Naive Bayes Classifier - Example -classify- play tennis - forecast

Naïve Bayes Classifier - Example -classify- play tennis - forecast

• Let’s build a classifier that predicts whether I should play tennis given the forecast. 
• It takes four attributes to describe the forecast; namely, 

1. the outlook, 
2. the temperature, 
3. the humidity, and 
4. the presence or absence of wind. 

• Furthermore, the values of the four attributes are qualitative (also known as categorical). 
• They take on the values shown below.
• 𝑶𝒖𝒕𝒍𝒐𝒐𝒌 ∈[𝑺𝒖𝒏𝒏𝒚,𝑶𝒗𝒆𝒓𝒄𝒂𝒔𝒕, 𝑹𝒂𝒊𝒏𝒚]
• 𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆∈[𝑯𝒐𝒕,𝑴𝒊𝒍𝒅, 𝑪𝒐𝒐𝒍]
• 𝑯𝒖𝒎𝒊𝒅𝒊𝒕𝒚 ∈[𝑯𝒊𝒈𝒉, 𝑵𝒐𝒓𝒎𝒂𝒍]
• 𝑾𝒊𝒏𝒅𝒚 ∈[𝑾𝒆𝒂𝒌, 𝑺𝒕𝒓𝒐𝒏𝒈]
• The class label is the variable, Play and takes the values Yes or No.
• 𝑷𝒍𝒂𝒚∈[𝒀𝒆𝒔, 𝑵𝒐]
• We read-in training data below that has been collected over 14 days

• 
  
  

Classification Phase

Let’s say, we get a new instance of the weather condition, 

 𝑿^′=(𝑶𝒖𝒕𝒍𝒐𝒐𝒌=𝑺𝒖𝒏𝒏𝒚, 𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆=𝑪𝒐𝒐𝒍, 𝑯𝒖𝒎𝒊𝒅𝒊𝒕𝒚=𝑯𝒊𝒈𝒉, 𝑾𝒊𝒏𝒅=𝑺𝒕𝒓𝒐𝒏𝒈)  

 that will have to be classified (i.e., are we going to play tennis under the conditions specified by 𝑋^′).

With the MAP rule, we compute the posterior probabilities.

 This is easily done by looking up the tables we built in the learning phase.