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Now that we've discussed the final step on how our Naive Bayes Classifier makes decisions, we should talk
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about where the probabilities that feed into this decision making actually come from.
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And this means backing up a bit and talking about statistics. Now this is the part that no one gets excited
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about.
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I've yet to hear somebody say "Yes, statistics!
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My favorite topic!", but the thing is, statistics is everything in machine learning and this project will
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give us a chance to get some exposure.
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All right.
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So we're interested in calculating the probability that an email is spam.
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However, it's not like we can simply work out the probability the same way we would work out the probability
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of say flipping heads on a coin flip or rolling a six with a die. With coins and dice, working out the
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probabilities is fairly straightforward.
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But let's review some of these concepts nonetheless because they're gonna come in handy later.
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Now with coins, we know that there's two sides and a flip has a 50/50 chance of showing heads. With this
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dice here,
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we know that there are six sides and we've got a 1 in 6 or roughly 17% chance of rolling
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a six or any particular number.
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Now let me ask you a question outside of the realm of flipping coins and rolling dice,
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how would you work out your probability of getting hit by lightning?
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Yeah, I know, you could probably ask Google and get the answer, but if you had to calculate it yourself,
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how would you do it? Well,
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the simplest way to do this is by dividing two numbers, the total number of times people get hit by lightning
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and the total number of lightning strikes.
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Now I trawled through Wikipedia for you and I've dug out these figures. About 240000 people are injured
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by lightning every year.
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Now, 240000 actually sounds like quite a lot of people but there are an order of magnitude more lightning
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strikes. Every year around 350 million lightning bolts actually strike the ground.
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So then, just given these two numbers, what's the chance of you being hurt by lightning?
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Well, it'll be 240000 divided by 350 million or 0.07%.
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The point I'm trying to get across here is how to use basic probability.
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We took some observations, like the number of times a lightning struck a person and the total number
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of times we observed lightning in a year
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to calculate this figure.
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Now, suppose we had to work out the chance of an email being spam.
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Any email that is, right, any email in the whole world. We can apply the same technique as in the lightning
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example. The chance of an email being spam should also depend on two things, namely one, how many spam
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emails were sent; and two, how many emails were sent in total. With these two quantities in hand,
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we can work it out. So I trawled the internet and here's what I pulled up. In 2017,
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there were an estimated 148 billion spam emails sent.
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That's right, billion. And the total number of emails being sent was approximately 269
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billion.
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So that means, if a new email comes into your inbox, the probability of that email being spam or having
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been spam in 2017 was 55%.
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And this is simply based on the observation of the frequencies, namely the total number of spam emails
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divided by the total number of all email traffic.
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So you can think of calculating the basic probability as step one.
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We figured out the overall probability of spam, but we can't build a classifier with this alone.
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So what's step two?