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Hello, everyone, and welcome to this new section in which we look at other methods of evaluating our

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model other than the binary accuracy which will be seen so far.

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So in this section we'll look at how to compute the true positives, false positives, true negatives,

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false negatives, the precision, the recall, the A under the curve, how to come up with conversion

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metrics like this.

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And finally, how to plot out an rosy curve like this one, which permits us select the threshold more

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efficiently.

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Don't forget to subscribe and hit the notification button so you never miss amazing content like this.

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Let's now look at other ways of evaluating our model other than the accuracy which we've seen so far.

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To better understand why working with all of the accuracy isn't always a great idea, we have to take

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into consideration the fact that our model on a test set has 94% accuracy.

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Now, this means that we have six out of 100 predictions, which are actually false.

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Now, what if I get to the hospital and I'm told that I don't have malaria when in fact I actually have

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this disease?

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So that said, the model predicts an infected and I actually have the parasite in my bloodstream.

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Now, this particular situation becomes very dangerous because the patient gets back home thinking he

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or she doesn't need any treatment, whereas that patient actually has this parasite.

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You see that even with a 94% accuracy, we wouldn't be able to save ourselves from such chaotic model

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predictions.

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Now, in another example, you have a situation where the actual is, let's put it out here.

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So in another example, we can have a situation where the actual is on parasitized.

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So actually you do not have this parasite, but the model predicts that you have the parasite.

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Now, in this case, although we have a wrong prediction, we have actually a less chaotic situation

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as compared to this previous case here since.

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At least actually you are uninfected.

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If we consider negative, that's this negative to be uninfected and positive to be passed to contain

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the parasite.

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That's P.

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So yeah, we consider we have positive and then we have negative.

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So here we have negative, uninfected and positive parasitized.

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Now if we let this, you will find that this first situation where actually we have the parasites and

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the model predicts on parasitized is known as a false negative.

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So here we have this false negative.

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And this is because the model predicts negative when it isn't actually negative.

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So since we have this wrong prediction for negative, we call it a false negative.

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And in this case, where we have the model predicting parasitized that is positive when it's actually

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negative, we call this a false positive.

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So, yeah, we have FP.

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And here we have f DN.

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Now, there are two other scenarios that is with c, n, and TP for the T, and we have the true negative,

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the true negatives and the CP, the true positives for the t n We have the model predicting negative

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when actually we are negative.

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That is, we have the model saying this is uninfected when actually it's uninfected.

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So that's a true negative and then for the true positive, the model predicts a positive that's parasitized

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when actually it's parasitized.

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So that's a true positive.

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Now hopefully you've understood the concepts of true negatives, true positives, false negatives and

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false positives.

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We could then summarize all this information in this matrix known as the confusion matrix and this confusion

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matrix.

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We have the true negatives, the number of true negatives here, the number of true positives, the

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number of false negatives and the number of false positives.

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This means that if we have a test set of, say, 2750 different data points and then we run this or

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we evaluate this with our model, we'll be able to get this number of true negatives, get this number

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of false negatives, number of true positives, number of false positives, and hence better evaluate

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this model.

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So if we take this example where we've evaluated our model on the test set and then this model A produces

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this coefficient matrix and this Model B produces other conversion matrix, where here we see we have

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four the true negatives and true passes.

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We have 1000, 1000 as 2000 correctly predicted data points.

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And then here we have 1002 thousand, 2000 correctly predicted the points.

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And then for this model A, we have 700 false positives and 50 false negatives, whereas for Model B

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we have 50 false positives and 700 false negatives.

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Recall we are defined negative to be uninfected and positive to be parasitized, and hence if we are

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to choose a model between A and B, we'll try to choose that model which minimizes the number of false

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negatives.

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So we are not saying that we shouldn't minimize the number of false positives because we have to try

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to minimize all the false predictions.

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But then since we have false negatives, we are telling a sick person that he or she isn't sick.

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This at least, is worse than telling a healthy person that he or she is sick.

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And so we'll try to prioritize the number of false negatives.

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And based on this prioritization, we are going to prefer Model A since we have the smaller number of

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false negatives.

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And so your would choose model A over model B.

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Now, as a quick note, you may decide to say negative is for parasitized and positive is for uninfected.

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It isn't a must that this must be tied together like this.

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But for clarity, purposes is better to look at it this way since saying you are tested negative means

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you are uninfected and test a positive means you are parasitized.

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Now you should also note that depending on the kind of problem you want to solve, in some cases you

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will want to prioritize minimizing the number of false positive over the number of false negatives.

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So this actually depends on the problem you're trying to solve.

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But in this case, we are prioritizing the number of false negatives.

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Now, based on what we've seen so far, we're going to introduce several new performance metrics and

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all this take up these different formulas.

