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Information Analysis

Overview

Clicking the Select Nodes buttons defines three sets of nodes (X, Y, and Z) for analysis. The selection is done by directly selecting the nodes in the graph. By default, the Target node is associated with the Y set.

The breast-cancer network with the X, Y, and Z node sets colored red, blue, and green Information Analysis window with the three node sets listed side by side and a Select Nodes button under each

Information Analysis Report

Given the exponential growth of the state space, this analysis is performed only on the database.

Report header listing the two X nodes, the one Y node, and the two Z nodes

Unconditional Entropy

H(X)=−∑x∈Xp(x)log⁡2(p(x))\displaystyle H(X) = -\sum_{x \in X} p(x) \log_2(p(x))

Report row giving an unconditional entropy H(X) of 1.92436598 Individual Unconditional Entropy table: 1.36977963 for Concavity and 1.28481761 for Concave Points

Conditional Entropy

H(X∣Z)=−∑z∈Zp(z)∑x∈Xp(x∣z)log⁡2(p(x∣z))\displaystyle H(X \mid Z) = -\sum_{z \in Z} p(z) \sum_{x \in X} p(x \mid z) \log_2(p(x \mid z))

Conditional entropy H(X given Z) of 1.4037297, which is 72.945 percent of H(X) Individual Conditional Entropy table, each node with its conditional entropy and the ratio to its own

Unconditional Mutual Information

I(X,Y)=H(X)−H(X∣Y)\displaystyle I(X, Y) = H(X) - H(X \mid Y)

Unconditional Mutual Information I(X;Y) of 0.57850212, 30.06 percent of H(X) and 60.73 percent of H(Y)

Conditional Mutual Information

I(X,Y∣Z)=H(X∣Z)−H(X∣Y,Z)\displaystyle I(X, Y \mid Z) = H(X \mid Z) - H(X \mid Y,Z)

Conditional Mutual Information table: I(X;Y given Z) of 0.20741399 with its three ratios Individual Conditional Mutual Information for each of the two X nodes Mutual Information Individually Conditioned, one row per Z node

Total Correlation

C(X)=∑iH(xi)−H(X)\displaystyle C(X) = \sum_i H(x_i) - H(X)

Conditional Mutual Information table: I(X;Y given Z) of 0.20741399 with its three ratios

Conditional Total Correlation

C(X∣Z)=∑iH(xi∣Z)−H(X∣Z)\displaystyle C(X \mid Z) = \sum_i H(x_i \mid Z) - H(X \mid Z)

Conditional Mutual Information table: I(X;Y given Z) of 0.20741399 with its three ratios
Example: Most Relevant Explanations for Failure AnalysisHidden Variable Discovery