Your friend claims that he can write an effective Naive Bayes spam detector with only three features: the hour of the day that the email was received (H ∈ {1, 2, . . . , 24}), whether it contains the words “free money” (W ∈ {yes, no}), and whether the email address of the sender is Known in his address book, Seen before in his inbox, or Unseen before (E ∈ {K, S, U}).

a. Flesh out the following information about this Bayes net:

(i) Graph structure.

(ii) Parameters.

(iii) Size of the set of parameters.

Suppose now that you labeled three of the emails in your mailbox to test this idea:

b. Use the three instances to estimate the maximum likelihood estimate of the parameters.

c. Using the maximum likelihood parameters, find the predicted class of a new datapoint with H = 3, W = no, E = U.

d. You observe that you tend to receive spam emails in batches. In particular, if you receive one spam message, the next message is more likely to be a spam message as well. Explain a new graphical model which most naturally captures this phenomena. 

(i) Graph structure.

(ii) Parameters.

(iii) Size of the set of parameters.

Transcribed Image Text:

spam or ham?HWE spam ham ham 3 yes S 14 no K 15 no K