This tutorial shows how to implement a small object-oriented Bayesian network (OOBN) in HUGIN GUI. The OOBN we are about to construct is the one modeled in the Diseases example in the Basic Concepts section. Two other tutorials are available: In the second tutorial we show how to construct the Apple Tree example from the Basic Concepts section, and in the third tutorial we will extend this example to an influence diagram.

The qualitative (or structural) representation of our OOBN is shown in Figure 1. In this tutorial, we shall ignore the specification of the CPTs.

Figure 1: OOBN representing the Diseases problem

If you want to understand the design of this OOBN, you should read about it in the Basic Concepts section. Were we to construct this time-sliced network as a BN, we would get the network shown in Figure 2.

Figure 2: BN representation of the Diseases problem

Creating the Time-Slice Model
A BN is a special case of an OOBN. What makes a network an OOBN is the existence of instance nodes (i.e., nodes that represent instances of other networks). Thus, we start out by creating a new empty network by selecting the "New" menu item in the "File" menu. This gives us a new network window containing an empty network called "unnamed ", where x is some integer. It starts up in Edit Mode which allows us to start constructing the OOBN immediately (the other main mode is Run Mode which allows you to use the OOBN).

In Figure 2, we observe that each of the three time slices contains four nodes: D1, D2, S1, and S2, where D1 and D2 represent two different diseases with states "Present" and "Absent", and S1 and S2 represent symptoms that both may be observed as consequences of each of the diseases. We shall assume that S1 and S2 represent symptoms with two possible outcomes, "Observed" and "Unobserved". As each of the time slices are identical, both at the qualitative (or structural) level and quantitative level (i.e., the CPTs are identical, including those that describe the temporal aspect, namely P(D1_2|D1_1), P(D2_2|D2_1), etc.), we need only construct a model describing a generic time slice and then connect three instances of this network.

Creating the Nodes
First, we construct the generic time-slice model, containing the four nodes D1, D2, S1, and S2. The nodes all represent discrete chance variables. Therefore, we select the Discrete Chance Tool and create the four nodes by clicking the left mouse button at four different locations in the network pane while keeping the Shift key down (to avoid reselecting the tool for each node). We then change the default names of the nodes and their default state names using the Node Properties pane. Second, we select the Link Tool and create the link from D1 to S1 by dragging the mouse cursor (i.e., pressing the left mouse button and moving the mouse cursor while keeping the button pressed) from a point inside D1 to a point inside S1 and then releasing the mouse button. Again, we keep the Shift key pressed, and create the other three links in the same manner. The result is illustrated in Figure 3.

Figure 3: BN for a single time slice of the Diseases problem

Output Nodes
Now, in order for a network for a single time-slice have parent nodes in the immediately preceding network, we need to be able to refer to nodes outside the network in Figure 3. In a conventional BN, this is not possible. Thus, as D1 and D2 are going to be parents of D1 and D2, respectively, in the next time slice, we must declare D1 and D2 as output nodes, making them visible outside the network (or rather through instances of the network).

Input Nodes
Also, in the network in Figure 3, we should be able to specify the temporal aspect, namely the CPTs P(D1|D1 prev) and P(D2|D2 prev), where the nodes "D1 prev" and "D2 prev" are placeholder nodes for D1 and D2, respectively, in the immediately preceding time slice. Such placeholder nodes are referred to as input nodes, and shouldn't be confused with real nodes. A real node, which is type consistent with an input node, can be bound to that input node. That is, an input node becomes identical with the node that is bound to it. However, if an input node hasn't got a binding associated with it, the network containing the input node can still be used (i.e., compiled in to a junction tree and used for inference). In that case the input node is treated as a real node. That is, each input node has a CPT associated with it just as any ordinary node, but this CPT is used only if no nodes have been bound to the input node in a network containing an instance of the network in which the input node is defined.

Input nodes and output nodes are collectively referred to as interface nodes.

