Developer Guide and Reference

  • 2021.4
  • 09/27/2021
  • Public Content
Contents

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.

Details

The aet of intrinsic parameters LaTex Math image. is empty. Algorithmic-specific transformation
T
, algorithm-specific vector
U
, and power
d
of Lebesgue space [Adams2003] are defined as follows:
LaTex Math image.
  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
    ): LaTex Math image.
    Alternatively, if
    selection
    parameter was set to
    random
    , generate
    j
    randomly.
  2. If
    stepLengthSequence
    was not provided by the user, compute the learning rate: LaTex Math image. (the diagonal element of the Hessian matrix)
  3. Update the
    j
    -th component of vector LaTex Math image.:
    LaTex Math image.
    Note: for example, if a non-smooth term LaTex Math image., where
    p
    is the number of features in the training data set, the objective function should compute prox operator as follows:
    LaTex Math image.
Convergence check is performed each
p
iterations:
  • LaTex Math image., LaTex Math image.
  • For LaTex Math image., the infinity norm (LaTex Math image.) is defined as follows:
LaTex Math image.

Computation

Coordinate Descent algorithm is a special case of an iterative solver. For parameters, input, and output of iterative solvers, see Iterative Solver > Computation.
Algorithm parameters
In addition to the input of a iterative solver, Coordinate Descent algorithm accepts the following parameters:
Parameter
Default Value
Description
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
Performance-oriented method.
engine
SharePtr< engines:: mt19937:: Batch>()
Pointer to the random number generator engine that is used internally during each iteration to choose a random component of the minimum result vector to be updated.
positive
false
A boolean value. When set to
true
, it forces the coefficients to be positive.
selection
cyclic
Value that specifies the strategy of certain coordinate selection on each iteration. Except for default
cyclic
value, Coordinate Descent also supports:
  • random
    – on each iteration the index of coordinate is selected randomly by the engine.
skipTheFirstComponents
false
A boolean value. When set to
true
, Coordinate Descent algorithm will skip the first component from optimization.

Examples

C++ (CPU)
Java*
There is no support for Java on GPU.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.