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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the primary goal of gradient-based methods?
π‘ Hint: Think about what 'optima' can mean in optimization.
Question 2
Easy
Define what a learning rate (Ξ±) is in the context of optimization.
π‘ Hint: Consider how it affects how quickly you might reach the optimum.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the learning rate (Ξ±) do in the Gradient Descent method?
- Controls the step size
- Determines final accuracy
- Sets the number of iterations
π‘ Hint: Think of it as the amount of progress you make in each update.
Question 2
True or False: Stochastic Gradient Descent uses the entire dataset to compute gradients.
- True
- False
π‘ Hint: Reflect on how SGD is defined.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a function f(x) = x^2 + 4x + 4. Use Gradient Descent with a learning rate of 0.1 to find the minimum starting from x = 0. Show your calculations through two iterations.
π‘ Hint: Calculate the gradient before each move and adjust accordingly.
Question 2
Use Newtonβs method to optimize the function f(x) = x^2 - 2x + 1. Confirm you find a minimum and demonstrate the Hessian's role.
π‘ Hint: Identify the critical points and compute second derivatives dynamically.
Challenge and get performance evaluation