Practice Problems:
Parameter Estimation for Bayes Nets
1. Bayes Net parameters
For each BN below, write down the set of probabilities that the BN must
store as parameters.
A
B
C
A
D
B
B
C
D
C
A
D
2. Parameter Estimation
A
B
C
a. Estimate each parameter of this BN using MLE and the
dataset on the right.
b. Do the same thing, now using Laplace smoothing and K=1.
A
+a
+a
+a
+a
-a
-a
-a
-a
B
+b
+b
-b
-b
+b
+b
-b
-b
Total:
C
+c
-c
+c
-c
+c
-c
+c
-c
Count
20
0
30
0
10
50
30
10
150
3. Naïve Bayes Classifier
Suppose I wanted to build a model that could tell me the probability that I will still be dating
someone in a month, based on impressions from a first date. Let's use a NBC to build this
model, and let's use the following random variables as inputs for the model:
-
Our first date was enjoyable (true or false)
We like the same kinds of movies (true or false)
He/she has laughed at more than one of my jokes (true or false)
I have laughed at more than one of his/her jokes (true or false)
He/she dresses well (true or false)
He/she owns a car (true or false)
a. Draw the graph of a NBC for this model.
b. Write down the set of probabilities that the NBC must store as parameters.
c. Using the (hypothetical) data set below, find maximum likelihood estimates for each of
the model parameters.
Good first
date
+
+
+
Same
movies
+
+
+
Laughed
at me
+
+
+
Laughed at
him/her
+
+
Total:
Dresses
well
+
-
Owns
car
+
+
-
Still dating
after 1 month
+
+
Count
1
3
2
4
2
12
d. Use the model you have estimated to make predictions for the following dates:
Good first
date
+
-
Same
movies
+
-
Laughed
at me
-
Laughed at
him/her
+
-
Dresses
well
+
+
Owns
car
+
P(Still dating after 1
month=+)
e. Change the parameter estimates you made to laplace smoothing estimates, with K=1.
f. Use the new model to make predictions for the same dates:
Good first
date
+
-
Same
movies
+
-
Laughed
at me
-
Laughed at
him/her
+
-
Dresses
well
+
+
Owns
car
+
P(Still dating after 1
month=+)