| Lam Bacchus | Figure 1 Graph G1 | Joint Probabilities | CSC 720 | Spring 2001 | ||
| A | B | C | P(C|A,B) | P(B|A) | P(A) | P(A,B,C) |
| T | T | T | 0.7 | 0.8 | 0.3 | 0.168 |
| T | T | F | 0.3 | 0.8 | 0.3 | 0.072 |
| T | F | T | 0.1 | 0.2 | 0.3 | 0.006 |
| T | F | F | 0.9 | 0.2 | 0.3 | 0.054 |
| F | T | T | 0.8 | 0.1 | 0.7 | 0.056 |
| F | T | F | 0.2 | 0.1 | 0.7 | 0.014 |
| F | F | T | 0.2 | 0.9 | 0.7 | 0.126 |
| F | F | F | 0.8 | 0.9 | 0.7 | 0.504 |
| 1.0000 |
P(B) = .168 + .072 + .056 + .014 = .31
P(C) = .168 + .006 + .056 + .126 = .356
Mutual Information in G1:
W(A,B) = .24 * log2(.24/(.3*.31)) + .06 * log2(.06/(.3*.69)) + .07 * log2(.07/(.7*.31)) + .63 * log2(.63/(.7*.69)) = .348
W(B,C) = .200
W(A,C) = .066
| Lam Bacchus | Figure 1 Graph G2 | Joint Probabilities | CSC 720 | Spring 2001 | ||
| A | B | C | P(C|B) | P(B|A) | P(A) | P(A,B,C) |
| T | T | T | 0.75 | 0.8 | 0.3 | 0.180 |
| T | T | F | 0.25 | 0.8 | 0.3 | 0.060 |
| T | F | T | 0.15 | 0.2 | 0.3 | 0.009 |
| T | F | F | 0.85 | 0.2 | 0.3 | 0.051 |
| F | T | T | 0.75 | 0.1 | 0.7 | 0.0525 |
| F | T | F | 0.25 | 0.1 | 0.7 | 0.0175 |
| F | F | T | 0.15 | 0.9 | 0.7 | 0.0945 |
| F | F | F | 0.85 | 0.9 | 0.7 | 0.5355 |
| 1.0000 |
P(B) = .180 + .060 + .0525 + .0175 = .31
P(C) = .180 + .009 + .0525 + .0945 = .336
Mutual Information in G2:
W(A,B) = same as G1
W(B,C) = .249
W(A,C) = .117
Cross-Entropy: C(G1,G2) = .168 * log2(.168/.180) + .072 * log2(.072/.06) + .006 * log2(.006/.009) + .054 * log2(.054/.051) + .056 * log2(.056/.0525) + .014 * log2(.014/.0175) + .126 * log2(.126/.0945) + .504 * log2(.504/.5355) = .008
Cross-Entropy: C(G2,G1) = .008