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We could see right here we have the precision, which is the not the number of true positives divided

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by the number of true positives, plus the number of false positives recalled Trump.

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True positives divided by a number of true positives, plus number of false negatives.

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The accuracy, the number of true negatives, plus number of true positives, divided by a number of

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true negatives plus true positives plus false negatives plus false positives.

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So we'll stop for this first three for now.

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Now what do you notice?

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You'll notice that in this position, recall we have this true positive, true, positive.

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And here true positive, true, positive.

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What differentiates them is the fact that in the position we have false positive, the denominator and

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the recall, we have false negative in the denominator.

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This means that if the number of false negatives is high, that is, we have let's say we have a constant,

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a constant K divided by a high value.

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So constant divided by a high value, so constant, divided by high here we're going to have a low output.

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And so if we want to have a low recall, then we need to have a high number of false negatives.

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And if we want to have a low precision, then we need to have a high number of false positives.

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Now, in our case, we're trying to minimize the number of false negatives.

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And since we're trying to minimize the number of false negatives, it means that we're trying to maximize

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the recall since minimizing this denominator will entail maximizing this overall TP on TP plus F and

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and so here we're trying to prioritize the recall over the precision.

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Now, if you look at the accuracy, you'll notice that we have ten plus.

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TP And ten plus.

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TP Right here, ten plus.

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TP Ten plus.

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TP And we have F and plus FP.

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If you are keen enough, you should see that this accuracy doesn't give any priority for whether the

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false negatives or the false positives.

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It treats this two as the same.

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But as we've seen previously in the real world, in solving real world problems, many times we would

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have to prioritize.

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Hence, the accuracy may not always be the best metrics for our problem.

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In our case, we find that using the recall is even better than using the accuracy.

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As with the recall, we get to reduce or with the recall, we get to see whether our model does well

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at minimizing the number of false negatives.

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Now we also have this F one car two times the precision times.

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Recall the suppression of this recall divided by the precision, plus recall the specificity, the number

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of true negatives, divided by number of true negatives, plus number of false positives.

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And then we also have this RC plot right here, our assistance for receiver operating characteristics.

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Here we have the true positive rate and the false positive rate.

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The true positive rate is the number of true positive.

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Double number of true positive plus number.

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All false negatives, which happens to be the recall.

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And then the false positive rate is a number of false positives divided by a number of false positives,

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plus the number of true negatives, which if you look carefully, you'll find that it's equal one minus

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the specificity which has been defined right here.

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Before getting to understand this RC plot which we've put out here, let's recall this two models which

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we had described previously, that's Model A and Model B, where Model A had a smaller number of false

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negatives as compared to Model B.

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Now, if we pick out just as Model A, and then we are interested in reducing this or let's say we pick

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our Model B, suppose we pick our Model B, our interested in reducing this number of false negatives

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right here.

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Then one solution could be that of modifying the threshold.

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So if we have a threshold of 0.5, meaning that a both like we have this 0.5 below 0.5, we consider

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a negative above 0.5, we consider a positive that is parasitized and then below uninfected.

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Then what I could do here is reduce this threshold.

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So if I take this threshold to say a value of 0.2, let's take this here.

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So I've reduced this threshold now to 0.2.

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You'll see that for most of the predictions, our model is going to say that this is a parasitized output.

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Since now this threshold has been reduced.

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This means that if we have a model prediction of 0.3, which initially would have been uninfected,

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now this Model C is this as parasitized.

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And so this makes it now more difficult for our model to have false negatives, since our model now

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has this tendency of predicting that given an input image is parasitized.

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That said, we now look, we now need to look for a way that we could automate this process.

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That is, we want to be able to choose this threshold correctly or rightly, because if, let's say

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we take a threshold of say, 0.001, it means that anytime our model predicts less than 0.01, it's

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an uninfected and then greater than 0.01 is parasitized, then this will be very dangerous for the overall

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model performance as now most times we would have the model predicting that the input is parasitized.

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And so our M here is to pick this threshold such that this number of true positives and true negatives

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we've had right here don't get reduced.

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Now, the way we could look at this is now by using this Rosie plot with this RC plot where you actually

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have your is the different true positive rates and false positive rates you would have at a given threshold.

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So this means that a point picture is just a given threshold.

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Now let's suppose that the threshold 0.5 is about yours.

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So let's pick this.

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Let's suppose that this is 0.5.

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We could pick another threshold.

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Let's say this one is say 0.2 and so on and so forth.

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Let's say this one is 0.1.

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Now, we could have another model with this different Rosie plot, another one with this kind of Rosie

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plot.

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But note that overall, our aim is to ensure that this false positive rate is minimized and the true

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positive rate is maximized.

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So if we have an RC plot, which is like this so let's let's re draw this.

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If we have this kind of Rosie plot that is one that goes up straight like this and then comes this way,

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we have this right here.

