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Fitting a model
to data is typically done by finding the
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parameter values
that minimize some loss function.
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There are many
possible loss functions. What criterion
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should we use for
choosing one?
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Choose
one that makes the math easy (squared error)
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Choose
one that makes the fitting correspond to
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maximizing
the likelihood of the training data given
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some
noise model for the observed outputs.
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Choose
one that makes it easy to interpret the learned
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coefficients
(easy if mostly zeros)
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Choose
one that corresponds to the real loss on a
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practical
application (losses are
often asymmetric)
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