Which statement best describes the use of gradient descent in linear classification?

Question

BlackTom AI · Accepted Answer

To tackle the question, I’ll restate the prompt and each option to ensure clarity before analysis.
Question: Which statement best describes the use of gradient descent in linear classification?
Options:
1) It is used to maximize the objective function.
2) It is used to randomly initialize the parameters of the classification line.
3) It is used to minimize the error between predicted and actual class labels by adjusting the decision boundary parameters.

Analysis of each option:
Option 1: 'It is used to maximize the objective function.' In gradient descent, the typical goal is to minimize a loss or cost function, not maximize the objective. Maximization would correspond to gradient ascent, which is a different optimization method. Therefore, this description conflicts with the standard purpose of gradient descent in most linear classifiers, where we want to reduce error, not increase it.

Option 2: 'It is used to randomly initialize the parameters of the classification line.' While initialization is a step in training models, gradient descent itself is not about randomness of initialization. Random initialization is a separate preparatory step; gradient descent operates after initialization to adjust parameters iteratively. So, this option misattributes the core function of gradient descent.

Option 3: 'It is used to minimize the error between predicted and actual class labels by adjusting the decision boundary parameters.' This aligns with the core idea of gradient descent in linear classification. We define a loss function that measures prediction error (such as hinge loss for SVM or logistic loss for logistic regression), and gradient descent updates the model parameters (the weights that define the decision boundary) in the direction that reduces that loss, thereby improving classification accuracy. The phrase 'adjusting the decision boundary parameters' correctly describes updating the slope and intercept of the linear decision boundary.

Additional considerations: The phrase 'minimize the error between predicted and actual class labels' captures the typical objective in supervised learning with linear classifiers, where the training process seeks to align predictions with ground-truth labels by lowering the loss. The concept of gradient descent as an optimization routine is fundamentally about moving parameters to reduce error, not about maximizing an objective or performing initialization, which makes this option the accurate description among the provided choices.

Learning AI Through Visualization 4 Module 4 Quiz

Which statement best describes the use of gradient descent in linear classification?

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