Creating the Interface Nodes
Now, let's try to put all this into practice. First, we declare D1 and D2 as output nodes. This is done by clicking the "Output" check box in the Node Properties pane for each of them. The color of the D1 and D2 then changes the the selected color for interface nodes (as set in the Network Properties pane) to indicate their new status as output nodes.

To create the two input nodes, "D1 prev" and "D2 prev", we first create two ordinary nodes and set their names to D1_prev and D2_prev (and/or their labels to "D1 prev" and "D2 prev"), respectively, in the Node Properties pane. Also, in the Node Properties pane for each of these two new nodes, we click the "Input" check boxes to declare them as input nodes. Similar to D1 and D2, the color of "D1 prev" and "D2 prev" changes the the selected color for interface nodes. In addition, the appearance of the borders of "D1 prev" and "D2 prev" changes from solid to dashed, which indicates that they are not real nodes.

Finally, we create links from "D1 prev" and "D2 prev" to D1 and D2, respectively. The result of these operations appear in Figure 4.

Figure 4: BN for a single time slice of the Diseases problem, including specifications of interface nodes

Creating the Diseases Model

Figure 5: The network pane contains the three instance nodes that represent three instances of the time-slice model shown in Figure 4

Each instance node appear as a rectangle with rounded corners. We note that the nodes declared as interface nodes in the generic time-slice model appear in each of the instance nodes. The input nodes appear in a row at the top of the instance node, and, similarly, the output nodes appear at the bottom of the instance node.

Next, we need to bind the output nodes of instances DiseasesSlice_1 and DiseasesSlice_2 to the input nodes of instances DiseasesSlice_2 and DiseasesSlice_3, respectively. This is done by creating links (via the Link Tool) from the output nodes to the corresponding input nodes. The resulting model appears in Figure 6.

Figure 6: The output nodes of an instance are bound to input nodes of another instance using the Link Tool

Obviously, the model would look nicer if the order of appearance of the input nodes were reversed. If we select the Select Tool, we can easily alter the order of appearance of the interface nodes. We move an interface node one position to the left (right if the Shift key is down) by placing the mouse cursor on top of the interface node and clicking the left mouse button. After reordering the network appears as in Figure 7.

Figure 7: The order of appearance of interface nodes can be altered through simple mouse clicks

Finally, it is often desireable to be able to collapse one or more of the interface nodes in order to hide away irrelevant details, thereby making the network much less cluttered. Again, if we activate the Select Tool, we can collapse (expand) an expanded (collapsed) instance node, simply by clicking the left mouse button right outside the node. Alternatively, we can choose the "Collapse Instance Nodes" ("Expand Instance Nodes") menu item in the "View" menu, which collapses (expands) all instance nodes.

The OOBN in Figure 7 with the instance nodes collapsed appear in Figure 8.

Figure 8: The OOBN in Figure 7 with the instance nodes collapsed

Compiling the OOBN
Now, assuming the CPTs of the time-slice model in Figure 4 has been filled in (see the tutorial on BNs for details), it is the time to compile the network and see how it works:

Running the OOBN
In Run Mode, the network window is split into two by a vertical bar (see Figure 10). To the left is the node list pane and to the right is the network pane.

Figure 10: The network window in Run Mode. To the left is the node list pane (with all nodes collapsed) and to the right is the network pane

You can view the probabilities of a node being in a certain state by expanding the node in the node list pane. You expand (collapse) a node by clicking its plus (minus) icon in the node list pane. A node can also be expanded (collapsed) by selecting (deselecting) it in the network pane. You can also expand (collapse) all nodes at once by pressing the expand (collapse) node list tool in the tool bar just to the right of the node properties tool.

Unlike basic nodes, instance nodes don't have belief monitors associated with them, as they represent entire (sub)networks. Instead we must expand the instance node, whereby we get to see the list of nodes of the (sub)network that the instance node represents (see Figure 11).

Figure 11: The nodes of the network represented by an instance node, get displayed in the node list pane when the instance node gets selected

 

For more details on the Run Mode, please see the tutorial on BNs.

This finishes the third tutorial.