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Chris Evers Problem Set 3, Problem 10 Analysis ------------------------------------- Network 1 3 2 A B C A C B C A 0.3 0.7 B 0.75 0.25 C 0.1 0.3 0.45 0.15 -------------------------------------- Network 2 4 4 Cloudy Sprinkler Rain WetGrass Cloudy Sprinkler Cloudy Rain Sprinkler WetGrass Rain WetGrass Cloudy 0.5 0.5 Sprinkler 0.5 0.1 Rain 0.2 0.8 WetGrass .0 .9 .9 .99 -------------------------------------- Network 3 1 0 A A 0.3 0.7 -------------------------------------- Network 4 2 1 A B A B A 0.3 0.7 B 0.75 0.25 -------------------------------------- Network 5 4 3 A B C D A C B C C D A 0.3 0.7 B 0.75 0.25 C 0.1 0.4 0.4 0.8 D 0.5 0.5 -------------------------------------- The above specified 5 different networks of varying size and CPT's. Analysis Chart Num Samples | 10 | 100 | 500 | 1000 | ----------------------------|---------------|---------------|---------------|---------------| Network 1 |Gibbs: 0.2|Gibbs: 0.14|Gibbs: 0.154|Gibbs: 0.158| P(C|A=1,B=1) |Weighted: 0.1|Weighted: 0.16|Weighted: 0.156|Weighted: 0.152| ----------------------------|---------------|---------------|---------------|---------------| Network 2 |Gibbs: 1.0|Gibbs: 0.95|Gibbs: 0.963|Gibbs: 0.990| P(Rain|Cloudy=1,WetGrass=1) |Weighted: 0.857|Weighted: 0.963|Weighted: 0.971|Weighted: 0.973| ----------------------------|---------------|---------------|---------------|---------------| Network 3 |Gibbs: 0.8|Gibbs: 0.65|Gibbs: 0.708|Gibbs: 0.689| P(A) |Weighted: 0.7|Weighted: 0.73|Weighted: 0.67|Weighted: 0.717| ----------------------------|---------------|---------------|---------------|---------------| Network 4 |Gibbs: 0.2|Gibbs: 0.22|Gibbs: 0.234|Gibbs: 0.235| P(B|A=1) |Weighted: 0.2|Weighted: 0.25|Weighted: 0.288|Weighted: 0.258| ----------------------------|---------------|---------------|---------------|---------------| Network 5 |Gibbs: 0.75|Gibbs: 0.51|Gibbs: 0.497|Gibbs: 0.478| P(D|A=0,B=1) |Weighted: 0.3|Weighted: 0.5|Weighted: 0.508|Weighted: 0.497| ----------------------------|---------------|---------------|---------------|---------------| The above chart compares constant probabilities from each of the 5 networks, using various numbers of samples, and both the Gibbs and Likelihood Weighting algorithms. Some conclusions can be drawn about how each variable affects the outputted probability. First of all, as the number of samples increased, the probabilities converged to actual probability given in the CPT. In the case of network 5, where C is a hidden variable, the lower num_samples gave very unreliable guesses. The Gibbs and Weighted algorithms also gave quite different results, all things remaining constant. I think that the difference actualyl depends on the structure of the network, because the values differed much in network 5, where it has an unknown hidden variable. The algorithms also gave surprisingly different results in network 3, which only has one variable. The weighted algorithm actually gave more consistent results, where Gibbs varied more, with only one variable.
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