Assume that your hypothesis function for linear regression is of the form f(x) = w0 + w1x and that the current values of w0 and w1 are 1 and 2 respectively. Further assume that you are using a learning rate (alpha) of 0.001

What is the new w0 value associated with the point (1, 12), after one gradient update?

Question

Assume that your hypothesis function for linear regression is of the form f(x) = w0 + w1x and that the current values of w0 and w1 are 1 and 2 respectively. Further assume that you are using a learning rate (alpha) of 0.001

What is the new w0 value associated with the point (1, 12), after one gradient update?

BlackTom AI · Accepted Answer

To update w0 after observing the point (x, y) = (1, 12) with the current weights w0 = 1 and w1 = 2, we first compute the current hypothesis output h for x = 1: h = w0 + w1*x = 1 + 2*1 = 3.
Next, we consider the typical mean-squared-error (MSE) loss with a 1/2 factor on a single data point: L = (1/2)(h - y)^2. The gradient of L with respect to w0 is ∂L/∂w0 = (h - y) because ∂h/∂w0 = 1.
Compute the error term: h - y = 3 - 12 = -9.
The gradient descent update for w0 with learning rate alpha = 0.001 is w0_new = w0 - alpha * (∂L/∂w0) = 1 - 0.001 * (-9) = 1 + 0.009 = 1.009.
Thus, after one gradient update using this common formulation, the new w0 value becomes 1.009.
Note: if a different loss formulation were used (for example, omitting the 1/2 factor in L or using a different gradient convention), the numeric update could differ. However, with the standard MSE/1/2 convention, this is the result.

类似问题

Which if the following answers are correct regarding "Gredient descent"?Select all the correct answers.

Why does the gradient descent algorithm not work for training a linear classifier?

Which parameter determines the size of the improvement step to take on each iteration of Gradient Descent?

Optimization algorithms like gradient descent are typically used in machine learning for which of the following (select all that apply):

The learning rate (α - alpha) as related to gradient descent is best described as:

Which of the following statements about gradient descent and learning rate is true?

Which statement is correct?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单