Explain Logistic Regression Fundamentals
Overview
This question evaluates understanding of logistic regression fundamentals, covering probabilistic modeling, Bernoulli likelihood and logit-link derivation, loss and gradient characterization, calibration and miscalibration remedies, regularization trade-offs, feature scaling and interactions, class imbalance strategies, evaluation metrics for skewed data, coefficient interpretation, and common failure modes. It is commonly asked in technical interviews to assess both theoretical and practical competencies in supervised learning within the Machine Learning domain, with a level of abstraction spanning conceptual derivation and practical application of model behavior and evaluation.
Amazon
Sep 6, 2025, 12:00 AM
Machine Learning Engineer
Onsite
Machine Learning
0
0
Logistic Regression from First Principles
Assumptions and Notation
- Binary classification with labels y ∈ {0, 1} and features x ∈ R^d.
- Linear score z = wᵀx + b; probability p(x) = P(y=1 | x).
Tasks
- Derive logistic regression starting from a Bernoulli likelihood and the logit link.
- Derive the negative log-likelihood (log-loss) and gradients for w and b.
- Explain the logit link function and how decision thresholds relate to costs.
- Discuss probability calibration: when it works, how to measure it, and how to fix miscalibration.
- Compare L1 vs L2 regularization (optimization, sparsity, correlation, calibration).
- Explain effects of feature scaling and modeling interactions.
- Describe strategies for handling class imbalance.
- Choose appropriate evaluation metrics for imbalanced data.
- Interpret coefficients via odds and odds ratios.
- Identify common failure modes and guardrails.
Solution
Login required
Show