Statistical learning approaches

Imagine that you need to design a spam-filtering algorithm starting from this initial (over-simplistic) classification based on two parameters:

Parameter	Spam emails (X1)	Regular emails (X2)
p1 - Contains > 5 blacklisted words	80	20
p2 - Message length < 20 characters	75	25

 

We have collected 200 email messages (X) (for simplicity, we consider p₁ and p₂ mutually exclusive) and we need to find a couple of probabilistic hypotheses (expressed in terms of p₁ and p₂), to determine:

We also assume the conditional independence of both terms (it means that h_p1 and h_p2 contribute conjunctly to spam in the same way as they were alone).

For example, we could think about rules (hypotheses) like: "If there are more than five blacklisted words" or "If the message is less than 20 characters in...