Developer Guide

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Coordinate Descent algorithm

The Coordinate Descent algorithm follows the algorithmic framework of iterative solver with one exception: the default method (
defaultDense
) of Coordinate Descent algorithm is a case of the iterative solver method with the batch equal to the number of observations in the training data set.
Set of intrinsic parameters
S
t
is empty. Algorithmic-specific transformation
T
, and algorithm-specific vector
U
and power
d
of Lebesgue space [ Adams2003 ] are defined as follows:
  1. Define the index
    j
    to update the component of a coefficient as a remainder in the division of the number of current iteration (
    t
    ) by the number of features in the training data set (
    p
    ):
    j
    = mod(
    t
    ),
    p
    Alternatively, if ‘selection’ parameter was set to ‘random’, generate
    j
    randomly.
  2. If
    stepLengthSequence
    was not provided by user, compute the learning rate:
    (diagonal element of the Hessian matrix)
  3. Update the j-th component of vector
    :
    Note: for example, if a non-smooth term
    , where
    p
    is the number of features in the training data set, the objective function should compute prox operator as follows:
Convergence check is performed each
p
iterations:
  • For
    , the infinity norm (
    )
    is defined as follows:

Product and Performance Information

1

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Notice revision #20110804