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Implement Batch Gradient Descent for Linear Regression | Amazon Interview Question

Implement Batch Gradient Descent for Linear Regression

Last updated: Mar 29, 2026

Quick Overview

This question evaluates a candidate's understanding of linear regression, mean squared error, and batch gradient descent, including vectorized prediction, gradient computation, and parameter updates within the Machine Learning domain.

Amazon

Jul 12, 2025, 6:59 PM

Data Scientist

Technical Screen

Machine Learning

Batch Gradient Descent for Linear Regression (MSE)

Scenario

You are building a linear regression model from scratch and will optimize its parameters using batch gradient descent.

Assume you have:

Feature matrix X \in R^{n \times d} (n samples, d features)
Target vector y \in R^{n}
A weight vector w \in R^{d} and a scalar bias b (intercept)

Task

Write Python-style pseudocode for batch gradient descent that minimizes mean squared error (MSE) for linear regression. Briefly explain what each step in your pseudocode does.

Your pseudocode should cover:

Initialization of parameters (w, b)
Vectorized prediction
Error and loss (MSE)
Gradient computation
Parameter updates
Looping and stopping conditions (e.g., max iterations, tolerance)

Solution

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