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So if we have this kind of Rosie plot, then we will be able to pick out this threshold right here,

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0.6 We'll be able to pick this threshold because at this threshold for this threshold at this point,

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the true positive rate is at as high as value that is of one.

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And then the false positive rate is at its lowest possible value that is of zero.

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So yeah, we have one and then zero.

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So here we go, we have this and then we pick out this threshold.

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Now this value of x could be five, could be four or whatever.

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So we have zero point whatever value will lead us to this.

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Nonetheless, many times we wouldn't have this kind of plots, so we'll do it plus, which will look

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like this, this and so on and so forth.

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Now, once given a plot like this one, let's suppose we have a plot like this one, the Emir two axis

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of the right equation.

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If I want to make sure that my recall is always maximized, which is our case, we will try to ensure

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that we pick out this points around this.

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So we try to pick out this points to the top right here.

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Let's take some of this off.

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So as we're saying, if we want to maximize our recall, is that normal?

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That will pick out threshold values which will take us around this region because it's around this region

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that our recall is maximized.

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Let's do this.

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So you could see that clear.

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Okay.

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Now, the problem with picking a point around this is that when you pick a point around this, the false

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positive rates is increased.

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So you need to find that balance between this false positive rate and true positive rate.

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So it would be much logical to pick a point around this right here so we could pick around this region

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instead.

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Of this previous region right here.

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Now, you can see that in this region.

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Let's say we pick this point.

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We pick this point.

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Your false positive rate now is smaller.

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While your true positive rate is or your recall is maximized, though it isn't the best possible recall

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we could have.

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But trying to focus on getting that recall of one will lead you into trouble.

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Since getting a recall of one in this case will increase our false positive rate.

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And then if we're dealing with a problem where we're trying to maximize the precision, then in that

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case, we want to ensure that this false positive rate is minimized.

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And so in this kind of problems, we want to pick a point around this.

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So you see, we want to pick this kind of value since our lists are false, positive rate is minimized.

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But then if you want to go and pick a point around this year, you would have a false positive rate

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of zero.

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But doing this will get you this into trouble because, yeah, you're going to have a true positive

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rate, which is very small.

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And so you need to get that balance.

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Now, if you have a problem where it doesn't really matter that it's you, I've been trying to prioritize

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the position or the recall and working with accuracy just fine, then you could pick out this point

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right here.

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So this is when you are having or you don't have to prioritize on any areas when you're trying to prioritize

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on the recall and yours is when you're trying to prioritize on the precision.

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But I just want grittiness with this tool that is the rosy plot.

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We are able to pick out this point and then automatically get that threshold we need to work with.

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And so when doing predictions, we will not or we may not use 0.5, but we're going to use a certain

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threshold which will suit these objectives.

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We've set initially.

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Now we'll now move to the area under the curve for the area under the curve.

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We generally use this when we compare comparing to models.

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Here we have this model, let's call it model A, It's not it's not actually this Model A is a different

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model A let's call this model alpha.

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And then we have this auto model which we shall call model beta.

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So we have model alpha and model beta.

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It's clear that model beta is better because it gives us better options.

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Now you'll see that if I find myself here, I get it better.

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True positive rate false positive rate balance as compared to when I find myself at this position.

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And so if we are comparing this to models, we could make use of the area under the curve by calculating

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this area covered here.

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So let's bound this.

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And then for Alpha, we have this a area under the curve popularly known as a you see a small U and

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then see which will give us this.

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And then for beta, we're going to have this area under the curve now which covers this area, plus

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this extra area right here.

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And so in general, if we have two models and then we want to compare them, then we could use this

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area under the curve, since it shows us how much freedom we have in playing around with this thresholds.

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We now get back to the code and see how we're going to implement this new matrix we've just talked about.

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So right here we have Matrix and then we have the false positives, we have the false negatives, we

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have the true positives, we have the true negatives, we have the precision, we have the recall,

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we have the AUC, AUC.

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And then since we're dealing with a binary classification problem here, we have binary accuracy, we

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run that, that's fine.

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And then right here, instead of having this matrix, we define this matrix list, which will contain

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the different matrix which we've just talked of.

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So we have the true positive false positive right up to the AUC.

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Let's run this compile and then feed our model.

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You'll see that as we train we have the true positives, false positives, true negatives, false negatives,

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accuracy, precision recall, and AUC scores which are being given to us.

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As you could see, the other results we obtained, we're going to go ahead to evaluate our model.

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So let's get to the model evaluation.

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We run this test data and then we have our model evaluated.

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There we go.

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Our model has been evaluated.

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As you could see, we have this.

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Last 0.35.

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Number of true positives 1323.

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Number of false positives.

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Number of true negatives.

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False negatives.

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Accuracy.

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Precision recall and AUC.

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So that's what we have for this model.