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Hello.

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Welcome back.

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In this lesson we are going to write a new function known as the logistic regression model and this

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function is going to encapsulate the other functions we've written.

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We're going to pass our training image our test image the training and test labels as well as things

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like a lending rate a number of iterations and this function is going to train the entire model and

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then uh give us the m the the the resort for both the train inaccuracy and the test accuracy.

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So we're gonna construct such a function in this lesson.

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I'm gonna save this.

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I call this number seven and then I'll come down here to write a new function def or call this

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log write model in the first document is going to be the X train the next document is gonna be the Y

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train training labels and then the test data x test then the labels for the test y test and then number

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of iterations

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we can set a default at 1000 all those that you I want something else and then lending rate

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set a default to zero point four.

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Yeah I think we have enough.

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So we have this new function log rack Model X train y train okay.

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So yeah.

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Kristin let's see what we have from this end.

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Okay

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sorry go the.

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Okay I'm going to create some space here.

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I don't like this

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Okay so we start off by initializing a war weight and bias.

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So we call our weight and by his function our initialize function.

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So when I say WB the return is going to be stored in W and B and I'll call the function which is initialize

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zeros

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let's see over here

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and then what I want to do is say X strain does the dimension extra in does shape index zero.

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Right.

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Once that is done we're gonna perform the gradient descent by calling we'll learn our land function

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and we're going to store the remember our land function returns parameters gradient and cost.

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So I'm gonna come over here and see parameters s s s return value 1 or return variable 1 parameters.

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We're going to have gradient gonna have costs and the name of the function is learn and then we're going

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to pass the weight to bias as argument the training set the training label.

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Let's see what's left wage bias training set the training label a number of iterations Len Lenin rate.

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Okay.

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Number of iterations lending rate like this.

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Okay so after this we can we can retrieve the parameters W M B from the dictionary from the remember.

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Um this is Paramus is a dictionary we're going to have to be and be stored in it.

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Right.

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I'm gonna come down here because we need and for further computation.

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So I'll see w e course firearms all over here we stored it in a new word court parameters I'll copy

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this then I'll pass stop you in here and then B equals parameters I'll pass be here right.

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Once that is done we can call our predict function and then I'm gonna see a y y prediction

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y prediction for test set equals predict and then this takes the view B and then the data is X test

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the test set we're gonna do y prediction for train and then this we see it predict of course stop you.

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B X and then crane and then once we've done this we can go and print the resort

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we can print the um the test accuracy and the training accuracy during the process.

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So I'm gonna come down here.

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I simply say print and then I'll say test accuracy

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and I'm gonna do this or do this I'm gonna format it's a bit we're going to print the mean so I'll come

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here and say that's for months and then one hundred minus and Peter to me and then and Peter it's absolute

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value.

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We're going to basically subtract the m the y hat which is the predicted value from the expected value

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which is y and then yeah and then we multiply by one hundred and all of that subtracted from one hundred.

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I'm gonna say y prediction

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y prediction underscore

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test minus Y test and then I'm gonna come out here and then multiply this by one hundred

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mission.

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How many brackets do I have.

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I have three of them.

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Yeah.

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Right.

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So we're going to do the same for the M.

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Let's see what we have.

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Yeah we're gonna do the same for the test.

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Uh the training accuracy.

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This was for test accuracy.

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It would have to check for typos.

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We're not tested for a while.

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Okay so this is train

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and this is going to be this word here.

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It's going to be train and this as well.

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Right after we've done this we can return some information about our model such as the M that cost the

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Y prediction the D.

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Um yeah the train and test we can basically take some of the the results we get from this computation

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start in a dictionary to return so that we can have like the M what's the word we can have we can't

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have information about our model essentially.

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I don't want to say to them the parameters obviously we're going to sort of pretend the parameters as

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well but we can return things like the lending rate the number of iterations that y prediction test

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the Y training test et cetera.

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So when I have a dictionary here when I say d equals and then I'm going to return cost I'm gonna give

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it a label cost and this will return costs then I'm gonna say why predictions.

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We can analyze this later this is yeah why prediction test.

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And this of course is gonna be why prediction test

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and then we're going to have Y prediction Crane this is going to be my prediction train.

