Apple·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Apple Data Scientist technical screen focused on deriving the logistic regression loss from scratch, including regularization. Pretty standard ML theory question but they wanted you to walk through every step out loud.

Questions Asked (1)

Write the logistic regression loss function for binary classification, including the per-example loss, the total loss over n examples, and optionally the L2-regularized objective.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew this cold but still fumbled the notation a bit under pressure.

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AI HintsAI Generated

Suggested Approach

Start by defining the per-example loss using the negative log-likelihood for binary cross-entropy, then sum or average over n examples to get the total loss. Optionally, add an L2 regularization term to the objective and explain its purpose. Keep the notation clean and consistent, and mention that logistic regression outputs probabilities via the sigmoid function.

Pro tip: Emphasize that the loss is convex, which guarantees convergence to the global minimum, and mention that L2 regularization helps prevent overfitting—this shows you understand both theory and practical trade-offs.

1. Define the model output

State that logistic regression predicts probability p = σ(w·x + b), where σ is the sigmoid function. This sets the context for the loss.

2. Write the per-example loss

For a single example (x, y) with y ∈ {0,1}, the loss is L(y, p) = -[y log(p) + (1-y) log(1-p)]. Explain that this is the negative log-likelihood.

3. Write the total loss over n examples

Sum the per-example losses: J(w,b) = -Σ_{i=1}^n [y_i log(p_i) + (1-y_i) log(1-p_i)]. Optionally, mention that averaging (dividing by n) is common for optimization.

4. Add L2 regularization (optional)

Include the L2 penalty term: J_reg(w,b) = J(w,b) + λ ||w||^2 (or λ/2 ||w||^2). Explain that λ controls regularization strength and helps prevent overfitting.

5. Summarize and discuss properties

Mention that the loss is convex and differentiable, and that regularization trades off bias and variance. This shows deeper understanding.

Key Points to Mention

Binary cross-entropy loss formula: -[y log(p) + (1-y) log(1-p)]
Sigmoid function for probability output: p = 1/(1 + e^{-(w·x + b)})
Total loss as sum or average over n examples
L2 regularization term: λ ||w||^2 (or λ/2 ||w||^2)
Convexity of the loss function and its implications for optimization
Role of regularization in preventing overfitting and controlling model complexity

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