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Parallelism is featured by allowing several classifiers to be overlapping, that is,
to be localised partially in the same areas of the input space. Hence, they compete
locally by providing different models for the same data, and cooperate globally
by providing a global model only in combination. Coordination of the different
classifiers is handled on one hand by the model component that combines the
local models into a global model, and on the other hand by the model structure
search that removes or changes classifiers based on their contribution to the full
model.
Credit assignment is to assign external reward to different classifiers, and is
mapped to regression and classification tasks that fit the model to the data, as
the reward is represented by the output. In sequential decision tasks, credit assi-
gnment is additionally handled by the reinforcement learning algorithm, which
will be discussed in detail in Chap. 9.
Lastly, the role of discovering new rules, that is, classifiers with a better
localisation, is performed by the model structure search. How to use current
knowledge to introduce new classifiers depends strongly on the choice of repre-
sentation for the condition and action of a classifier. As the presented work
does not make any assumptions about the representation, it does not deal with
this issue in detail, but rather relies on the body of prior work (for example,
[41, 38, 163, 144, 147, 203]) that is available on this topic.
3.3
Summary and Outlook
The task of LCS has been identified to find a good model that forms a hypo-
thesis about the form of the data-generating process, based on a finite set of
observations. The process maps an input space into an output space, and the
model provides a possible hypothesis for this mapping. The task of finding a
good model is made more complex as only a finite set of observations of the in-
put/output mapping are available that are perturbed by measurement noise and
the possible stochasticity of the process, and this task is dealt with by the field
of model selection. The difference between minimising the expected risk, which
is the difference between the real data-generating process and our model, and
minimising the empirical risk, which is the difference between the observations
available of that process and our model, has been emphasised.
Regression, classification and sequential decision tasks differ in the form of the
input and output spaces and in the assumptions made about the data-generating
process. For both regression and classification tasks it is assumed that the process
to be representable by a smooth function with an additive zero-mean noise term.
While sequential decision tasks as handled by RL also have a regression task at
their core, they have special requirements on the stability of the learning method
and therefore receive a separate treatment in Chap. 9.
A model was characterised as being a collection of possible hypotheses about
the nature of the data-generating process, and training a model was defined
as finding the hypothesis that is best supported by the available observations of
that process. The class of parametric models was introduced, characterised by an
 
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