This assignment is designed to:
In addition to the material in recent lectures, consider a brief tutorial on the topic of influence in Bayes nets.
Show your work. Be clear and concise. This assignment must be typed.
[10 points] Consider the graphical model (shown above) over five binary random variables. Factor the joint distribution represented by the entire model shown in the figure according to the explicit independence assumptions represented in the model.
[20 points] List the independence relations captured in the model (in the above figure) between the following pairs of random variables. Be sure to consider all of the cases in which the (three) other variables in the model have known values and when they do not.
2015: Note: Assume that the CPTs in the model contain values such that if influence is possible between a pair of nodes – given values of other variables in the model – using the heuristics we have discussed, then conditional independence will not hold. Under that assumption, the structure of the graph will be sufficient to tell you that a given conditional independence statement is false.
[24 points] More independence:
2015: Note: Assume that the CPTs in the model contain values such that if influence is possible between a pair of nodes – given values of other variables in the model – using the heuristics we have discussed, then conditional independence will not hold. Under that assumption, the structure of the graph will be sufficient to tell you that a given conditional independence statement is false.
[10 points] Write the four probabilities $P(L=0 | M=m,S=s)$ (for $m \in \{0,1\}$ and $s \in \{0,1\}$), both with the symbols and the resulting values.
[10 points]
[16 points] Compute $P(T=1, R=0, L=0)$. Show your work.
[10 points] Compute $P(T=1 | R=0, L=0)$. Show your work.
Your typed report should include:
Organize your report and use clear headings and explanations where needed.
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