For this mini-project, you will be using the bayes net tool available at: http://www.aispace.org/bayes/index.shtml The tool is reasonably intuitive to use. Nevertheless, a very nice interactive tutorial on the tool usage is available in the same page. Problem: We have decided to use the bayes-network technology to model the Springfield nuclear power plant (where Homer Simpson is gainfully employed). Here is our understanding of the domain (this is all official based on my conversations with Bart). The presence of inferior plutonium or low quality heavy water (D20) in the plant reactor leads to a core melt-down in the reactor. When core-meltdown occurs, it tends to irradiate the employees (such as Homer) causing them to glow in the dark. Core-meltdown also tends to shutoff the power grid which in turn causes the slurpees in Apu's convenience store (called Squishees at Kwikee Mart) to melt and get watery. Here are a bunch of probabilities I got from the Springfield Statistics Beureau: The dependency between Core Meltdown and Inferior Plutonium and Low Quality Heavy Water can be modeled as a "Noisy-OR" distribution. Inferior plutonium fails to cause core melt down with a probability of 0.7; and low quality heavy water fails to cause core meltdown with a probabilityof 0.8. Core-meltdown leads to glowing-in-the-dark employees with probability 0.5. What with lax quality control over at Springfield plant, even under normal circumstances, Homer and his buddies tend to glow in the dark with probability 0.05. Core-meltdown causes slurpee liquification with 0.9, and over at Apu's slurpees tend to get watery even without a core-meltdown with probability 0.1. Finally, the probability that Springfield plant gets inferior-quality plutonium is 0.3 and that it gets low-quality heavy water is 0.4 (you know that wacky Burns--he is always trying to buy cheap stuff and make more bucks). Tasks: Do all these tasks. Write down your observations for each task. Include snapshots of the bayes net tool as appropriate. Part I. [Bayesnet] 1. Create the bayes network that you have above in the bayes net tool. Enter the conditional probability tables as appropriate. To show that you have done this task, you need to (1) include a bitmap of the network (use Alt-Printscreen in windows) and (2) include the .xml format representation of the network (you can output this by going to the edit menu, and selecting the first command). 2. Now go to the solve pane and evaluate the following queries--in that order. *Comment* on whether the relative values are in accordance with our intuitions. P(IP) P(IP|ASL) P(IP|CM) P(IP|CM,ASL) P(IP|CM,LHW) If in the above, any of the probabilities don't change when extra evidence is added, use the D-Separation criterion you learned in the class to verify that it is as expected (for example, if P(IP|CM) is the same as P(IP|CM,ASL) then it must be the case that IP is conditionaly independent of ASL given CM). (You can accomplish these easily by "monitoring" the IP node, and observing/de-observing the appropriate variables). (Glossary: IP--Inferior Plutonium. ASL-->Apu's Slurpees liquify. CM-->Core Meltdown. GID-->Glow in the Dark, LHW-->Low quality Heavy Water). Part II [Relations with logic] 1. Modify the network such that the causations are "perfect" and "exhaustive" (e.g. Inferior plutonium _always_ causes Core Melt down, and core meltdown will not be true if none of its causing variables are true). Confirm that you modified it by including a .xml format representation of the new network. [Note: You will only change the causations. You will keep the prior probabilities of IP and LHW as before. ] 2. Write down a set of propositional logic statements that capture the knowledge encoded in the bayes network. 3. Evaluate the following probabilities in this bayes network P(IP|ASL) P(IP|ASL,~LHW) P(IP|ASL,~GID) Interpret the answers. Comment on whether these answers are in line with what propositional logic would have us derive given the formulation in II.2. Part III [Reformulating Bayesnet] Consider the following alternative way of specifying this bayes net. Here, we introduce the random variables in the following order into the network: 1. Apus's slurpees are liquified 2. Core melt down occured 3. Employees glow in the dark 4. Low quality heavy water 5. Inferior quality plutonium 1. Show the network that will result if we specified the numbers this way (need both the topology as a screen dump, and the .xml format representation). Note that you also need to put in the CPTs (conditional probability tables) for each variable. To do this, you will have to use the network as it existed at the end of Part I.1. as the expert--and get the required CPTs by querying the network. Comment on whether this network is better or worse in terms of number of probabilites that you needed to assess. Once you specify the entire new network, to see that this and the earlier network are equivalent, compute the the following thre probabilities for the new network--and compare your values with the answer for I.2. P(IP) P(IP|ASL) P(IP|CM) P(IP|CM,ASL) P(IP|CM,LHW) Part IV: We found out more information about the causes behind Inferior Plutonium (IP) and Low Quality Heavy Water (LHW). It turns out that Mr. Burns' stinginess is partly to blame for these. We know that Mr. Burns _is_ stingy with 0.99 probability. We also found that when he is stingy, he is likely to buy inferior plutonium with probability 0.3 and low quality heavy water with probability 0.4. When he is not stingy, he buys IP with 0.0001 probability and low quality heavy water with 0.0002 probability. 1. Modify the bayes network to show this improved understanding of the domain. Show the topology as well as the .xml representation 2. Is the new network singly connected or multiply connected? If it is multiply connected, please provide an equivalent singly connected network (once again, you will need to show the topology and .bn representation).

Subbarao Kambhampati Last modified: [Oct 27, 2015]