## Developer Guide and Reference

• 2021.6
• 04/11/2022
• Public Content
Contents

# Logistic Regression

Logistic regression is a method for modeling the relationships between one or more explanatory variables and a categorical variable by expressing the posterior statistical distribution of the categorical variable via linear functions on observed data. If the categorical variable is binary, taking only two values, “0” and “1”, the logistic regression is simple, otherwise, it is multinomial.

## Details

Given n feature vectors of n p-dimensional feature vectors a vector of class labels , where and is the number of classes, describes the class to which the feature vector belongs, the problem is to train a logistic regression model.
The logistic regression model is the set of vectors that gives the posterior probability for a given feature vector and class label for each . See [Hastie2009].
If the categorical variable is binary, the model is defined as a single vector that determines the posterior probability Training Stage
Training procedure is an iterative algorithm which minimizes objective function where the first term is the negative log-likelihood of conditional given , and the latter terms are regularization ones that penalize the complexity of the model (large values), and are non-negative regularization parameters applied to L1 and L2 norm of vectors in .
For more details, see [Hastie2009], [Bishop2006].
For the objective function minimization the library supports the iterative algorithms defined by the interface of daal::algorithms::iterative_solver. See Iterative Solver.
Prediction Stage
Given logistic regression model and vectors , the problem is to calculate the responses for those vectors, and their probabilities and logarithms of probabilities if required. The computation is based on formula (1) in multinomial case and on formula (2) in binary case.

## Usage of Training Alternative

To build a Logistic Regression model using methods of the Model Builder class of Logistic Regression, complete the following steps:
• Create a Logistic Regression model builder using a constructor with the required number of responses and features.
• Use the
setBeta
method to add the set of pre-calculated coefficients to the model. Specify random access iterators to the first and the last element of the set of coefficients [ISO/IEC 14882:2011 §24.2.7]_.
If your set of coefficients does not contain an intercept, interceptFlag is automatically set to
False
, and to
True
, otherwise.
• Use the
getModel
method to get the trained Logistic Regression model.
• Use the
getStatus
method to check the status of the model building process. If
DAAL_NOTHROW_EXCEPTIONS
macros is defined, the status report contains the list of errors that describe the problems API encountered (in case of API runtime failure).
If after calling the
getModel
method you use the
setBeta
method to update coefficients, the initial model will be automatically updated with the new coefficients.
Examples
C++ (CPU)
Java*
There is no support for Java on GPU.
Python*

## Batch Processing

Logistic regression algorithm follows the general workflow described in Classification Usage Model.
Training
For a description of the input and output, refer to Classification Usage Model.
In addition to the parameters of classifier described in Classification Usage Model, the logistic regression batch training algorithm has the following parameters:
Training Parameters for Logistic Regression (Batch Processing)
Parameter
Default Value
Description
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
The computation method used by the logistic regression. The only training method supported so far is the default dense method.
nClasses
Not applicable
The number of classes. A required parameter.
interceptFlag
True
A flag that indicates a need to compute penaltyL1 L1 regularization coefficient
L1 regularization is not supported on GPU.
penaltyL2 L2 regularization coefficient
optimizationSolver
All iterative solvers are available as optimization procedures to use at the training stage:
Prediction
For a description of the input, refer to Classification Usage Model.
At the prediction stage logistic regression batch algorithm has the following parameters:
Prediction Parameters for Logistic Regression (Batch Processing)
Parameter
Default Value
Description
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
The computation method used by logistic regression. The only prediction method supported so far is the default dense method.
nClasses
Not applicable
The number of classes. A required parameter.
resultsToCompute
computeClassesLabels
The 64-bit integer flag that specifies which extra characteristics of the logistic regression to compute.
Provide one of the following values to request a single characteristic or use bitwise OR to request a combination of the characteristics:
• computeClassesLabels
for
prediction
• computeClassesProbabilities
for
probabilities
• computeClassesLogProbabilities
for
logProbabilities
Output
In addition to classifier output, logistic regression prediction calculates the result described below. Pass the
Result ID
as a parameter to the methods that access the results of your algorithm.
Prediction Output for Logistic Regression (Batch Processing)
Result ID
Result
probabilities
A numeric table of size containing probabilities of classes computed when
computeClassesProbabilities
option is enabled.
logProbabilities
A numeric table of size containing logarithms of classes’ probabilities computed when
computeClassesLogProbabilities
option is enabled.
Note that:
• If
resultsToCompute
does not contain
computeClassesLabels
, the
prediction
table is
NULL
.
• If
resultsToCompute
does not contain
computeClassesProbabilities
, the
probabilities
table is
NULL
.
• If
resultsToCompute
does not contain
computeClassesLogProbabilities
, the
logProbabilities
table is
NULL
.
• By default, each numeric table of this result is an object of the
HomogenNumericTable
class, but you can define the result as an object of any class derived from
NumericTable
except for
PackedSymmetricMatrix
and
PackedTriangularMatrix
.

## Examples

C++ (CPU)
Batch Processing:
Java*
There is no support for Java on GPU.
Batch Processing:
Python* with DPC++ support
Batch Processing:
Python*
Batch Processing:

#### Product and Performance Information

1

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