Data Dependences
The Data Dependences page of the Learning Wizard allows you to
investigate the strengths of the marginal dependences between pairs of
variables, using a slider.
Please note that the actions performed in the Data Dependences page
have no effect on the resulting Bayesian-network model. The purpose
of this Data Dependences page is only to gain insight into the
strenghts of the pairwise dependences.
The Data Dependences page of the Learning Wizard initially shows the
independence graph learned from data. This graph is directed, but with
no directed cycles (i.e., it's a DAG). The DAG represents the
conditional and marginal dependences and independences found in the
data. The links, however, cannot necessarily be interpreted as causal
links. The directions of the links only ensure that the dependences
and independences found can be read from the DAG, using e.g. Pearl's
d-separation criterion.
Notice that the DAG is learned only indirectly, based on measures of
conditional and marginal dependences and independences found in the
data.
To further investigate the dependences and independences found in the
data, an undirected graph can be shown, where each link represents a
marginal dependence with strength
larger than one minus the current slider value. To see how to switch
between the directed and the undirected graphs, see the description of
the toolbar.
The Data Dependences page contains a toolbar, including the following
functionalities:
This function displays a directed independence graph (i.e., a DAG).
The DAG gets displayed by pressing the button 
Please note that the Show Directed Graph and the Show Undirected Graph
modes are mutually exclusive (i.e., the two associated buttons act as
a couple of radio buttons).
This function displays an undirected independence graph. This graph is
not necessarily identical to the directed graph with the directed
links replaced by undirected ones. Each link in the undirected graph
represents a marginal dependence
with strength greater than one minus the current slider value. The
undirected graph gets displayed by pressing the button 
As mentioned above, please note that the Show Directed Graph and the
Show Undirected Graph modes are mutually exclusive (i.e., the two
associated buttons act as a couple of radio buttons).
This function gives you the opportunity to show the must-exist links
specified in the Structural Constraints page. These links are
shown/hidden by pressing the toggle button 
Please note that whenever this toggle button is selected the slider
gets disabled to avoid overlaps between enforced links and links
appearing and disappearing during sliding.
This function gives you the opportunity to show the must-not-exist
links specified in the Structural Constraints page. These links are
shown/hidden by pressing the toggle button 
Please note that whenever this toggle button is selected the slider
gets disabled to avoid overlaps between enforced non-links and links
appearing and disappearing during sliding.
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={}.
The marginal dependence
between A and B is defined as one minus the marginal p-value
associated with {A,B}. Thus, a marginal dependence of 0 means that
A and B are completely independent, and 1 means that they are
completely dependent.
The current slider value represents a threshold such that only links
in the current (directed or undirected) graph with marginal p-values less than the threshold are
shown (or, equivalently, links with marginal dependence greater than one
minus the threshold value). Thus, the slider provides a means of
detecting the marginal strengths of the links. This can be very useful
in determining which links should be forced to be included (see the
help page for the Structural Constraints page of the Learning Wizard
for a more detailed discussion of this issue).
The value of the lower endpoint of the slider can be decreased by
pressing the button
or by dragging the slider ticks
downwards, using the mouse.
Please note that the minimum value of the lower endpoint of the slider
equals the maximum of the smallest floating point number available and
the smallest marginal p-value over all links in
the graph.
The value of the lower endpoint of the slider can be increased by
pressing the button
or by dragging the slider ticks
upwards, using the mouse.
Please note that the maximum value of the lower endpoint of the slider
equals 1E-10.
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.