Question

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).

Your tasks:

a. Define the topology of a Bayesian Belief Network that encodes these causal relationships.

b. The table below lists a set of instances from the house alarm domain. Using the data in this table, create the conditional probability tables (CPTs) for the network you created in part (a) of this question.


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


c. 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?


d. 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?

Answer 1

Answer:

for a and b see pictures attached,

c. Because both the parent nodes for ALARM are known, the probability distribution over  ALARM is independent of the feature STORM. Consequently, we can read the relevant  probability distribution over ALARM directly from the conditional probability table for the ALARM node. Examining the conditional probability table, we can see that when BURGLAR = true, and CAT = true, then ALARM = true is the MAP prediction. In other words,  the network would predict that the alarm would sound in this situation.

d. In this case, the values of the parents of the target feature are unknown. Consequently, we

need to sum out both the parents for each value of the target. The network would calculate

the probability of the event ALARM = true as follows:

see figures

Answer 2

Answer:

c. Yes

d. no

Explanation: