Implement Batch Gradient Descent for Linear Regression

Q: Implement Batch Gradient Descent for Linear Regression

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.

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Question

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)

Implement Batch Gradient Descent for Linear Regression

Batch Gradient Descent for Linear Regression (MSE)

Scenario

Task

Solution

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Implement Batch Gradient Descent for Linear Regression

Overview

Batch Gradient Descent for Linear Regression (MSE)

Scenario

Task

Solution

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