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Abstract:
In Gaussian process regression the covariance between the
outputs at input locations
x
and
x'
is usually assumed to depend on the distance
(x - x'
)
T
W
(
x - x'
), where
W
is a positive definite matrix.
W
is often taken to be diagonal, but if we allow
W
to be a general positive definite matrix which can be tuned on the
basis of training data, then an eigen-analysis of W shows that we
are effectively creating hidden features, where the dimensionality
of the hidden-feature space is determined by the data. We
demonstrate the superiority of predictions using the general matrix
over those based on a diagonal matrix on two test problems.
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