Lab Manual: Predicting Beach Visit using Naïve Bayes Classifier

Objective:

To apply the Naïve Bayes classifier to predict if given conditions are suitable for visiting the beach based on past data.

Theory:

Naïve Bayes is a probabilistic classifier based on Bayes' theorem, assuming independence among features. The theorem states:

 P(Y|X) = P(X|Y) P(Y)/P(X)

where:

• (P(Y|X)) is the posterior probability of class (Y) given feature (X).

• (P(X|Y)) is the likelihood of (X) given class (Y).

• (P(Y)) is the prior probability of class (Y).

• (P(X)) is the prior probability of feature (X).

For prediction, we compute probabilities for both classes (Yes/No for Beach visit) and select the one with the highest probability.

Given Data:

The dataset includes attributes: Outlook, Temperature, Humidity with the target class Beach? (Yes/No).

Numerical Computation:

To classify:

1. (Cloudy, Mild, Normal)

2. (Sunny, Low, High)

We calculate probabilities for both conditions using the dataset.

Step 1: Compute Priors

 P(Yes) = 4/10

P(No) = 6/10

Step 2: Compute Likelihoods

For each feature given Yes/No:

Example: 

P(Outlook=Cloudy | Yes) = 1/4

P(Outlook=Cloudy | No) = 2/6

Following the same approach, compute for Temperature and Humidity.

Step 3: Compute Posterior

Using Bayes' theorem, compute: [ P(Yes | X)  AND P(No | X) ] for given conditions and determine the class with the highest probability.

Python Implementation:

Below is the Python implementation to train and predict using Naïve Bayes.

import pandas as pd

from sklearn.naive_bayes import CategoricalNB

from sklearn.preprocessing import LabelEncoder

# Given dataset

data = {

    'Outlook': ['Sunny', 'Sunny', 'Sunny', 'Sunny', 'Rain', 'Rain', 'Rain', 'Cloudy', 'Cloudy', 'Cloudy'],

    'Temp': ['High', 'High', 'Low', 'Mild', 'Mild', 'High', 'Low', 'High', 'High', 'Mild'],

    'Humidity': ['High', 'Normal', 'Normal', 'High', 'Normal', 'High', 'Normal', 'High', 'Normal', 'Normal'],

    'Beach': ['Yes', 'Yes', 'No', 'Yes', 'No', 'No', 'No', 'No', 'Yes', 'No']

}

# Convert to DataFrame

df = pd.DataFrame(data)

# Encoding categorical variables

le = LabelEncoder()

for col in ['Outlook', 'Temp', 'Humidity', 'Beach']:

    df[col] = le.fit_transform(df[col])

# Train Naïve Bayes model

X = df[['Outlook', 'Temp', 'Humidity']]

y = df['Beach']

model = CategoricalNB()

model.fit(X, y)

# Predict for given conditions

test_data = pd.DataFrame([[1, 2, 1], [0, 0, 0]], columns=['Outlook', 'Temp', 'Humidity'])

predictions = model.predict(test_data)

# Decode prediction

print(le.inverse_transform(['Beach'])[predictions])

Results & Conclusion:

The model predicts whether the given conditions are suitable for visiting the beach. The accuracy depends on the dataset and assumptions of Naïve Bayes.

Tasks for Students:

1. Compute probabilities manually for one case.

2. Modify the dataset and check how predictions change.

3. Compare Naïve Bayes with other classifiers.