CS 371 - Introduction to Artificial Intelligence Homework #6

1. Read chapter 13 and sections 14.1, 14.2, and 14.5.  Also read section 4.4 of "Probabilistic Reasoning in Intelligent Systems" by Judea Pearl.
2. Stochastic Simulation:  Implement stochastic simulation of a Bayesian network as described in Section 4.4.3 of "Probabilistic Reasoning in Intelligent Systems" by Judea Pearl.  Much convenient groundwork has been done for you.  In file bnSimulate.tar, you will find a collection of files that parse input and construct a Bayesian network for you.  You should only be concerned with two files: BNStochasticSimulation.java, which you modify, and BNNode.java, which you do not modify.  Within BNStochasticSimulation.java, there is a single method for you to implement: simulate.  Do not modify other parts of the code.
• Input Format:  To enter Table 1 of the above reference, you would create a file like sample.in:

P(a) = {.20}
P(b|a) = {.20, .80}
P(c|a) = {.05, .20}
P(d|b,c) = {.05, .80, .80, .80}
P(e|c) = {.60, .80}
evidence
-d
e

The grammar for the input file is as follows:
<inputFile>  <--  <cptList> [ "evidence" <evidenceList>] <EOF>
<cptList>  <--  ( <cpt> )+
<cpt> <--  "P" "(" <varName> [ "|" <parentList> ] ")" "=" "{" <pvalueList> "}"
<parentList>  <--  <varName> ( "," <varName> )*
<pvalueList>  <--  <pvalue> ( "," <pvalue> )*
<evidenceList>  <--  <evidence> ( "," <evidence> )*
<evidence>  <--  "-" <varName> | <varName>
where <varName> is an alphanumeric variable name starting with a letter, and <pvalue> is a probability value.

CPT entries should be topologically sorted so that variables are not used as conditioning variables before their own CPT entry has been defined.  For example, if "P(b|a)  = ..." came before "P(a) = ..." above, the parser would complain.  Evidence is optional, but if there is no evidence, omit the keyword "evidence" as well.  Variable names are case sensitive.

Output Format:  Output format should mimic that of the sample output files.  For example, the output from the command
java BNStochasticSimulation 10000000 2000000 < sample.in > sample.out
would yield output of the form:
(Bayesian network information omitted.)
...
______________________________________________________________________
After iteration 2000000:
Variable, Average Conditional Probability, Fraction True
a, 0.09748785356892184, 0.097478
b, 0.09742460714035203, 0.097626
c, 0.031191558153934026, 0.031382
______________________________________________________________________
After iteration 4000000:
Variable, Average Conditional Probability, Fraction True
a, 0.09741916070759787, 0.0974705
b, 0.09741049285045494, 0.097506
c, 0.031176752524133284, 0.0313245
______________________________________________________________________
After iteration 6000000:
Variable, Average Conditional Probability, Fraction True
a, 0.09748330237820788, 0.09761716666666667
b, 0.0974821559496393, 0.09763166666666667
c, 0.03120110850466848, 0.0313455
______________________________________________________________________
After iteration 8000000:
Variable, Average Conditional Probability, Fraction True
a, 0.09740884107956631, 0.097467125
b, 0.09740182857956917, 0.097492875
c, 0.031173577904451428, 0.0312755
______________________________________________________________________
After iteration 10000000:
Variable, Average Conditional Probability, Fraction True
a, 0.09732317572895542, 0.097338
b, 0.09733498930038403, 0.0973159
c, 0.03114377427753685, 0.0312345

The first command line parameter is the number of iterations.  The second is the frequency of result reporting.

Note that for each non-evidence node we print both the average conditional probability and the fraction of iterations the variable has been assigned true.

BNNode class: see javadoc documentation.

As your first exercise, implement the stochastic simulation method such that your output is similar to that above.  For guidance, the exact conditional probability of variable a for the above problem is .0972762646.
 

Todd Neller