The modern paradigm for data compression is modeling followed by
coding. Within this paradigm the problem of optimal coding with respect
to a model is fully solved. Inductive modeling techniques used for
compression operate despite considerable noise, employ positive
examples only, and yet effectively identify sources of the kind that
are encountered in practice.
The problem of data compression provides an excellent test-bed for
inductive modeling. It allows one to assess the merits of adaptive
as opposed to non-adaptive approaches. For example, it can be shown
that the penalty incurred by adaptation is less than the cost of
transmitting an explicit model for the source. It also illustrates
that modeling criteria such as "identification in the limit" may
be inappropriate because typical sources have time-varying
characteristics. In practice speed of convergence is just as important
as asymptotic performance.
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