So here we have E equals two Y minus Y hat.
We had, as we defined already in this example, this is a function of input, x mason over teta, which
is over parameter.
So let me just replace it Y minus instead of Y had I'm going to just write function of X based on our
teta, which is W and Bias's, which we can change is over teta.
Are looking for minimizing the error.
We want to minimize this error.
I'm just going to raise both sides by to you square that say equals do this one over Y minus F of X
base and overtime destroying teta.
So it would Shorthair Raceway to all the changes, all the things that we can change here is just over
parameter to the teta star is nothing but the arc of mean e a square.
This is a value of optimized parameters.
Let's take a look at this example one more time.
In this example, we have only one input, therefore we had one output, but sometimes we just don't
have only one input.
And there are more.
Let me just.
Should we I have I therefore the output would be lying if I am for this system.
Why I had so meaning for each data.
We need to optimize the error and then find the best way to optimize the whole system for all the data.
For example, in our patient and doctor system, let's say we have more than one patient, we have 1000
patients.
We should have I would be from one to two one thousand and have one thousand samples.
We have 1000 data.
Therefore we need to show it.
We need X of eye and Y off-line.
Let's back over there and just write in another rate.
I'm going to divide this part so I can continue here.
The e f i it can be patient number two.
Patient number fifty five equals two.
Why am I minus y.
I had I just goes from one to two and number of over samples here we are looking for minimizing the
error so mean one over and which is over the number of samples that we have.
And I can just simply take this off and, and I.
From one E score, I this is nothing but a mean square error, and this is not a specificly for artificial
neural network.
We can also use this one for Fosi systems.
This is called M.
S.
E or.
Mean.
A square error.
Later, when we are working with Matlab, we will see how important these days and we will see how can
we adjust the parameter to have these menas where error in the best way.
This one was overbuy and this one was over.
We had from the previous example.
So later on, Matlab, you will see if we have 1000 data.
There are different positions, but we need to minimize the errors.
We need to find a system to give the best option.
It means minimizing the error this distance.
It should be minimized.
We cannot really satisfy all the data for all the samples, but we can just minimize the error and see
which line can fit better.
Base number that we can already write a formula for the mean square error.
We can show it with one hour and some from I from one to end number of over samples that we have in
here inside a brocade.
We have five I minus function of X of I base no teta square.
So this is a general formula for calculating, miniskirted and as I mentioned, it's not only for artificial
neural network.
We can use these firmware for different systems such as Fawzy systems.
Whenever we are looking for optimization, we can just use this mini square error formula of our goal
in optimization is just to minimize the error.
Using this meeno square formula that we just calculated, we can simply achieve our goal.
In this example, teta would be our weight and bias's for our neural network.
If I is equal to y i minus y hat of I this we had.
If I use the output of our neural network and I can go from one to end goal, let's just replace this
plant wheat F.I. then we can see that with Difficulty Square because this is just the minimum of a square
after error.
We were looking for the methods of finding these coefficients of variations.
In next session we will talk about optimization methods to find these coefficients.