**Question:** When maximizing a function, the gradient at a given point will always point in _____.**Notes:** In machine learning, when we are trying to learn parameters to solve a problem, the direction of the gradient will be crucial to finding "good" parameters!**Options:** - any direction - the direction of steepest ascent - the direction away from the origin - the direction of steepest descent Given\( f(x) = wx + b \)compute the partial derivative for the following equation with respect to \( w \):\[\frac{\partial}{\partial w} \frac{1}{2} \left( f(x) - y \right)^2\]**Notes:** This function is what we call the *squared error* and is one of the most popular performance measures (measure of loss or how well the ML algorithm is doing) for regression problems. We will be computing its derivative (i.e., gradient) frequently! Further, partial derivatives are used to compute the derivative with respect to each variable in a function. Also recall that partial derivatives are used to compute a gradient which will be a crucial concept for how machine learning algorithms learn! While technically we are only taking the derivative with respect to a single variable here, it is important to start to get familiar with the notation \( \frac{\partial}{\partial w} \) which is used for partial derivatives.- \( x \)- \( (f(x) - y)x \)- \( 2(f(x) - y)x \)- \( (f(x) - y) \)

As per the guideline we have given solution for the first question. You can find the solution in step 2.Solution: question 1: correct option: the direction of steppest ascent The gradient vector will always point in the direction of the function's steepest increase. Additionally, its size will reveal the direction of the plane's slope. There are so many different slopes there! Each gradient vector component only provides the slope in one dimension. There is a component for each direction in the gradient of a multivariable function. Additionally, the gradient points in the direction of the greatest rise, much like the conventional derivative. The gradient vector is known to point in the direction with the greatest rise. A negative gradient vector, on the other hand, points in the direction with the greatest drop.

Engineering

Computer Engineering

When maximizing a function, the gradient at a given point will always point in Notes: In machine learning, when we are trying to learn parameters to solve a problem the direction of the gradient will be crucial to finding "good" parameters! any direction the direction of steppest ascent the direction away from the origin O the direction of steppest descent

When maximizing a function, the gradient at a given point will always point in Notes: In machine learning, when we are trying to learn parameters to solve a problem the direction of the gradient will be crucial to finding "good" parameters! any direction the direction of steppest ascent the direction away from the origin O the direction of steppest descent

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

Given

\( f(x) = wx + b \)

compute the partial derivative for the following equation with respect to \( w \):

\[
\frac{\partial}{\partial w} \frac{1}{2} \left( f(x) - y \right)^2
\]

**Notes:** This function is what we call the *squared error* and is one of the most popular performance measures (measure of loss or how well the ML algorithm is doing) for regression problems. We will be computing its derivative (i.e., gradient) frequently! Further, partial derivatives are used to compute the derivative with respect to each variable in a function. Also recall that partial derivatives are used to compute a gradient which will be a crucial concept for how machine learning algorithms learn! While technically we are only taking the derivative with respect to a single variable here, it is important to start to get familiar with the notation \( \frac{\partial}{\partial w} \) which is used for partial derivatives.

- \( x \)
- \( (f(x) - y)x \)
- \( 2(f(x) - y)x \)
- \( (f(x) - y) \)

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Bresenham's circle drawing technique requires a value of p, a decision parameter, to be determined. Bresenham's method for drawing a circle is detailed in this article.