12 .Naïve Bayesian Classification Numerical Solved Example in Machine Learning Vidya Mahesh Huddar

Welcome back. In this video, I will discuss how to apply new base algorithm for the given data set. And here we need to classify the new example into one of the class. This is a example number 12. Link for the previous examples are given in the description below. This is a given data set. In this we have three attributes, color, type, and origin. Stolen is a target class. For this data set, we need to apply new base classification algorithm and we need to predict whether the new example that is color is equal to red, type is equal to SUV, origin is equal to domestic is classified as either yes or no. Base theorem is the foundation of a new base classification and is expressed as probability of C given X which is equal to probability of C multiplied with probability of X given C divided by probability of X. Where probability of C given X is a posterior probability. Probability of C is nothing but a prior probability. Probability of X given C is a conditional probability. Here we need to calculate the posterior probability for the class yes and no. That is in the first case we need to replace uh C by yes and in the second case we need to replace C by no. So once you replace C by yes, uh the posterior probability will be probability of yes given X which is nearly equal to probability of yes. Here the probability of In this case, we need to replace X by the new example attribute values. That is a red, SUV, and domestic. So which is equal to probability of red given yes multiplied with probability of SUV given yes, multiplied with the probability of domestic given yes. And in the second case, we need to replace C by no. Once you replace C by no, the posterior probability will be probability of no given X, which is equal to the probability of no multiplied with the probability of red given no, probability of SUV domestic given no. In both of the cases, probability of X is common, so we are not considering this one. Because of this, we are considering nearly equal to. In the first step of new base algorithm, we need to calculate the prior probability. So, in this, we have totally 10 examples. In that, five examples are belong to yes, and five examples are belongs to no. Therefore, the probability of yes is equal to the number of yes examples divided by total number of example, that is 5 / 10, which is equal to 0. 5. And probability of no is equal to 5 / 10, which is equal to 0. 5. Next, we need to calculate the conditional probability for yes. In this case, we have total 10 examples. In this 10 examples, five examples are belongs to yes. So, I have taken only those examples here. And here, we need to calculate the posterior probability, that is probability of yes given X. In this, we need the probability of yes, that is a prior probability, which is already calculated. Now, we need to calculate the probability of red given yes. So, in this case, we can see that we have the three red examples. So, the conditional probability, that is probability of red given yes is equal to 3 divided by number of yes examples, that is a five. So, which is equal to 3 divided by 5. Next, we need to calculate the probability, that is a conditional probability of SUV given yes, which is equal to Uh in this case, we have one example of a type SUV. So, 1 / 5. Next, we need to calculate the probability of domestic given yes. In this case, we have the two examples belongs to domestic. So, which is equal to 2 / 5. Once you find the required values, next we need to substitute those values here. So, once you substituted those values, that is a prior probability and these are the conditional probabilities. Here, we need to simplify this one. So, once you simplify this one, we will get the posterior probability uh that is yes given X is nearly equal to 0. 024. Next, we need to calculate the conditional probability for no. In the In total 10 examples, uh five examples are belongs to no. In this case, we need to calculate the probability of no, that is a prior probability for the no. This is already calculated. Next, we need to calculate the probability uh red given no. That is a conditional probability. So, in this case, we have a two red

examples. Those are belongs to no. So, the conditional probability uh red given no is equal to 2 / 5. Next, we need to calculate the probability of SUV given no. In this case, we have three examples belong to SUV. So, 3 / 5. And domestic given no, which is equal to 3 / 5 because here we have the three examples belong to domestic. So, it is 3 / 5. Once you find the required values, next we need to substitute those values here. Uh that is a prior probability and conditional probabilities. Once you calculate this one, we will get the probability of no given X is nearly equal to 0. 075. Finally, we need to compare the posterior probability of yes given x and posterior probability of no given x. So, if you observe carefully, posterior probability of no given x is greater than posterior probability of yes given x. It means that the new example is a classified as no class. This is how we can classify the new example into one of the class by using the new base algorithm. I hope the concept is clear. If you like the video, do like and share with your friends. Press the subscribe button for more videos. Press the bell icon for regular updates. Thank you for watching.