Pattern Recognition Lecture 2: Regression II
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Questions and Answers

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?

<p>The cost function is a quadratic function of the parameters (C)</p> Signup and view all the answers

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

<p>To determine the step size in the update step of the algorithm (C)</p> 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?

<p>The cost function is a function of the parameters, while the parameters are constants (A)</p> Signup and view all the answers

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

<p>Gradient descent may overshoot the minimum and fail to converge (D)</p> Signup and view all the answers

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

<p>Gradient descent will converge slowly (C)</p> Signup and view all the answers

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

<p>Try values like 0.001, 0.01, 0.1, 1 (B)</p> Signup and view all the answers

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

<p>The step size decreases (A)</p> Signup and view all the answers

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

<p>It avoids overshooting the minimum (C)</p> Signup and view all the answers

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

<p>To minimize the difference between predicted and actual values (A)</p> Signup and view all the answers

What does the parameter θ1 represent in linear regression?

<p>Slope of the regression line (B)</p> Signup and view all the answers

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

<p>To minimize a function by iteratively moving towards its minimum (D)</p> Signup and view all the answers

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

<p>Learning rate or step size (C)</p> Signup and view all the answers

How are parameters updated in Gradient Descent?

<p>Updating all parameters simultaneously at each iteration (A)</p> Signup and view all the answers

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

<p>Gradient Descent may converge slowly (C)</p> Signup and view all the answers

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