Prior Knowledge

Before the Learning Wizard learns the marginal and conditional probabilites from the data, it is possible to specify prior distributions for the variables.

This is useful if prior knowledge about the (conditional) distributions for (some of) the variables exists. It is possible to include such knowledge in the model before the marginal and conditional probabilities are learned. By including the knowledge before the learning, the resulting probabilities will be based on both the prior knowledge and the data. The weight of the prior knowledge is inserted by specifying experience counts.

An example of the use of both prior probability distributions and their experience counts is given in the last part of this text.

Specifying Prior Conditional Probabilities

Prior distributions can be specified separately for each variable in the learned structure. When a variable is selected in the “Variable” combo box, its conditional probability table is displayed, and the prior distributions can be entered.

It is possible to either randomize or reset the prior probabilites. This is done by using the appropriate button at the bottom of the panel.

Randomizing the probability distributions can be used to test the “robustness” of the results found from data with missing values. The randomized probability distributions are used as the base when learning the probabilities. Since each missing value is found by looking at the current conditional probability table (after propagation of all evidence from the case), a randomized prior probability distribution may affect the outcome of the learning. If a node has a model, then the conditional probability table corresponding to the expressions specified in the model is generated.

Specifying Experience Counts

Experience counts are specified in the same manner as the prior conditional probabilities. That is, the variable for which experience counts are to be inserted is selected from the “Variable” combo box, and experience counts are entered for each parent configuration.

It is also possible to reset one or all of the experience tables by pressing one of the buttons, as was the case for the prior probability tables. However, it does not make sense to randomize the experience counts. Instead, it is possible to delete and (obviously) create experience tables.

If a variable does not have an experience table, its probability table will not be altered during the learning process. That is, if the distribution of a variable is known with 100 % accuracy, the experience table can be deleted. This will speed up the learning process a bit.

Experience tables are implicitly only when the “Prior Knowledge” step is performed as a step of the Learning Wizard (and not as a step of the EM Learning Wizard).

Prior Distribution Example

In this example, the data contains information on the fairness of two brands of six-faced dice. The data includes 1000 cases.

Die B, say, is a completely new brand of which nothing is known, and die A is a well known brand, which has always scored high on fairness.

To incorporate this knowledge into the learned domain, nothing is entered into the tables of die B. This will let the resulting probabilites depend solely on the data.

For die A, we will enter the value 0.1666 (one sixth) in all the fields, thus specifying fairness (note that we might as well have left the fields at 1, since the values are normalized so that they will sum to 1; what is important is that the values are all equal).

This, however, is not enough. It only describes part of our knowledge. We should also specify our confidence in the fairness of die A. This is done by selecting the “Experience”-pane, and entering experience counts in the table.

The entered experience counts will determine the weight of the inserted knowledge compared to the data. If we want to let the data have the same weight as the inserted knowledge, we should specify an experience count of 1000. This value tells the learning algorithm that the inserted knowledge has the weight of 1000 cases (and thus the same weight as the data). That is, the more confidence we have in the prior knowledge, the higher the experience counts should be set.