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We're going to have w.

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This would be w as well.

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Great to have B this would be B as well.

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Going to have a board lending rate

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this is going to be the lending rate.

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Then we're going to have a number of iterations

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it's gonna be a number of iterations.

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Right.

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Okay.

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So once we've done this we can return our dictionary

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rich and D.

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Like this.

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Okay so this is going to be our motto.

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This is going to create a model and B.

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And once it's done is gonna predict and then print out the test and create accuracies for us and we

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would have the characteristics of the model as well as its parameters stored in this dictionary court

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D which is going to be written for us so we can test it out by training our model um to try to model

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I'm going to come down here too.

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Yeah.

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I'm gonna come down here.

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So this is our pre processing code.

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Oh put comments here

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pre processing.

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And then decide here

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training.

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Okay.

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So I'm gonna say a d e course and then I'm simply going to call a function log rig model.

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I suspect we may have some typos because we've not tested for a while so kindly bear with me.

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And did um or parameters.

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The first one is train set.

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We're going to take train set X

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so before we can pass our data to our model we have to normalize it first.

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Remember we didn't perform normalization yet so to normalize we take the largest value in this set and

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then we divide each element by that value.

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So since it's an image the the largest value it's an 8 bit image.

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So the largest value is gonna be two hundred and fifty five.

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So we're going to divide everything by that.

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So I'm gonna create a new variable here or put a comment first.

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Normalize

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normalized data and I'm gonna create a verbal see a train set.

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X equals.

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I'm gonna take this this entire set and then I'm gonna divide by two forty five and then I'll see test

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set I'll do the same for test sets.

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We need not normalize the want D binary one in zero to tell us whether it's an E It's a cat or not a

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cat.

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We need not normalize the y values.

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Okay.

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So I see test set to set X and this equals test set to flatten divided by 245

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okay.

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So now over here in our functional model function we going to pass the um the normalized input.

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Yeah.

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So I'm gonna come here train set x.

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Copy this paste it Crane said why we have train set y somewhere.

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Copy this pasted over here to set x test.

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Copy this paste the Y here.

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Test set y.

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Paste this over here.

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And then a number of iterations

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I'm gonna set this to two thousand iterations Len and rate

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when I set it to zero point zero zero five.

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Yeah.

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So this is it.

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So let's inspect for typos before we build.

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Okay so um over here the first mission I saw is that we are using D.W. here but we've not extracted

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it from the dictionary.

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We have to remember it t w NDP were returned from the propagation function but they are kept in a dictionary.

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We need to pull them out before we can apply them here.

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So to do that we've got to sort of pull them out

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of CDW because the name of the dictionary is GRUNTS AND THEN WHAT I WANT IS D W and then I'm going to

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see a DP across the same dictionary Gratz

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DP like this.

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So now we've extracted them also in our predictive function here we would have to reshape the w the

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wait before we can compute the activation.

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So I'll come over here and see W equals w dot to reshape

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then I'm gonna say X top shape we're going to do index zero

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by one over here like this.

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Okay.

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Um lost track once more before we um would build.

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Um yeah.

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This function for instance.

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Yeah.

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The return here should not be in the for loop.

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So we've got to come out of the loop and then let's see.

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Okay.

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Looks good mm mm mm mm mm mm mm mm mm mm.

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This 0 function

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right.

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The error has to do with this the fourth argument in our function.

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Let's see the fourth argument is the whitest but.

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But over here I'm still send in train set to this word here should be test.

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So we have the crane and X the train and Y.

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The test x test y number of iterations we've set it to two thousand and then a lending rate of zero

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point zero five three pointers or five.

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Okay let's run and see if this works I'm gonna save right.

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It's working so.

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Okay.

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The error reduce and we've run this number of iterations so far.

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Right.

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And it s completes our test accuracy it says over here

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our test accuracy.

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Let me.

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Let me reshape this a bit for you

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our test accuracy is 70 percent and in the train accuracy is 99.

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So it is a bit of over fitting going on here.

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The um the difference between the two is too large but no problem.

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We're going to test with our own image and also we go into um later on we're going to develop a better

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neural network.

