Developer Guide for Intel® Data Analytics Acceleration Library 2019 Update 5

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: