1.3. Prove that the LMS weight update rule described in this chapter performs a

Question

1.3. Prove that the LMS weight update rule described in this chapter performs a gradient descent to minimize the squared error. In particular, define the squared error E as in the text. Now calculate the derivative of E with respect to the weight wi, assuming that V(b) is a linear function as defined in the text. Gradient descent is achieved by updating each weight in proportion to - Therefore, you must show that the LMS training rule alters weights in this proportion for each training example it encounters. P with respect to the weighi

Explanation / Answer

SOLUTION:-

WE HAVE FOLLOWING CONDITION AS PER QUESTION:-
Vtr(b)=V^(discent(b))

V^(b)=w0+6i=1wixi

Calculation for Derivative of E=(Vtr(b)V^(b))2

Here it is very important to understand that We have used abstract board states to find a distinct set of values of each x with respect to V^ and Vtr

So, (Vtr(b)V^(b)) will be calculated as given below:-

wn(xnxn) due to
Vtr = w0 + wixi

Now, ( E / wi ) will gives the expression (Vtr(b)V^(b))

So now we can see that Gradient Descent is achieved by updating each weight in proportion to –( E / wi ) also we can say that LMS Training rule alters weights in this proportion for each training example it encounters.

(HENCE PROVED)

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