Example of Bernoulli Naive Bayes

Let us discuss this Bernoulli Naive Bayes classifier with one example. So what we are assuming here, my all the variables are binary variables and represented by the two values, zero and one. So, this is the dataset where my dataset records are represented by the four different attributes, right? So we are ignoring here the name of the animal, right? So my four variables are: give birth, can fly, live in water, and have legs. And based on these four attribute values, right, features, we want to predict whether the given animal is a mammal or non-mammal. The given animal is a mammal or non-mammal. So in the dataset, there are total 20 records, and if you observe, if you observe, there are total seven records that are having the class label mammals and the remaining 13 records that are having the non-mammals. So my dataset contains here the four different attributes that represent the type of the animal—that is, whether that animal gives birth, can fly or live in water or has legs—and based on these feature values, we want to predict whether the given animal is a mammal or non-mammal, right? So here, if you observe, all the features are the binary features. So here, "give birth" is having only two values, yes and no; "can fly" has only two values, that is, no and yes; then "live in water" again, yes, no; and "have legs" here, yes, no. Right? So based on these binary variables, we want to predict. We want to build the model using a Bernoulli Naive Bayes classifier, and we want to predict the class of the new query here. So, assume here, assume here, in the dataset there are total 20 records, right? Total 20 records. And assume **a** is the attribute here; the solution represents **a** as the attribute, **m** represents the mammals class, and **n** represents the non-mammals class, right? So, as you know, the formula for the Bayes' theorem, right? Here, we use Bayes' theorem to predict the class of the new query for the given class. So, this is my query given here: give birth is yes, can fly yes. My new example or new animal, where we don't know the class label, is given here, right? So, these are the values of this new example or query point: yes, no, live in water yes, have legs no. So, what will be the class label? So, I’ll apply the Naive Bayes classifier, right, where we calculate the probability of every attribute for all the class labels in the dataset. So here, my class labels are mammals and non-mammals. First, we will calculate for the mammals for all the attributes, and then we will calculate for non-mammals for all the attributes. So here is the solution: out of seven records here (seven records are in the dataset, those are mammals), here you can see: one, two, three, four, five, six, and seven. Total seven records are there, those are mammals. The remaining thirteen are your non-mammals. So, out of seven, my six are there, they can give birth yes. Here, we want to compare with my query values, right? So, out of seven, six are there where give birth is yes. Then, in the second attribute, again we want "can fly" as no. So, out of seven records, six are there where my can fly value is no. Then, out of seven, two are there where living in water is yes. Out of seven, again, two are there where my have legs is no. So, if you find the product of this for the mammals class, we get this probability: 0.06. You know the data formats. We discussed the formula for calculating the probability of the query for the given class, right, as per Bayes' theorem, right? So, it is a product of these values. Then calculate for the non-mammals. So, out of 13, 1 is there where my birth is yes. Out of 13, 10 are there where can fly is no. Out of 13, 3 are there where living in water is yes, and out of 13, 4 are there where have legs is no. So, if you find this product, you get this probability: 0.00042. So, we multiply this probability with the individual probability of mammals class and the non-mammals class. So, mammals class into this value, you will get the probability of the query for the given class as mammals. Then, if you multiply this product (probability of non-mammals) with this product that we calculated here, right, we get this probability, right? So, here is where we are getting 0.0027. So, if you observe, student, if you observe, we check for the maximum probability. So, probability of attribute for the class level mammals into probability of mammals is greater than the probability of attributes for the non-mammals in the probability of non-mammals. So, because this probability is greater, my new query belongs to mammals. So, if you observe, the formula is the same as what we discussed in the previous sessions, right? Naive Bayes classifier only, my attributes are here the binary attributes.