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It is
mathematically easy to fit linear models to data.
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We
can learn a lot about model-fitting in this relatively simple
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case.
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There are many
ways to make linear models more powerful while
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retaining their
nice mathematical properties:
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By
using non-linear, non-adaptive basis functions, we can get
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generalised
linear models that learn
non-linear mappings from
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input
to output but are linear in their parameters – only the linear
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part
of the model learns.
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By
using kernel methods we can handle expansions of the raw
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data
that use a huge number of non-linear, non-adaptive basis
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functions.
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By
using large margin kernel methods we can avoid overfitting
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even
when we use huge numbers of basis functions.
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But linear
methods will not solve most AI problems.
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They
have fundamental limitations.
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