Contents

# 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
Numeric table of size (
p
+ 1) x 1 with the input argument
θ
of the objective function.
data
Numeric table of size
n
x
p
with the data
x
ij
.
dependentVariables
Numeric table of size
n
x 1 with dependent variables
y
i
.

## 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 1 x
n
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
p
x
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 1 x
nDependentVariables
with L1 regularized coefficients.
penaltyL2
0
The numeric table of size 1 x
nDependentVariables
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
NULL
The numeric table of size 1 x
m
, 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
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 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

#### Product and Performance Information

1

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Notice revision #20110804