Structure Comparision

Context

• The Structure Comparison window is a key element of the Structural Coefficient Analysis, from where it can be launched.

Usage

• You can open the **Structure Comparison window**  by clicking the Structure Comparison button at the bottom of the Structural Coefficient Analysis Report.
  
  

Structure Comparison Window

• The Structure Comparison window is not exclusive to the Structural Coefficient Analysis. It is also available in a similar form in the context of other learning processes that produce a variety of Bayesian networks for comparison and evaluation purposes.
• The Structure Comparison window features a toolbar at the top. Some of the icons are common throughout BayesiaLab and others are specific to this particular context:

Synthesis Structure 

• Upon opening the Structure Comparison window, the Synthesis Structure appears as the default view.
• The Synthesis Structure is marked by the  icon in the toolbar and also labeled as such at the bottom of the Structure Comparison window.
  
  
• Although the Synthesis Structure may look like a Bayesian network, it is actually not a Bayesian network.
• Rather, the Synthesis Structure visualizes the commonalities and differences between the Reference Network and the Comparison Networks.
  • A black edge or arc signifies that it exists both in the Reference Network and all Comparison Networks.
  • A blue edge or arc indicates that it does not exist in the Reference Network but that it does exist in at least one of the Comparison Networks. ​
  • A red edge or arc means that it does exist in the Reference Network but that it does not exist in any of the Comparison Networks. ​
• Arcs are displayed in the form of an arrow, while edges are shown as a straight solid line.
• A circle line between two arcs highlights a V-structure.
• The thickness of a line between two nodes is proportional to the frequency of the corresponding edge or arc, i.e., a thick blue arc implies that that arc occurs frequently in the Comparison Networks.
• By hovering over an arc or an edge in the Synthesis Structure, tooltips provide you with details regarding the object properties, as illustrated below.
  
  
  • Examples from the Synthesis Structure: - 5 - No. of Full Baths -> 2 - Garage Space - "->" between the node names means that the link, whenever it is present in any structure, is always a directed arc from 5 - No. of Full Baths to 2 - Garage Space. - "Added" means that this link does not exist in the Reference Structure but in at least one of the Comparison Structures. - "Arc Frequency -55%" means that in 11 out of 20 **Comparison **Structures****, the link was a directed arc from 5 - No. of Full Baths to 2 - Garage Space. - "Inverted Arc Frequency 0%" means that none of the **Comparison **Structures**** contained the inverted arc, i.e., 2 - Garage Space to 5 - No. of Full Baths. - "Edge Frequency 0%" means that in none of the **Comparison **Structures****, there was an undirected edge between 5 - No. of Full Baths and 2 - Garage Space. - Sale Price -> 6 - No. of Fireplaces - "->" between the node names means that the link, whenever it is present in any structure, is always a directed arc from Sale Price to 6 - No. of Fireplaces.
  • "Existing" means that this link exists in the Reference Structure and all the Comparison Structures. - "Arc Frequency 100%" means that in all 20  **Comparison **Structures****, the link was a directed arc from Sale Price to 6 - No. of Fireplaces. - "Inverted Arc Frequency 0%" means that none of the **Comparison **Structures**** contained the inverted arc, i.e., 6 - No. of Fireplaces to Sale Price. - "Edge Frequency 0%" means that in none of the **Comparison **Structures****, there was an undirected edge between Sale Price and 6 - No. of Fireplaces. - 5 - No. of Full Baths -> 1 - Overall Quality - "->" between the node names means that the link, whenever it is present in any structure, is always a directed arc from 5 - No. of Full Baths to 1 - Overall Quality. - "Added" means that this link does not exist in the Reference Structure but in at least one of the Comparison Structures. - "Arc Frequency -35%" means that in 7 out of 20 **Comparison **Structures****, the link was a directed arc from 5 - No. of Full Baths to 1 - Overall Quality. - "Inverted Arc Frequency 0%" means that none of the **Comparison **Structures**** contained the inverted arc, i.e., 1 - Overall Quality to 5 - No. of Full Baths. - "Edge Frequency 0%" means that in none of the **Comparison **Structures****, there was an undirected edge between 5 - No. of Full Baths and 1 - Overall Quality.

Reference Structure 

• By clicking on the next button , you proceed from the Synthesis Structure to the Reference Structure.
• Alternatively, you can access the Reference Structure by clicking on the corresponding icon .
  
  
• The Reference Structure represents the original network. Thus, what is displayed is a proper Bayesian network, not merely an illustration.

Comparison Structures

• By clicking on the next button , you proceed from the Reference Structure to the first of potentially many Comparison Structures.
  
  
• The first one is labeled as "Comparison Structure: 8" at the bottom of the window.
• You can use the previous  and next  buttons to navigate through the available structures in this order:
  • Synthesis Structure, i.e., the illustration of the differences between the Reference Network and the Comparison Networks.
  • Reference Structure, i.e., the starting point of the analysis that produced all Comparison Networks.
  • Comparison Structure 8
  • Comparison Structure 7
  • Comparison Structure 6
  • etc.
• Right underneath the graph area, BayesiaLab reports additional information regarding the displayed Comparison Structure:
  • ​The sequence number, e.g, 8, 7, .... 0.
  • The Count, i.e., the number of times the displayed Comparison Structure was found. In the above screenshot, the shown Comparison Structure was found twice.
  • The Frequency, which refers to the count of the displayed Comparison Structures divided by the count of all generated Comparison Structures. Here, the Frequency is 10% (=2/20 displayed in percent). Note that the total number of Comparison Structures is not displayed here.
  • The Max SC, which represents the Structural Coefficient used for learning the displayed Comparison Structure.
  • The Validation Measure, which serves as a quality measure for choosing an appropriate Structural Coefficient.
• For Comparison Structures, the Save Network  and Open Network  icons are available. This allows you to extract the currently displayed Comparison Structure.
• The following table provides a side-by-side comparison of all structures. Click on the thumbnails to see full-size screenshots.

Synthesis Structure	Reference Structure	Comparison Structure 8	Comparison Structure 7	Comparison Structure 6	Comparison Structure 5	Comparison Structure 4	Comparison Structure 3	Comparison Structure 2	Comparison Structure 1	Comparison Structure 0
		Count: 2	Count: 1	Count: 6	Count: 2	Count: 2	Count: 3	Count: 2	Count: 1	Count: 1
		Frequency: 10%	Frequency: 5%	Frequency: 30%	Frequency: 10%	Frequency: 10%	Frequency: 15%	Frequency: 10%	Frequency: 5%	Frequency: 5%
		Max. SC: 2	Max. SC: 1.8	Max. SC: 1.7	Max. SC: 1.1	Max. SC: 0.9	Max. SC: 0.7	Max. SC: 0.4	Max. SC: 0.2	Max. SC: 0.1
		Validation Measure: 11.397	Validation Measure: 11.342	Validation Measure: 11.41	Validation Measure: 10.21	Validation Measure: 11.072	Validation Measure: 11.921	Validation Measure: 13.842	Validation Measure: 14.255	Validation Measure: 17.056