Phase 4: Privacy-Preserving AI · 50 min · Python · numpy · scikit-learn

Differential Privacy — The Math of Privacy

Differential privacy is a promise: the output would be almost the same whether or not your data was in it.

Hiring signal: Differential privacy appears in 60%+ of RAI postings. Being able to explain epsilon (ε), the privacy budget, and the accuracy-privacy tradeoff with measured numbers is a distinguishing skill for RAI engineering candidates.

What you will learn

Explain the formal definition of differential privacy (ε-DP)
Explain the Laplace mechanism and how noise is calibrated to epsilon
Demonstrate the privacy-utility tradeoff with different epsilon values
Articulate the privacy budget concept and composition rules

The Problem

In Lesson 1, you saw that models leak training data through membership inference. The fix is to make the model's output insensitive to any single individual's data — so that an attacker can't tell whether a specific person was in the training set. This is what differential privacy (DP) provides, with a mathematical guarantee.

The Formal Definition

A randomized algorithm $M$ is $\varepsilon$-differentially private if, for all datasets $D_1$ and $D_2$ that differ in at most one element (one person's data), and for all possible outputs $S$:

$$P(M(D_1) \in S) \leq e^{\varepsilon} \times P(M(D_2) \in S)$$

In plain English: the probability of any output is at most $e^{\varepsilon}$ times higher with your data than without it. When $\varepsilon$ is small (close to 0), $e^{\varepsilon} \approx 1 + \varepsilon$, meaning the output barely changes whether or not your data is included.

Epsilon (ε)	Privacy Level	Typical Accuracy Impact	Use Case
0.1	Very strong	Significant (5-10% drop)	Medical research with strict privacy
0.5	Strong	Moderate (3-5% drop)	Census data, government statistics
1.0	Moderate	Small (1-3% drop)	Commercial ML with privacy requirements
3.0	Weak	Minimal (<1% drop)	Less sensitive applications
10+	Very weak	Negligible	Privacy in name only

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Laplace Mechanism, The Privacy Budget, Building the DP Demo, What's Next — plus a hands-on lab, quiz, and project artifact.

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