Logistic Loss
Logistic loss is an objective function being minimized in the process of
logistic regression training when a dependent variable takes only one of two values,
0
and 1
.Details
Given 
of 
,
where 
describes the class to which the feature vector 
belongs,
the logistic loss objective function 
has the following format 
, where
n
feature vectors
of n
p
-dimensional feature vectors, a vector of class labels ,
where describes the class to which the feature vector belongs,
the logistic loss objective function
has the following format , where
is defined as
with
,
,
, 
For a given set of the indices 
,
, 
:
,
, :- The value of the sum of functions has the format:
- The gradient of the sum of functions has the format:
where
For more details, see [Hastie2009].
Computation
Algorithm Input
The logistic loss 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  with the input argument  of the objective function.The sizes of the argument, gradient, and hessian numeric tables do not depend on interceptFlag .
When interceptFlag is set to false , the computation of  value is skipped,
but the sizes of the tables should remain the same. |
data | A numeric table of size  with the data  .This parameter can be an object of any class derived from NumericTable . |
dependentVariables | A numeric table of size  with dependent variables  .This parameter can be an object of any class derived from NumericTable ,
except for PackedTriangularMatrix , PackedSymmetricMatrix , and CSRNumericTable . |
Algorithm Parameters
The logistic loss algorithm has the following parameters.
Some of them are required only for specific values of the computation method’s parameter
method
: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 computation method. |
numberOfTerms | Not applicable | The number of terms in the objective function. |
batchIndices | Not applicable | The numeric table of size  , 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 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:
|
interceptFlag | true | A flag that indicates a need to compute  . |
penaltyL1 | 0 | L1 regularization coefficient |
penaltyL2 | 0 | L2 regularization coefficient |
Algorithm Output
For the output of the logistic loss algorithm, see Output for objective functions.