Network bayésien

The Réseaux bayésiens are at the same time:

Of the models of representation of knowledge
Of the " machines with calculer" conditional probabilities

For a given field (for example medical), one describes the causal relations between variables of interest by a graph .

In this graph, the relations of cause for purpose between the variables are not deterministic, but probabilized . Thus, the observation of a cause or several causes systematically does not involve the effect or the effects which depend on it, but modifies only the probability of observing them.

The private interest of the networks bayésiens is to take account simultaneously of knowledge a priori of experts (in the graph) and of the experiment contained in the data.

The networks bayésiens are especially used for the diagnosis (medical and industrial), the analysis of risks, the detection of the Spam S and the dated mining.

A very simple example in the modeling of the risks

An operator working on a machine is likely to be wounded, if it uses it badly. This risk depends on the experiment of the operator and the complexity of the machine. “Experiment” and “Complexity” are two determining factors of this risk (fig. 1)

Of course, these factors do not make it possible to create a deterministic model. If the operator is tested, and the simple machine, that does not guarantee that there will be no accident. Other factors can play: the operator can be tired, disturbed, etc the supervening of the risk is always random, but the probability of supervening depends on the identified factors.

The diagram below represents the structure of causality of this model (graph).

The following represents the probabilisation of the dependence: it is seen that the probability of accident increases if the user is tested little or the complex machine.

One sees here how to integrate knowledge of expert (determining factors) and data (for example, the table of probability of accident according to the determinants can come from statistics).

Construction of networks bayésiens

To build a network bayésien it is thus:

To define the graph of the model
To define the tables of probability of each variable, conditionally with its causes.

The graph is also called the " structure" model, and tables of probabilities its " paramètres". Structure and parameters can be provided by experts, or calculated starting from data, even if in general, the structure is defined by experts and the parameters calculated starting from experimental data.

Use of a network bayésien

The use of a network bayésien is called " inférence". The network bayésien is then truly a " calculating machine probabilities conditionnelles". According to information observed, one calculates the probability of the data not observed. For example, according to the symptoms of a patient, one calculates the probabilities of various pathologies compatible with these symptoms. One can also calculate the probability of symptoms not observed, and deduce from them the complementary examinations most interesting.

Software bonds & Tools

Association for Uncertainty in Artificial Intelligence: http://www.auai.org/
Bayesia: http://www.bayesia.fr
Hugin: http://www.hugin.com
ProBayes: http://probayes.com
Netica: http://www.norsys.com
Elvira: http://leo.ugr.es/~elvira
Bayes Net Toolbox: http://bnt.sourceforge.net/
Structure Learning Package: http://bnt.insa-rouen.fr/
Bayesian-Programming.org: Probabilities like alternative to logic for perception, the inference, the training and the action]

Reading

the networks bayésiens , P. Naïm, P. Wuillemin, P. Leray, O. Pourret, A. Becker, Eyrolles 2004 http://www.eyrolles.com/Sciences/Livre/9782212111378/livre-reseaux-bayesiens.php

See too

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