Gradient Descent.pdf - Gradient Descent Problem of Hiking...

This preview shows page 1 - 3 out of 8 pages.

Gradient Descent - Problem of Hiking Down a Mountain Udacity Have you ever climbed a mountain? I am sure you had to hike down at some point? Hiking down is a great exercise and it is going to help us understand gradient descent. Whats the goal when you are hiking down a mountain? - To have fun and to reach the bottom. Let’s focus on reaching the bottom for now. What is the red dot doing when it’s hiking down? It’s always going in the downward direction, until it hits the bottom. Let’s call our friend calculus and see what she has to say about this. Derivatives Before we hop in, let me remind you a little bit about derivatives. There are different ways to look at derivatives, two of the most common ones are Slope of the tangent line to the graph of the function Rate of change of the function 1
Image of page 1

Subscribe to view the full document.

Following are some of the common derivatives: d ( x 2 ) dx = 2 x d ( - 2 y 5 ) dy = - 10 y 4 d (5 - θ ) 2 = - 2(5 - θ ) (negative sign coming from - θ ) Sounds great! What if, we have more than one variable in our function? Well, we will talk about partial derivatives then! Let’s look at some examples: ∂x ( x 2 y 2 ) = 2 xy 2 ∂y ( - 2 y 5 + z 2 ) = - 10 y 4 ∂θ 2 (5 θ 1 + 2 θ 2 - 12 θ 3 ) = 2 ∂θ 2 (0 . 55 - (5 θ 1 + 2 θ 2 - 12 θ 3 )) = - 2 (Can you convince yourself where the - is coming from?)
Image of page 2
Image of page 3

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern