Lec 2.3: Computational Graphs for Logistic Regression
Hi, In this lecture we will talk about computational graphs.
Before we begin, let us start with understanding what are derivatives.
A derivative is a fancy word for change in slope value. For example, if x changes with a certain value, what is the corresponding change of y? If x changes again with the same value, how much does y change again? We illustrate a graph with two examples to show how that might be different to establish an understanding of derivates. Derivates, in this case, are the change of height/width which gives the slope change.
Now let us hold on to this thought of what derivates are for a minute, and let us talk about computation graphs and tie both concepts together.
(Next slide)
(recap equations of logistic regression)
(Simplified y-hat to a for sake of writing down calculations)
Now let us take an example of input with 2 parameters. According to the logistic regression equation, this corresponds to 2 Wt's and a b.
A Computation graph basically organizes the computation of a specific function.
(Explanation of the flow of computational graph, forward and backward propagation provided.)
(Next slide)
To minimize the cost function, we want to know if we change the value of "a", how much will the loss function change? Let us derive that.
Next, if we change the value of "z" how much will the value of "a" be affected?
Next, if we change the value of "w1" how much will the value of "z" will be affected?
Taking all of the derivates into account, we have a chain rule of derivates that will help us calculate the gradient change.
(Next slide)
Now we can plug the output of this into the equations presented previously for the cost functions, but we show the loss function instead. There we see how tuning the values of w1, w2, and b1 effects the value of the y-hat which in turn we can use to compare how accurate our model is with the actual value "y"
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Chain rule derivation:
http://www.win-vector.com/blog/2011/0...
Alternative form:
https://www.wolframalpha.com/input/?i...
Derivative Calculator:
https://www.derivative-calculator.net/
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