Explain AUC, activations, ensembles, and imbalance

Q: Explain AUC, activations, ensembles, and imbalance

This is a Machine Learning interview question from Boston Consulting Group for Data Scientist roles. View the full question and solution on PracHub.

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Question

Machine Learning Metrics and Modeling Choices — Multi-part

You are given model scores and binary labels for a small dataset and asked to compute ROC AUC manually, then answer modeling and evaluation questions.

Given:

Scores s = [0.10, 0.40, 0.35, 0.80, 0.60]
Labels y = [0, 1, 0, 1, 0]

Answer all sub-questions precisely:

1) AUC / Ranking

Compute ROC AUC exactly via pairwise positive–negative comparisons (no libraries). Treat ties as 0.5 if any.
List the ROC points (FPR, TPR) by thresholding from highest score to lowest and compute the AUC by trapezoids; both methods should match.
With extreme class imbalance (1% positives), explain how you would interpret AUC vs Average Precision (AP) and which you would favor.

2) Output Activations and Losses

For each scenario, choose an output-layer activation and loss, and justify:

(a) Single-label multi-class (K = 7)
(b) Multi-label (K = 7)
(c) Bounded regression in [0, 1]
(d) Unbounded regression with outliers

Also discuss vanishing gradients for sigmoid/tanh and why leaky-ReLU or GELU might help in hidden layers.

3) MSE vs MAE

Explain optimization and robustness differences: gradients, influence of outliers, and mean vs median optimality.

4) Ensembles

Contrast bagging vs boosting in terms of bias/variance and when you’d choose each for noisy data.

5) Overfitting

Name two concrete, testable diagnostics (with plots/metrics) and two mitigation tactics that won’t leak validation information.