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Tools | Resampling | Arc Confidence

Arc Confidence measures the confidence/robustness/variability of the machine learned arcs.

One of the three resampling methods is used for generating  data sets  that are thus utilized for learning  networks .

History

Arc Confidence has been first updated in version 7.0.

New Feature: Arc and Edge Frequencies

As of version 8.0, two tables describing Arc and Edge Frequencies are available at the end of the Arc Confidence Analysis Report

Arcs and Edges result from the conversion of the Bayesian network into its corresponding Essential Graph.

  • Edges represent the links that can be reversed without changing the representation of the joint probability distribution;
  • Arcs represent the links that cannot be inverted without changing the representation of the joint probability distribution. 


These three graphs are equivalent. They all represent:

  • a direct dependency between N1 and N3,
  • a direct dependency between N3 and N2,
  • an indirect dependency between N1 and N2 (via N3),
  • a conditional independency between N1 and N2 given N3.

They are represented with the following Essential Graph:

This graph does not have any other equivalent graph.

It represents:

  • a direct dependency between N1 and N3,
  • a direct dependency between N2 and N3,
  • an independency between N1 and N2,
  • a conditional dependency between N1 and N2 given N3.

The corresponding Essential Graph is the same as the Bayesian network:


Example

Let's suppose the ground truth network we are looking for is described below:

Its Essential Graph is as follow:

Let's assume we have a data set that contains samples from this joint distribution.

After creating 100 data sets with Bootstrap and learning 100 networks, we got the following tables:

Below is the corresponding Synthesis Structure: