Belief updating and learning in semi qualitative probabilistic networks

One of the most exciting prospects in recent years has been the possibility of using Bayesian networks to discover causal structures in raw statistical data—a task previously considered impossible without controlled experiments.Consider, for example, the following intransitive pattern of dependencies among three events: are the effects is mathematically feasible but very unnatural, because it must entail fine tuning of the probabilities involved.The assumptions necessary for a causal interpretation of a Bayesian network will be discussed in Chapter 1.

This metric trades off network complexity against the degree of fit to the data, which is typically expressed as the likelihood of the data given the network.The desired dependence pattern will be destroyed as soon as the probabilities undergo a slight change.Such thought experiments tell us that certain patterns of dependency, which are totally void of temporal information, are conceptually characteristic of certain causal directionalities and not others.Data (usually scarce) is used as pieces of evidence for incrementally updating the distributions of the hyperparameters (Bayesian Updating).It is also possible to machine learn the structure of a Bayesian network, and two families of methods are available for that purpose.

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