1. Bayes Net Inference/Learning Lab

2. Causal ordering Which of the following Bayes Nets exhibits a causal ordering of the variables? Battery dead No oil No gas Lights work Gas gauge Oil light Car won’t start Battery dead No oil No gas Lights work Gas gauge Oil light Car won’t start Graph AGraph B

3. Enumeration Compute the following probabilities for the Bayes Net below, using Enumeration: A BC AP(A) +a.6 -a.4 ABP(B|A) +a+b.6 +a-b.4 -a+b.7 -a-b.3 BCP(C|B) +b+c.8 +b-c.2 -b+c.3 -b-c.7 Compute: P(+c, -b, -a) P(+c, -b) P(-a | +c, -b)

4. Gibbs Sampling Query: P(-b | +d). Initial random sample: {-a, -b, +d, +c} C A B D AP(A) +a.6 BP(B) +b.2 ABCP(C|A,B) +a+b+c.5 +a-b+c.6 -a+b+c.2 -a-b+c.3 CDP(D|C) +c+d.7 -c+d.6 Variable chosen: A, r  0.5 Sample generated: Variable chosen: D, r  0.6 Sample generated: Query of Interest: P(-b | +d)

5. Maximum Likelihood Estimation B A C How many parameters need to be learned for this Bayes Net? Determine the maximum likelihood estimates for each of the parameters of this Bayes Net, using the dataset below. ABCCount +a+b+c20 +a+b-c25 +a-b+c55 +a-b-c40 -a+b+c5 -a+b-c75 -a-b+c40 -a-b-c120

6. Naïve Bayes Spam Classifier Below is a dataset of Spam and Ham messages. Draw the graph for a Bayes Net for a NBC for these messages. Clearly indicate what each variable means, and the edges between variables. You do not need to show parameters. MessageLabel lose 15 lbs for summerSpam lose weight fastSpam gain 15 lbs of muscle fastSpam visit this summerHam borrow a 15 lbs weightHam fast muscle tissueHam

7. Laplace Smoothing What is the number of classes K for your NBC? Use Laplace smoothing over these messages (same messages as before) to estimate parameters for your NBC for spam detection. MessageLabel lose 15 lbs for summerSpam lose weight fastSpam gain 15 lbs of muscle fastSpam visit this summerHam borrow a 15 lbs weightHam fast muscle tissueHam