Controlling values of variables

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Controlling values of variables

In causal probabilistic models, there is an additional class of inference problems: Predicting the effects of external intervention. In the context of Bayesian networks, computing the effects of observations amounts to belief updating after setting evidence for the observed network variables. The effect of intervention, on the other hand, is a change in the network structure, related to external manipulation of the system modeled by the network, followed by setting the values of the manipulated nodes and updating beliefs.

We will explain control values with the help of the following example:

Consider a model for the operational status of a Command Center. The command center depends on the status of Communications and Radar. Radar depends on the Antenna Structure and the power supplied by the Generator. Communications rely on the power supplied by Generator. The Generator relies on Fuel Supply to generate power.

We have created a Bayesian network that models these causal relations.

This network is included among the example models as CommandCenter.xdsl.

Once this network is loaded, you should see the following diagram in the Graph View.

command_center

Now suppose the model is an enemy's command center and the decision maker's objective is to disrupt its operations. We can act on the Communications by, for example, jamming its outgoing signal with noise. This can be viewed as an external intervention that results in Communications not working, i.e., essentially setting the value of variable Communications to state Absent.

Communications will be Absent regardless of the values of other variables in the network (and, in particular, its parent variable, Generator).

Control Value is used to model such type of situations.

Let us control the value of the Communications node to state Absent.

1. Right click on Communications node and select Control Value from the node's pop-up menu that appears.

2. Select Absent from the Control Value sub-menu.

command_center_manipulation

This action has the following effects:

Since the state of a controlled node does not depend on the value of its parents, there is a temporary change in the network structure. GeNIe shows this by dimming the arc connecting the parent nodes to the controlled node. In our case, the arc connecting Generator and Communications is dimmed as shown below:

command_center_manipulated

Now that we have controlled the value of the Communications node, GeNIe sets the value of the controlled node to the value imposed by the manipulation. So the value of Communications is set to Absent. To indicate that the node is controlled, GeNIe displays the control_value_icon status icon on the node. Note that the Communications node has the control_value_icon status symbol.

To inspect the effects of intervention, we will need to update the model. After updating the model, you can view the values of each node.

Notice that the intervention only changes the posterior probabilities of the descendants of the controlled node. The control value operation is not available for those nodes that have observed or manipulated descendants. Controlling the value of a descendant of an observed node would lead to a theoretical problem, which one could summarize briefly as a desire to modify the past.