CSE 4308/5360 - Assignments - Programming Assignment 5

Due dates:
Interim report: Wednesday, August 4, 2010, 11:55pm
Full assignment: Wednesday August 11, 11:55pm.

Summary

The goal in this assignment is to get practice on designing Bayesian networks, estimating probability distributions in Bayesian networks, and implementing Bayesian networks.

Part 1: Designing a Bayesian network graph

20 points

George doesn't watch much TV in the evening, unless there is a baseball game on. When there is baseball on TV, George is very likely to watch. George has a cat that he feeds every night, although he forgets every now and then. He's much more likely to forget when he's watching TV. He's also very unlikely to feed the cat if he has run out of cat food (although sometimes he gives the cat some of his own food). Design a Bayesian network for modeling the relations between these four events:

baseball_game_on_TV
George_watches_TV
out_of_cat_food
George_feeds_cat

Your task is to connect these nodes with arrows pointing from causes to effects. No programming is needed for this part, just include an electronic document (PDF, Word file, or OpenOffice document) showing your Bayesian network design.

Part 2: Learning Probabilities from Training Data

20 points

For the Bayesian network of Part 1, the text file at this link contains training data from every evening of an entire year. Every line in this text file corresponds to an evening, and contains four numbers. Each number is a 0 or a 1. In more detail:

The first number is 0 if there is no baseball game on TV, and 1 if there is a baseball game on TV.

The second number is 0 if George does not watch TV, and 1 if George watches TV.

The third number is 0 if George is not out of cat food, and 1 if George is out of cat food.

The fourth number is 0 if George does not feed the cat, and 1 if George feeds the cat.

Based on the data in this file, determine the probability table for each node in the Bayesian network you have designed for Part 1. You need to include these four tables in the drawing that you produce for question 1. You also need to submit the code/script that computes these probabilities.

Figure 1: A Bayesian network establishing relations between events on the burglary-earthquake-alarm domain, together with complete specifications of all probability distributions.

Part 3: Implementing a Bayesian Network

60 points

For the Bayesian network of Figure 1, implement a program that computes and prints out the probability of any combination of events given any other combination of events. If the executable is called bnet, here are some example invocations of the program:

To print out the probability P(Burglary=true and Alarm=false | MaryCalls=false).
```
bnet Bt Af given Mf
```
To print out the probability P(Alarm=false and Earthquake=true).
```
bnet Af Et
```
To print out the probability P(JohnCalls=true and Alarm=false | Burglary=true and Earthquake=false).
```
bnet Jt Af given Bt Ef
```
To print out the probability P(Burglary=true and Alarm=false and MaryCalls=false and JohnCalls=true and Earthquake=true).
```
bnet Bt Af Mf Jt Et
```

In general, bnet takes 1 to 6(no more, no fewer) command line arguments, as follows:

First, there are one to five arguments, each argument specifying a variable among Burglary, Earthquake, Alarm, JohnCalls, and MaryCalls and a value equal to true or false. Each of these arguments is a string with two letters. The first letter is B (for Burglary), E (for Earthquake), A (for Alarm), J (for JohnCalls) or M (for MaryCalls). The second letter is t (for true) or f (for false). These arguments specify a combination C1 of events whose probability we want to compute. For example, in the first example above, C1 = (Burglary=true and Alarm=false), and in the second example above C1 = (Alarm=false and Earthquake=true).
Then, optionally, the word "given" follows, followed by one to four arguments. Each of these one to four arguments is again a string with two letters, where, as before the first letter is B (for Burglary), E (for Earthquake), A (for Alarm), J (for JohnCalls) or M (for MaryCalls). The second letter is t (for true) or f (for false). These last arguments specify a combination of events C2 such that we need to compute the probability of C1 given C2. For example, in the first example above C2 = (MaryCalls=false), and in the second example there is no C2, so we simply compute the probability of C1, i.e., P(Alarm=false and Earthquake=true).

The implementation should not contain hardcoded values for all combinations of arguments, but instead should use the tables shown on Figure 1 and the appropriate formulas to evaluate the probability of the specified event. More specifically, for full credit, the code should include and use:

A Bayesian network class. The nodes of the network will be stored in a member variable (a list, vector, or array) of the Bayesian network class. The class should include a member function called computeProbability(b, e, a, j, m), where each argument is a boolean, specifying if the corresponding event (burglary, earthquake, alarm, john-calls, mary-calls) is true or false. This function should return the joint probability of the five events, and should call (with appropriate arguments) the computeProbability function of each node in the network (see description in the next bullet), and determine the overall result based on the results of the computeProbability function of the nodes.
A node class. Each node of the Bayesian network will be an object (or pointer) belonging to the node class. The parents of a node X will be stored as member variables of the object representing X. Class node must also implement a member function called computeProbability, that will take as an argument an array (or list, or vector) of Boolean arguments specifying values for all parents of the node, and returns the probability of the node being true given the values for its parents.

Grading

Each part will be graded as follows:

Part 1
- 8 points: Establishing a correct correspondence between nodes in the Bayesian network and events in the problem description.
- 8 points: Establishing correct connections between nodes in the Bayesian network, according to the problem description.
- 4 points: Using the correct direction for each arrow in the Bayesian network.
Part 2:
- 20 points: Estimating correctly each probability table from the training data.
Part 3:
- 20 points: Creating an executable that provides the correct output for each input.
- 20 points: Correctly implementing the Bayesian network class.
- 20 points: Correctly implementing the node class.

How to submit

Submit a ZIPPED directory called programming5.zip (no other forms of compression accepted, contact the instructor or TA if you do not know how to produce .zip files). The directory should contain source code, the answer for part 1 in a document, the answer (and code) for part 2, and the code for part 3. The submission should also contain a file called readme.txt, which should specify precisely:

Name and UTA ID of the student.
Where the answers are for part 1 and part 2.
What programming language is used.
How the code is structured.
How to run the code, including very specific compilation instructions, if compilation is needed. Instructions such as "compile using g++" are NOT considered specific. Providing all the command lines that are needed to complete the compilation on omega is specific.

Insufficient or unclear instructions will be penalized by up to 20 points. Code that does not run on omega machines gets AT MOST half credit (50 points).

Submission checklist

DID YOU INCLUDE the answer for part 1, answer AND code for part 2, and the code for part 3?
Is the code running on omega?
Is the submitted zipped file called programming5.zip?
Does the submission include a readme.txt file, as specified?