Probabilistic Models of

Human and Machine Intelligence

Spring 2018

Due: Jan 23

Build a joint
probability table, like the ones we discussed in class notes,
that represents the joint distribution over all variables, i.e.,
*Pr*(Gender, Age, Class, Outcome). This table should
have 32 entries because Gender ∈ {male, female}, Age ∈
{child, adult}, Class ∈ {1st, 2nd, 3d, crew}, and Outcome
∈ {death, survival}. You will use the data in this table for the
following tasks. There is nothing to hand in for Task 0.

Build a probability
table indicating *Pr*(death | Gender, Age, Class) for each
combination of gender, age, and class. Display this table in the
following way:

The rows of each table represent the different classes and the columns the different ages and genders. In each cell of the table, insert the conditional probability. Warning: Be alert to the possibility of a cell containing no data.

After you’ve built
the probability table, come up with a rule that uses the
probabilities to predict death or survival. Then make a second
table, a classification table, which lists death or survival for
each feature combination. Explain the rule you chose to
classify.

Build a Naive Bayes
classifier. To build the classifier, you must first construct
six one-dimensional tables: *Pr*(Class | death), *Pr*(Age
| death), *Pr*(Gender | death), *Pr*(Class |
survival), *Pr*(Age | survival), *Pr*(Gender |
survival). To be clear on this notation, for *Pr*(Age |
death), your table should have two rows, one for adult and one
for child, and you should compute, for each age group, the
probability of the deceased being in that age group. Also
compute the unconditional probabilities, *Pr*(death) and
*Pr*(survival), with *Pr*(death)+*Pr*(survival)=1.
From this information, compute *Pr*(death | Gender, Age,
Class) using the Naive Bayes assumption. In addition to the
probability table, build the classification table as well.

The classification tables you built in Tasks 1 and 2 are not identical. Discuss the advantages/disadvantages of each table for making predictions in case of another disaster like the Titanic (assuming it occurred at the same time in history). Under what circumstances would you expect an empirical table to provide better predictions? Under what circumstances would you expect the naive Bayes table to provide better predictions?