Pattern Recognition Lecture 2: Regression II

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What is the purpose of the gradient descent algorithm in the context of linear regression?

To visualize the cost function of the linear regression model

To compare the performance of different linear regression models

To generate random data for the linear regression model

To optimize the parameters of the linear regression model (correct)

What does the cost function $J(\theta_0, \theta_1)$ represent in the context of linear regression?

The learning rate used in the gradient descent algorithm

The sum of the squared differences between the predicted and actual outputs (correct)

The difference between the predicted and actual outputs

The predicted output of the linear regression model

What is the purpose of the update step in the gradient descent algorithm for linear regression?

To update the learning rate used in the gradient descent algorithm

To update the input data for the linear regression model

To update the cost function of the linear regression model

To update the parameters of the linear regression model (correct)

What is the relationship between the cost function $J(\theta_0, \theta_1)$ and the parameters $\theta_0$ and $\theta_1$ in the context of linear regression?

The cost function is a quadratic function of the parameters Signup and view all the answers

What is the role of the learning rate in the gradient descent algorithm for linear regression?

To determine the step size in the update step of the algorithm Signup and view all the answers

What is the main difference between the cost function $J(\theta_0, \theta_1)$ and the parameters $\theta_0$ and $\theta_1$ in the context of linear regression?

The cost function is a function of the parameters, while the parameters are constants Signup and view all the answers

What happens if the learning rate α is too large in gradient descent?

Gradient descent may overshoot the minimum and fail to converge Signup and view all the answers

What is the effect of a small learning rate α on the convergence of gradient descent?

Gradient descent will converge slowly Signup and view all the answers

How can you choose a good value for the learning rate α in gradient descent?

Try values like 0.001, 0.01, 0.1, 1 Signup and view all the answers

What happens to the step size of gradient descent as it approaches a local minimum?

The step size decreases Signup and view all the answers

What is the main advantage of not decreasing the learning rate α over time in gradient descent?

It avoids overshooting the minimum Signup and view all the answers

What is the purpose of the Cost Function in linear regression?

To minimize the difference between predicted and actual values Signup and view all the answers

What does the parameter θ1 represent in linear regression?

Slope of the regression line Signup and view all the answers

What is the main goal of Gradient Descent in machine learning?

To minimize a function by iteratively moving towards its minimum Signup and view all the answers

What does 'α' represent in the Gradient Descent algorithm?

Learning rate or step size Signup and view all the answers

How are parameters updated in Gradient Descent?

Updating all parameters simultaneously at each iteration Signup and view all the answers

What happens if the learning rate 'α' in Gradient Descent is too small?

Gradient Descent may converge slowly Signup and view all the answers

Pattern Recognition Lecture 2: Regression II

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