# Structural Uncertainties Help

The structure derived by the NPC algorithm contains ambiguous regions (i.e., groups of inter-dependent uncertain links) and/or other undirected links. The current page of the Learning Wizard provides you with an intuitive graphical interface for resolving these structural uncertainties.

Should you not wish to provide such information, just click the Next button, and the NPC algorithm will resolve the uncertainties. Note, however, that directionality for undirected links will be decided on a random basis, and that for those ambiguous regions with no information provided, all of the uncertain links will be removed, possibly resulting in a poor model.

For more information on the NPC algorithm and the notions of undirected links and ambiguous regions, see the help page of the previous page of the Learning Wizard.

## Undirected Links

Instead of randomly determining the directionality of the links of the learned structure that cannot be determined automatically from the data, the NPC algorithm gives the user the apportunity to determine the directionality of such links. The undirected links (not belonging to ambiguous regions) are drawn in black. When selected, such a link gets highlighted and the two directionality buttons get enabled:

or or or

Which of the above appearances of the pair of buttons are used depends on the relative positioning of the nodes of the selected link. Thus, it should be readily apparent which of the two buttons should be selected for achieving the desired directionality for the selected link. However, when positioning the mouse cursor on top of a button, a tool tip will appear after a short while, explaining precisely which direction is associated with the button in question.

Note that assigning directionality to a link may cause other links to automatically be directed. If, for example, there are undirected links between variables x and y, between y and z, and between x and z, then enforcing the directionalities x –> y and y –> z implies x –> z; otherwise, a directed cycle would occur.

## Ambiguous Regions

An ambiguous region consists of a set of inter-dependent uncertain links: Absence of a link in an ambiguous region depends on the presence of one or more of the other links of the region, and vice versa. For more information on ambiguous regions, see the help page of the previous page of the Learning Wizard. Each ambiguous region is easily identified as consisting of links in the same color. (Note that there can be so many ambiguous regions that colors have to be reused, making it difficult from the coloring alone to distinguish them.) Also, when selecting a link of an ambiguous region, all links of the region will be highlighted; the one selected will be drawn bold and the other links will be drawn with double lines.

When a link of an ambiguous region has been selected, the include/exclude link buttons get enabled:

When a decision has been made that a link should be present or absent, each of the other links of the ambiguous region will be affected in one of several ways:

- Unaffected.

- Disappear.

- Turned into an undirected link, not belonging to the region anymore.

- Turned into a directed link, not belonging to the region anymore.

Which of these consequence will be observed depends on the conditional independence and dependence statements (CIDs) found from the statistical tests performed by the NPC algorithm. For more information see the help page of the previous page of the Learning Wizard, or consult the references mentioned on that help page.

## Undo

Often it is impossible (or very hard) to predict the consequences of a decision made regarding directionality of an undirected link, or regarding the presence or absence of a link of an ambiguous region. Therefore, you will probably find the undo facility of the current page of the Learning Wizard quite useful. The most recent (non-undo) action performed can be undone by clicking the undo button:

Please note that an arbitrary number of operations performed can be undone by repeatedly clicking the undo button.

## Importing Information

Pressing the “Import”-button : , allows for import of all network information, such as node positions, labels, sizes, etc., from a net-file. This can be very useful, if the data relates to a network whose structure is known. In that case, you can simply import the labels and positions of the nodes. The learned network can then easily be compared to the existing one.

## p-Value

Whether or not there is going to be a link between a pair of variables, say A and B, in the independence graph learned from the data depends on the degree to which A and B are (conditionally) (in)dependent - if they are marginally dependent, there will be a link; otherwise there won’t be a link. This degree is quantified through so-called p-values associated with the hypothesis that the two variables are (conditionally) independent.

For each (small) set, C, of conditioning variables, a p-value for {A,B} is computed. This value expresses the probability that A and B are conditionally independent given C. The marginal p-value is the p-value corresponding to C={}.