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The concept of the sample space and the events of an experiment are also studied.
Let X be the sample space: and at be the label set:.
On the one hand, it only employs probabilities over sample space, and avoids putting probabilities over statistical hypotheses.
The proposed method utilizes global information about each class of training sample space and can generate RBF hidden neurons incrementally to adapt the sample space.
To generate valid Gaussian kernel functions, we find the most densely region in the sample space and then establish a Gaussian kernel to cover the region.
Hypothesis tests and estimations are sometimes criticised because their results generally depend on the probability functions over the entire sample space, and not exclusively on the probabilities of the observed sample.
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Indeed, in the modern axiomatic theory of probability, which eschews a definition of probability in terms of "equally likely outcomes" as being hopelessly circular, an extended form of equation (1) plays a basic role (see the section Infinite sample spaces and axiomatic probability).
The period of flame growth is prolonged with decreasing sample spacing and finally, at a small enough sample spacing, the flame distance keeps increasing until the flame disappears.
The nonlinear kernel mapping can improve the separability of sample spaces, and a nonlinear BP classifier can then supply a better classification surface.
Given the connection between sample spaces and event algebras as defined above, one sees that the event algebra of a refined sample space is larger than the original event algebra: i.e., it contains all the original projectors and others in addition; conversely, a coarsening leads to a new event algebra which is a subset of the old event algebra.
The introduction of the crossover elitist preservation strategy can increase the sampling space and the competition among individuals.
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