Evaluate TPR/FPR, sigmoid, and activations
Company: Goldman Sachs
Role: Machine Learning Engineer
Category: Machine Learning
Difficulty: hard
Interview Round: Take-home Project
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.
Quick Answer: 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.