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Chapter 2 : Exploiting the bayesian network
2.1 Inference and monitoring
With the modeling phase completed, we now turn to the validation mode in order to put the Bayesian network to use. To do this, we can click on the bottom left corner of the worksheet on the Validation icon, or we can use the «F2» function key («F1» allowing then to switch back to the modeling mode), or we can do that by using the View menu:
This mode gives access to the monitoring tool that allows seeing the probabilities of the different states of a variable, allows assigning a value to a variable with certainty (we call that an Evidence), and also allows assigning likelihood degrees to the states (Soft and Negative Evidences). As soon as the set of observations is modified, the probabilities of every node are updated to take the new information into account.
Monitoring lets the specialist verify the Bayesian network's consistency (choice of arcs, nodes and conditional probabilities) and measure the probabilistic interactions between the variables by using What If scenarios.
Access to the monitor of a given variable can take place in one of two ways: by right clicking on the variable (which opens the contextual menu associated to the node), or simply by double left clicking on the variable.
To illustrate the use of the monitors, let's suppose that the specialist wants to verify the «logical or» TbOrCa. He or she will monitor this variable as well as its father nodes (Tuberculosis and Cancer). Here is a part of the approach for verifying a logical 'Or':
The three monitors of the nodes being verified
The probabilities that are displayed with their exact values appear in bold face. If not, the exact value can be displayed in a tool tip by pressing the «V" key while pointing on the monitor. If we set the probability of Cancer to True at 100%, then the state value of TbOrCa becomes True with a probability of 100%. Conversely, if we set the probability of Tuberculosis to True at 100%, then the state value of TbOrCa becomes True with a probability of 100%., For this, all that we have to do is double click on the corresponding states in the monitors (or thanks to the monitor contextual menu, by right clicking on it and then select the desired value) and then verify the results of this action on the variable TbOrCa:
This is a way to verify, in part, that the logical 'Or' is working properly.
It is also possible to use the Soft Evidences to test the impact of TbOrCa on Cancer and Tuberculosis. There are two ways to activate the likelihood edition mode; by using the contextual menu associated to the monitor, or by pressing the < Shift > key while clicking on a modality. Once this mode is activated, the likelihood can be set by using the mouse or directly by entering the exact value. The green button validates the likelihoods and triggers the inference process that will update the probability distribution of TbOrCa, and then the probability distributions of Cancer and Tuberculosis.
2.2 Adaptive questionnaires (based on the target or on a state)
2.2.1 Adaptive Questionnaire based on a target variable
Here we are concerned with automatically and dynamically organizing the monitors (each time the set of observations is modified) while taking into account what information is being contributed to the knowledge of the target variable and the corresponding cost of the questions.
Adaptive questionnaires are only available in Validation mode: by launching the assistant from the Inference Menu.
This assistant allows:
to select the target variable,
to indicate if the questionnaire has to be oriented toward a specific target modality (cf. paragraph 2.2.2),
to reset or not the set of observations prior to the first ordering of the monitors, and lastly
to set the number of questions to display (i.e. number of monitors).
to launch the edit cost interface.
First we see the pink monitor which corresponds to the target variable. Then the monitors optimally ordered with respect to their cost and to the information they bring to the knowledge of the target value. In the first step below, the best question to ask to the patient is «Dyspnea». If this question cannot be asked or answered, the second one concerns the age, and so on. Without cost, it’s obvious that the best thing to do is an X-ray.
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When observing True for Dyspnea, all the other probabilities are updated to take into account this new information and the monitor are then re-ordered. The arrows that appear on the monitors are used to show the variation between the probabilities before and after the observation.
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As the patient smokes, the better question to ask is now Bronchitis and not, as initially estimated, performing an X-ray)
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2.2.2 Adaptive questionnaire based on a particular state of the target variable
This questionnaire is similar to the previous one but the questions' worth is measured on the knowledge of a particular value of the target variable, and not on the global knowledge of that variable. When the target is a variable only having two states, then these two questionnaires are equivalent.
2.3 Batch Exploitation
Except the adaptive questionnaire that makes it possible to exploit, in an interactive way, the Bayesian models, BayesiaLab proposes a tool for Batch exploitation (Inference menu- Batch Exploitation). This function takes a data base as input and allows using the Bayesian network to infer, for each line of the case base, the most probable value of the target variable with respect to the values of the other variables on the corresponding line. An assistant allows defining which fields will be included in the output file, some fields being sometime not taken into account in the Bayesian network but necessary in the output file (as for example the identifiers).
Two other fields are automatically added to the output file, the value of the predicted target value ($) and the probability of that modality ($$).
| N° | Age | $Cancer | $$Cancer |
| 1 | 89.05831 | False | 0.9998265758014836 |
| 2 | 54.47454 | False | 0.9999700205169252 |
| 3 | ? | False | 0.9997925521626105 |
| 4 | 93.48285 | False | 0.9998265758014836 |
| 5 | 42.232517 | False | 0.9999147468451574 |
| 6 | 45.99444 | False | 0.9998176641092605 |
| 7 | 80.94802 | False | 0.9998265758014836 |
| 8 | 30.676228 | False | 0.9999932134767724 |
| 9 | 65.22123 | False | 0.9998265758014836 |
| 10 | 68.29758 | False | 0.9998265758014836 |
| 11 | 47.897926 | False | 0.9999700205169252 |
| 12 | 49.40997 | False | 0.9999700205169252 |
| 13 | 95.25699 | False | 0.9992836641506526 |
| 14 | 35.907204 | False | 0.999996156376072 |
2.4 Improving the Bayesian network
Our specialist now has a Bayesian network that he can use thanks to the tools provided by BayesiaLab. If desired, this Bayesian network can be refined by learning on new data (cf. chapter 3 for the association of a data base to an existing Bayesian network, Associate Data Source) corresponding to new patients treated. In this way, the Bayesian network is constantly evolving.