# hw2 - CSCI 5512 Artificial Intelligence II(Spring'10...

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CSCI 5512: Artifcial Intelligence II (Spring’10) Homework 2 (Due Mar 17 by11:59 PM) 2. (30 points) [Programming Assignment] Consider the rain network in Figure 1. (a) (10 points) A Gibbs sampler ±or the problem will need the ±ollowing conditional prob- abilities: P(c|r,w,s), P(c|¬r,w,s), P(r|c,w,s), and P(r|¬c,w,s), as well as their com- plements: P(¬c|r,w,s), P(¬c|¬r,w,s), P(¬r|c,w,s), and P(¬r|¬c,w,s). Using the numeric values given in Figure 1 and using the ±ormula ±or conditional probability o± a variable given its Markov blanket, compute the numeric values o± the above conditional probabilities. (b) (15 points) Using the above conditional probabilities, estimate P(r|s,w) using Gibbs sampling ±or 100 and 10,000 steps. Condition on both possible values o± Sprinkler. In addition to the numeric estimates, you have to submit code ±or GibbsRain implementing Gibbs sampling ±or the rain network. The code should take one input argument: numSteps, the number o± steps, and output an estimate o± P(r|s,w). For language specifc and general coding instructions, please see detailed instructions at the end the homework. Please ±ollow these instructions care±ully. Code submitted without adhering to these instructions will not receive any credit. 1. (20 points) Consider the Rain network in Figure 1. Assume that WetGrass = true. For simplicity, we denote the events by c, s, r and w ±or Cloudy=true, Sprinkler=true, Rain=true and WetGrass=true respectively. Each o± the 4 variables in the network is

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## This note was uploaded on 02/07/2012 for the course CSCI 5512 taught by Professor Staff during the Spring '08 term at Minnesota.

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hw2 - CSCI 5512 Artificial Intelligence II(Spring'10...

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