3.Write about Generative Model. Apply the naïve Bayes algorithm to obtain Likelihood table
by finding the probabilities of given features.
Sl. No. Play
Outlook Sl. No. Play
Outlook
0 Rainy
Yes
7
Overcast Yes
1 Sunny
Yes
8
Rainy
No
2 Overcast Yes
9
Sunny
No
3 Overcast Yes
10
Sunny
Yes
4 Sunny
No
11
Rainy
No
5 Rainy
Yes
12
Overcast Yes
6 Sunny
Yes
13
Overcast Yes
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Welcome to our exploration of Generative Models and Naive Bayes algorithm. A generative model is a type of machine learning model that learns the joint probability distribution of input features and target variables. Unlike discriminative models that only learn the decision boundary, generative models can actually generate new data instances that resemble the training data. Naive Bayes is a classic example of a generative model that uses Bayes' theorem to make predictions.
Now let's examine our dataset. We have 14 instances of weather data with two attributes: Outlook and Play. The Outlook feature has three possible values: Rainy, Sunny, and Overcast. The target variable Play has two values: Yes and No. This dataset will help us demonstrate how Naive Bayes calculates probabilities. We can see the complete dataset here with all 14 instances clearly organized.
Now let's calculate the prior probabilities for our target variable Play. First, we count the total number of instances, which is 14. Next, we count how many instances have Play equals Yes, which is 10 instances. Then we count instances where Play equals No, which is 4 instances. The prior probability of Play equals Yes is 10 divided by 14, which simplifies to 5 sevenths. The prior probability of Play equals No is 4 divided by 14, which simplifies to 2 sevenths. We can verify our calculation is correct because 5 sevenths plus 2 sevenths equals 1.
Now we calculate the likelihood probabilities. For Play equals Yes, we have 10 instances total. Among these, Rainy appears 2 times, so P of Rainy given Yes equals 2 over 10, which is 0.2. Sunny appears 3 times, so P of Sunny given Yes equals 3 over 10, which is 0.3. Overcast appears 5 times, so P of Overcast given Yes equals 5 over 10, which is 0.5. For Play equals No, we have 4 instances total. Rainy appears 2 times, giving us 0.5. Sunny also appears 2 times, giving us 0.5. Overcast appears 0 times, giving us 0.0.
Here is our final likelihood table summarizing all conditional probabilities. The table shows P of Outlook given Play for each weather condition. Notice that Overcast has a probability of 0.5 when Play equals Yes, but 0.0 when Play equals No. This means Overcast weather always leads to playing, making it a perfect predictor. Rainy and Sunny conditions show different probability distributions between Yes and No outcomes. This likelihood table is the core of our Naive Bayes generative model, capturing the learned probability distributions from our training data.