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l1-norm penalized orthogonal forward regression
A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept
of leave-one-out mean square error (LOOMSE), by defining a new l1-norm penalized cost function in
the constructed orthogonal space and associating each orthogonal basis with an individually tunable
regularization parameter. Due to orthogonality, the LOOMSE can be analytically computed without
actually splitting the data set, and moreover a closed form of the optimal regularization parameter
is derived by greedily minimizing the LOOMSE incrementally. We also propose a simple formula for
adaptively detecting and removing regressors to an inactive set so that the computational cost of the
algorithm is significantly reduced. Examples are included to demonstrate the effectiveness of this new
l1-POFR approach
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