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Now we're using logistic regression is not the best way for doing this type of task later on we're going

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to see uh we went to first a four star have to lay a neural network and then we're going to increase

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with a deep neural network with multiple layers and then after that we're going to try using a convolution

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or neural network to see the results that we get.

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So this is the performance of our neural network.

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Right now we can increase the arm.

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We can learn to lend for a longer time.

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I'm going to increase number of iterations to three thousand and let's see what we get an improvement

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in the test accuracy.

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It's trained in

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okay it s it's become worse a problem.

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We're going to plot out plot out the graph and see the point at which it started moving from better

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to was.

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So now it's become 60 80 percent.

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Okay so I'm gonna go back to 2k right okay.

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Let's plot the um the cost us training and goes on let's see the graph.

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Let's see the performance um with this we can try to know at which point our neural network begun to

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um like the the part where we saw it move from 70 percent with two thousand iterations to 68 percent

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with two thousand words three thousand iterations we can see the graph and see that this number of iteration

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and gave us this amount of error and because of that we can decide on how much iteration we should apply

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to the model to give it the best that we can.

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Um if you don't understand all that I just said let's try it out.

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I'm gonna see costs cause I'm gonna squeeze this

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and then what I'm looking for is the dictionary we take in the cost from this and then we're going to

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plot this I'm gonna say P L T dot plot I want to plot cost I'm gonna add a bit of label to it I'm going

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to add a bit of labor to it Oh CPO t that's why label and the Y label is simply going to be cost and

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the X label is the iterations TLT dot X label

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and this is

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iterations

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and this is um per 50 50 yeah.

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So we said 50 we should print out the iterations we should collect it in 50 years let's see.

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We'll see about the

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we have to add to the piece of code to record the iteration every fiftieth iteration.

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I'm gonna come over here and I'll see if I modulo 50 equals zero

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then I want to record I seen costs cost this our list there and we're going to upend the cost.

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And this is what we're going to be plotting.

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Okay so iterations per 50.

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Right.

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So once that is done we can simply do peyote dot plot and then plotted or sure we can add a title to

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it if we want.

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Come over here CPO T dot title

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we can order lending rate

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now.

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We can simply fudge this from our dictionary or dictionary house lending rate.

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Yeah.

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We have lending rate the C.

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Yeah.

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This is lending rate so we can pull it from our dictionary so I can just see the string.

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What I want is a dictionary

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and in rate once that is done we can do POTUS show.

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Right.

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So let's see.

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So this will plot the um the iteration is this who plot the cost pie the cost by iteration graph the

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y axis is going to be the cost and the um the x axis is going to be the iteration so we should see the

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graph for actually as you see it starts from the top and begin to reduce as the US the model improves.

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Let's see what it looks like

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when I click here to run

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okay to learn in

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yeah says Well multiple let us know module called P L T.

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Yeah I suspect I know why this is

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yeah.

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Cos there's a typo here.

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I've got oh over here.

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Okay let's go

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Okay so that's where we go or what.

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Okay here's what we got.

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And then um I can just show this.

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So with essentially plotted this but every fifth yet iteration and I can see we started from the top

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here.

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This this is the cost from the top at iteration equals zero iteration of course to 250.

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This is this the cost that we had.

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And then as we continued continued reducing iteration of cost two thousand.

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We reduced to this.

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And this the best we could get for two thousand iterations.

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How about we see the um the three thousand iterations we tried earlier we showed the graph should tell

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us where things began to go wrong.

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I've changed a number of iterations to three thousand.

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Let's see what that looks like

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okay.

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This is sixty eight percent.

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Mm hmm.

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Let's try to zoom in and see if there's something we can see.

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Okay.

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It looks almost like the other one.

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Okay.

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I'm gonna close this.

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I'm gonna try five thousand iterations.

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See

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this what we have.

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What is.

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Yeah.

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Okay.

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5000 iteration gave us 70 percent again.

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Right.

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Okay.

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Enough experimenting with this so you can experiment with this you can change the number of iterations

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that lending rate and then see what you can do better than this.

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But given the little amount of data and given the type of neural network we using it.

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It's a quasi neural network I should say using logistic regression here is not a best tool to use but

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the performance is fine it's acceptable here.

295
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Okay so we can go on and on and test.

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We can test with which our own image if we want to.