Developer Guide and Reference

  • 2021.3
  • 06/28/2021
  • Public Content
Contents

Mean Squared Error Algorithm

Mean Squared Error Algorithm is not supported on GPU.

Details

Given LaTex Math image., a set of feature vectors LaTex Math image., and a set of respective responses LaTex Math image., the mean squared error (MSE) objective function LaTex Math image. is a function that has the format:
LaTex Math image.
LaTex Math image.
LaTex Math image.
In oneDAL implementation of the MSE, the LaTex Math image. is represented as:
LaTex Math image.
For a given set of the indices LaTex Math image., LaTex Math image., LaTex Math image., LaTex Math image., the value and the gradient of the sum of functions in the argument
x
respectively have the format:
LaTex Math image.
LaTex Math image.
where
LaTex Math image.
LaTex Math image.
LaTex Math image.

Computation

Algorithm Input
The mean squared error algorithm accepts the input described below. Pass the
Input ID
as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID
Input
argument
A numeric table of size LaTex Math image. with the input argument LaTex Math image. of the objective function.
data
A numeric table of size LaTex Math image. with the data LaTex Math image..
dependentVariables
A numeric table of size LaTex Math image. with dependent variables LaTex Math image..
Optional Algorithm Input
The mean squared error algorithm accepts the optional input described below. Pass the Optional
Input ID
as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID
Input
weights
Optional input. Pointer to the LaTex Math image. numeric table with weights of samples. The input can be an object of any class derived from
NumericTable
except for
PackedTriangularMatrix
and
PackedSymmetricMatrix
.
By default, all weights are equal to
1
.
gramMatrix
Optional input. Pointer to the :mathL`p times p` numeric table with pre-computed Gram matrix. The input can be an object of any class derived from
NumericTable
except for
PackedTriangularMatrix
and
PackedSymmetricMatrix
.
By default, the table is set to empty numeric table.
Algorithm Parameters
The mean squared error algorithm has the following parameters. Some of them are required only for specific values of the computation method parameter method:
Parameter
Default value
Description
penaltyL1
0
The numeric table of size LaTex Math image. with L1 regularized coefficients.
penaltyL2
0
The numeric table of size LaTex Math image. with L2 regularized coefficients.
interceptFlag
true
Flag to indicate whether or not to compute the intercept.
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
Performance-oriented computation method.
numberOfTerms
Not applicable
The number of terms in the objective function.
batchIndices
Not applicable
The numeric table of size LaTex Math image., where
m
is the batch size, with a batch of indices to be used to compute the function results. If no indices are provided, the implementation uses all the terms in the computation.
This parameter can be an object of any class derived from
NumericTable
except for
PackedTriangularMatrix
and
PackedSymmetricMatrix
.
resultsToCompute
gradient
The 64-bit integer flag that specifies which characteristics of the objective function to compute.
Provide one of the following values to request a single characteristic or use bitwise OR to request a combination of the characteristics:
value
Value of the objective function
nonSmoothTermValue
Value of non-smooth term of the objective function
gradient
Gradient of the smooth term of the objective function
hessian
Hessian of smooth term of the objective function
proximalProjection
Projection of proximal operator for non-smooth term of the objective function
lipschitzConstant
Lipschitz constant of the smooth term of the objective function
Algorithm Output
For the output of the mean squared error algorithm, see Output for objective functions.

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.