# Naive Bayes

Maybe where u start reading this, you may ask, “who the hell is bayes???”, well, trust me, i don’t know him well either . As far as i know, he is the founding of bayesian theorem, one the basic “uncertainty” (sorry if i misspell it ) theorem in artificial intelligence.

I want start to find more about bayes when i took decision support system course. The most painful thing is i got “statistical method” categories in final project. I’m bad when dealing with math or statistic. It’s really sucks. Moreover, i didn’t have enough time at the beginning. So i let my team, tiwi(oh.. god, not again), hanna, rina, and denny from statistic to made first progress.

Presentation before the mid exam was made by denny. I didn’t get the point though, because he is using anava method (it’s really complicated shit). I’m really don’t get the idea of anava. I’m afraid that thing is inapplicable in our project.

Time for made the final project is nearer every day. Luckily, i have some extra time to made progress with bayes. After searching and searching, i found that the easiest thing is create application with naive bayes classifier.

Ok, what the hell is naive bayes classifier? I’ll try to make simple explanation. Bayesian theorem is theorem about probability. It’s the basic for naive bayes classifier. Well, probability is easy, say you have a coin (one side is head and tail is another), if you throw it once, what is the probability of showing head, and what is the probability of showing tail. Let see.. is it 50% chance? Yup, you’re right.

The idea of naive bayes classifier is using the probability of some independence event and calculate an event which is influenced by independence event. The most simple example (i think) is the probability of play-tennis or not-to-play-tennis. Let’s go straight into the sample.

Let say, you have some of data like this :

 Day Outlook Temperature Humidity Wind Day1 Sunny Hot High Weak No Day2 Sunny Hot High Strong No Day3 Overcast Hot High Weak Yes Day4 Rain Mild High Weak Yes Day5 Rain Cool Normal Weak Yes Day6 Rain Cool Normal Strong No Day7 Overcast Cool Normal Strong Yes Day8 Sunny Mild High Weak No Day9 Sunny Cool Normal Weak Yes Day10 Rain Mild Normal Weak Yes Day11 Sunny Mild Normal Strong Yes Day12 Overcast Mild High Strong Yes Day13 Overcast Hot Normal Weak Yes Day14 Rain Mild High Strong No

Let see… just focus on first column, bout the outlook. Ok, now with that data, calculate, how much is the probability we play tennis in sunny day. Probability of playing tennis in sunny day is 2 / 9 = 2/9 = 22% chances. Remember, 9 obtained from total yes. We can also get the probability of rain-Yes, rain-No, etc.

Get the point? Ok, naive bayes is simple, we use that independence probability (rain-yes,rain-no,sunny-yes,sunny-no,etc) to calculate how much probability to play tennis or not. The good thing is, we don’t need every information, even partial data is enough to make a inference / decision.

This is how we calculate the probability of Play tennis = yes from data : Outlook = sunny, temperature = cool, and humidity = high. Ok, the probability for Sunny-Yes = 2/9, Sunny-No = 3/5, cool-Yes = 3/9, cool-No = 1/5, highHumid-Yes = 3/9 , highHumid-No = 4/5, Yes = 9/14 and No = 5/14.

Now we calculate the probability of play tennis.
p(PlayTennisYes) = p(Yes)*p(Sunny-Yes)*p(cool-Yes)*p(highHumid-Yes) / [(p(Yes)*p(Sunny-Yes)*p(cool-Yes)*p(highHumid-Yes)) + (p(No)*p(Sunny-No)*p(cool-No)*p(highHumid-No))]

Well, it’s hard to read, because i don’t understand LaTex though, sorry bout the equation, anyway, the simpler ways is the probability is yes*yes*yes / [(no*no*no) + (yes*yes*yes)].

The more advance use of bayesian theorem is bayesian network. In bayesian network, each probability is not independence, it’s depend on each other. Example is beach problem. How much people going to beach if not holiday? how much holiday depend on political situation, etc.