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This is a hard difficulty Machine Learning question, commonly asked during Onsite rounds at Amazon.

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This question is commonly asked for Machine Learning Engineer candidates at Amazon during technical interviews.

Explain Logistic Regression Fundamentals

Last updated: Mar 29, 2026

Quick 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

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

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