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At each point, the change in z divided by the change in Y is given by the slope of this line
Let's now pick a different value for X, and keep X at this new value.
The change in z divided by the change in Y is what we refer to as the partial derivative of Z with respect to Y.
Every point on the graph has a value for the partial derivative of Z with respect to Y.
Here, green indicates a positive value, and red indicates a negative value.
Every point on the graph also has a value for the partial derivative of Z with respect to X.
Awesome song and introduction
Main ideas behind Gradient Descent
Gradient Descent optimization of a single variable, part 1
An important note about why we use Gradient Descent
Gradient Descent optimization of a single variable, part 2
Review of concepts covered so far
Gradient Descent optimization of two (or more) variables
A note about Loss Functions
Gradient Descent algorithm
Stochastic Gradient Descent
Introduction to the gradient in the context of a function graph
Definition and explanation of the gradient operator
Example of calculating the gradient for a function
Visualizing the gradient as a vector field
Interpretation of the gradient as the direction of steepest ascent
Another example of a gradient vector field
Explanation of the significance of the length of the gradient vector
Preview of the next video
Computing the gradient
Directional derivative intuition
Evaluating the gradient at a point
What the dot product represents
How to interpret the dot product
When is the dot product maximized?
The direction of steepest descent is the gradient itself
Interpreting gradient length
Directional derivative
Directional derivative in direction of gradient