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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)
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:** 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
Transcribed Image Text:**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. - \( x \) - \( (f(x) - y)x \) - \( 2(f(x) - y)x \) - \( (f(x) - y) \)
Transcribed Image Text: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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