Problem Description:

This lab task is taken from the optional textbook Fundamentals of Machine Learning for Predictive Data Analytics.

The following is a description of the causal relationship between storms, the behavior of burglars and cats, and house alarms:

Stormy nights are rare. Burglary is also rare, and if it is a stormy night, burglars are likely to stay at home (burglars don't like going out in storms). Cats don't like storms either, and if there is a storm, they like to go inside. The alarm on your house is designed to be triggered if a burglar breaks into your house, but sometimes it can be set off by your cat coming into the house, and sometimes it might not be triggered even if a burglar breaks in (it could be faulty or the burglar might be very good).

The table below lists a set of instances from the house alarm domain.

ID	STORM	BURGLAR	CAT	ALARM
1	false	false	false	false
2	false	false	false	false
3	false	false	false	false
4	false	false	false	false
5	false	false	false	true
6	false	false	true	false
7	false	true	false	false
8	false	true	false	true
9	false	true	true	true
10	true	false	true	true
11	true	false	true	false
12	true	false	true	false
13	true	true	false	true

Your tasks:

• Define the topology of a Bayesian Belief Network that encodes the given causal relationships.
• Using the given instance data, create the conditional probability tables (CPTs) for the network you created. Use Laplace smoothing algorithm if necessary.
• What value will the Bayesian network predict for ALARM given that there is both a burglar and a cat in the house but there is no storm?
• What value will the Bayesian network predict for ALARM given that there is a storm but we don't know if a burglar has broken in or where the cat is? (Hidden variable problem.)