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Evaluate TPR/FPR, sigmoid, and activations

Goldman SachsMachine Learning Engineer · Online Assessment
HardMachine Learning EngineerOnline AssessmentMachine Learning

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This question evaluates competency in binary classification metrics (confusion matrices, TPR/FPR), basic neural network forward computation (sigmoid neuron z and output), and knowledge of activation function selection and pitfalls.

You have a 70-minute assessment with several ML-fundamentals multiple-choice questions. Answer the following (show calculations where applicable).

1) Confusion matrix vs. TPR/FPR

You are given four candidate confusion matrices (binary classification). For each matrix, rows are Actual and columns are Predicted.

Option A

  • TP=80, FN=20, FP=10, TN=90

Option B

  • TP=45, FN=5, FP=45, TN=5

Option C

  • TP=50, FN=50, FP=5, TN=95

Option D

  • TP=90, FN=10, FP=30, TN=70

Target requirements:

  • True Positive Rate (TPR / Recall) = 0.80
  • False Positive Rate (FPR) = 0.10

Question: Which option(s) satisfy both requirements?

2) Sigmoid neuron calculation

A single neuron computes: [ z = w^\top x + b ] [ \hat{y} = \sigma(z) = \frac{1}{1+e^{-z}} ] Given:

  • (w = [0.5, -1.0])
  • (x = [2.0, 1.0])
  • (b = 0)

Question: Compute (z) and (\hat{y}) (to 3 decimal places).

3) Activation functions

Consider the following activation functions: sigmoid, tanh, ReLU, Leaky ReLU, softmax.

Questions:

  1. Which activation is most commonly used in the output layer for multi-class single-label classification?
  2. Give two reasons ReLU-like activations are commonly used in hidden layers of deep networks.
  3. Name one common pitfall of sigmoid/tanh in deep hidden layers and why it happens.