2. (a). Consider two types of food (Traditional and Western)...

2. (a). Consider two types of food (Traditional and Western) with four characteristics as below: • Sweet • Creamy • Spicy • Soup-based Y predictor features All the characteristics are categorical variables with either T(True) or F(False). Table 2.1 shows the training dataset of 80 records that showing the number of foods with their respective characteristics. Let's assume there are no missing values in this dataset. Table 2.1 Characteristics Food Type Sweet Creamy Spicy Soup-based Traditional 30/40 5/40 35/40 30/40 Western 20/40 35/40 5/40 10/40 Using Naïve Bayes algorithm, determine the type of the food with the characteristics of Sweet (True), Creamy (False), Spicy (False) and Soup-based (True). Show your workings. (8/100)

Transcript

00:01 All right, so for part a here, part of the trick for this problem is recognizing how to actually read the table.

00:07 So i am going to note that i've added an extra row down here at the bottom for totals along each one of the different traits.

00:15 That being said, for figuring out the probability of each class, i'll say p of b is probability of banana, we need to look at the total across one of these sort of trait column pairs.

00:31 So we can see that the total across each of the trait column pairs is going to be 500.

00:37 And we know that we have a grand total of, or we're explicitly told, that we have a grand total of 1 ,000 fruit.

00:45 So we can estimate the probability of banana as 0 .5, the probability of orange, which i'll call or, as 300 over 1 ,000, which would be 0 .3, and probability of ot, for other, as 100 plus 100, so 200 over 1 ,000, or 0 .2.

01:08 Then, to figure out the conditional probabilities, i'll just do the conditional probability of the positive for each trait, since once we know the positive, we automatically know the negation would just be one minus the probability of the positive.

01:23 So for instance, we'd have probability of long, i'll say that's event l, given b, long given banana, is going to be equal to 400 over 500, which would reduce to 4 over 5, or 0 .8.

01:43 Probability of sweet given banana.

01:48 Is going to be equal to 350 over 500, or 0 .7, the probability of yellow, given banana, is equal to 450 over 500 for a result of 0 .9.

02:06 Then, going through and computing the same values for the other classes of fruit, i'll note that, of course, all of those values were just coming from the fact that we know we have a total of 500 bananas, and it was just taking the number of banana and the positive, or the number in the, intersection of banana and the positive for each one of the traits.

02:26 That being said, moving on to the probability of long given orange, well, we can see there are zero long oranges.

02:36 So that would be simply zero.

02:38 Probability of sweet, given orange, is equal to 150 over 300, which is clearly 0 .5.

02:51 And then the probability of yellow given orange, interesting.

03:00 I guess they're defining yellow as being a valid option for an orange.

03:06 Interesting way of describing the color of an orange, but we can see that that's 300 over 300 for a result of one.

03:13 It's guaranteed to be yellow, apparently.

03:17 And then lastly, for other.

03:20 We're looking for probability of long given other, so l given o -t would be equal to 100 over 100, or pardon me, 100 over 100, that's 0 .5, then probability of suite, probability of s given o -t, will be equal to 150 over 200, which, of course, that would be 15 over 20, or reducing that, 0 .75...

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