This tutorial introduces decision nets. These are Bayes nets where a form of utility (value, goodness) has been introduced, a set of decisions is possible, and it is desired to find the decisions that overall maximize the measure of utility.

With Netica, decision nets are the same as regular Bayes nets, except that two additional types of nodes are present, decision nodes and utility nodes. In a regular Bayes net, all the nodes are called nature nodes because they have only to do with modeling the nature or reality of the world, the likelihood of its being in any of its possible states. The concept of utility and the concept of decision are seen as outside of merely depicting reality, being more in the realm of goals, desires, and agendas.

Let us look at our first decision net to see what decision and utility nodes look and behave like.

The following net is a classic in the decision net literature. It is called Umbrella, and is due to Ross Shachter. It's purpose is to help us decide whether we should take our umbrella today, based on today's weather forecast.

There is a link from Weather to Forecast capturing the believed correlation y between the two (perhaps based on previous observations). There is a link from Forecast to Umbrella indicating that the decision maker will know the forecast when he makes the decision, but no link from Weather to Umbrella, since if he knew for certain what the weather was going to be, it would be easy to decide whether or not to take the umbrella.

The net has two nature nodes representing the weather forecast in the morning (sunny, cloudy or rainy), and whether or not it actually rains during the day (rain or no_rain). It has a decision node of whether or not to take an umbrella, and a utility node that measures the decision maker's level of satisfaction.

Visualization Note. In Netica, to aid in distinguishing them, decision and utility nodes are drawn somewhat differently than nature nodes. Utility nodes are typically drawn as six-sided figures, while decision nodes are typically drawn as rectangles with a distinctive colored background. The exact display properties depend on the display style. You can try out different visualizations using the "Style" menu.

Utility nodes are quite straightforward. They contain a table of utility values (in whatever units you want), one for each combination of parents for that node. Basically this is saying, this is how we value each of the possible worlds represented by my parents. Here is the utility table for the "Satisfaction" node in our net. (You can see the table by raising the node's dialog and clicking on "Table", or by selecting the node and clicking on the relation button: .)

Notice that because there are links from Weather and Umbrella to Satisfaction, there are four entries in our table, one for each combination of the weather being sunny or rainy, versus us taking our umbrella or not. The utility numbers in the table are based on our own private scale of relative happiness. We are most happy when it is not raining and we don't have to take an umbrella, and we assign this a measure of 100. We are next happiest when it is raining and we do take an umbrella: utility=70. We dislike carrying an umbrella on a sunny day: utility=20. And, we are most annoyed if it is raining and we didn't take the umbrella: utility=0. So, let us compile the net and see how it can help us decide to take the umbrella or not.

With the belief-bar style turned on, and the net compiled, the net looks like this.

The probabilities assigned to the weather are just the prior probabilities for weather in our area. We have not received a forecast yet. The number beside each decision choice indicates the expected utility of making that choice. The concept of "expected utility" or "expected value" is an old one. It is simply the number you get by multiplying the utility of an event by the probability of that event. Thus ExpectedUtility(A) = Utility(A) x p(A).

So in looking at our decision net, we can see that, without any weather forecast, that is with no evidence yet entered in the net, the expected value of taking the umbrella is 35, while that for leaving it at home is 70. Clearly the best choice given the available information is to leave the umbrella at home.

Now suppose we do get some information. We listen to the radio and the forecast is for sun. So we enter that value in our nature node, Forecast. The result is:

Try entering values for each of the other types of weather forecast and see how that affects our optimal decision, as depicted in the decision node. The decision net should tell you that only if the forecast is for rain, should we take our umbrella.

Of course, it cannot be overemphasized that these recommendations are a combination of both the nature model (the nature nodes) and the valuation we place on the possible worlds in that model. If we change our valuation, the best decisions could change. As an exercise, try changing the utility values in the Satisfaction node. Suppose you are a freedom loving mountain man, so you don't mind getting wet very much, but you hate being encumbered by an umbrella. In that case your best bet might be to not ever bother with carrying an umbrella, and rather just take your chances at getting wet. It's only water. You'll just dry off by the fire!

Decision nets combine both a scientific component (the world, its states, and their relative likelihood), and a value component (how we like those states). Getting a handle on the scientific component, though sometimes difficult, is at least a well-defined process. It is a matter of proper scientific method: clear definition of variables and their states, quantifiable measurements of observables, etc. Getting a handle on the value component can sometimes be more difficult, if there is not clear way to measure it. Sometimes, money is used as a measure, but a dollar can be worth more to one person than another, and its value is also relative to the amount of money its recipient already has. In the final analysis, we must acknowledge that utility and value are subjective, psychological concepts and are thus intrinsically less easy to observe and measure. But a decision net will only be as valuable as the quality of both its scientific and its valuation components, so be sure you can justify both components, before trusting the net's decisions.

Decision theorists have devised several "tricks" for helping people to quantify subjective values. Here are some of the simpler ones you may find useful:

1. Bidding auction.

For additional reading on this subject, check any good textbook on Decision Theory.