1.3.2.

Privacy Implications

2.2.

The Formal Definition of Differential Privacy

2.2.1.

Pure Differential Privacy

2.2.1.1.

Formal Statement of ε-DP

2.2.1.2.

Multiplicative Privacy Guarantee

2.2.1.3.

Properties and Implications

2.2.2.

Approximate Differential Privacy

2.2.2.1.

Formal Statement of (ε, δ)-DP

2.2.2.2.

The Privacy Loss Parameter Epsilon

2.2.2.2.1.

Role of Epsilon in Bounding Privacy Loss

2.2.2.2.2.

Interpreting Epsilon Values

2.2.2.2.3.

Choosing Epsilon in Practice

2.2.2.3.

The Probability of Failure Delta

2.2.2.3.1.

Role of Delta in Relaxing the Guarantee

2.2.2.3.2.

Approximate vs Pure DP Trade-offs

2.2.2.3.3.

Choosing Delta in Practice

2.3.

Privacy Loss Random Variable

2.3.1.

Definition and Interpretation

2.3.2.

Use in Privacy Analysis

2.3.3.

Connection to Information Theory

2.4.

Sensitivity Analysis

2.4.1.

Global Sensitivity

2.4.1.1.

2.4.1.1.1.

Definition and Calculation

2.4.1.1.2.

Examples of L1-Sensitivity

2.4.1.1.3.

Geometric Interpretation

2.4.1.2.

2.4.1.2.1.

Definition and Calculation

2.4.1.2.2.

Examples of L2-Sensitivity

2.4.1.2.3.

Geometric Interpretation

2.4.2.

Local Sensitivity

2.4.2.1.

Definition and Motivation

2.4.2.2.

Smooth Sensitivity

2.4.2.3.

Sample and Aggregate Framework

2.4.3.

Sensitivity of Common Functions

2.4.3.1.

Counting Queries

2.4.3.2.

2.4.3.3.

Maximum and Minimum

2.4.3.4.

Histogram Queries

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1. Foundations of Data Privacy

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3. Core Mechanisms for Achieving Differential Privacy