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Published in:
2009 | OriginalPaper | Chapter
Efficient Hold-Out for Subset of Regressors
Authors : Tapio Pahikkala, Hanna Suominen, Jorma Boberg, Tapio Salakoski
Published in: Adaptive and Natural Computing Algorithms
Publisher: Springer Berlin Heidelberg
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Hold-out and cross-validation are among the most useful methods for model selection and performance assessment of machine learning algorithms. In this paper, we present a computationally efficient algorithm for calculating the hold-out performance for sparse regularized least-squares (RLS) in case the method is already trained with the whole training set. The computational complexity of performing the hold-out is
, where
is the size of the hold-out set and
n
is the number of basis vectors. The algorithm can thus be used to calculate various types of cross-validation estimates effectively. For example, when
m
is the number of training examples, the complexities of
N
-fold and leave-one-out cross-validations are
O
(
m
3
/
N
2
+ (
m
2
n
)/
N
) and
O
(
mn
), respectively. Further, since sparse RLS can be trained in
O
(
mn
2
) time for several regularization parameter values in parallel, the fast hold-out algorithm enables efficient selection of the optimal parameter value.