Objective function

Intel® oneAPI Data Analytics Library Developer Guide and Reference

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ID 772611

Date 7/13/2023

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Objective function

Some classification algorithms are designed to minimize the selected objective function. On each iteration its’ gradient and sometimes hessian is calculated and model weights are updated using this information.

Operation	Computational methods	Programming Interface
dense_batch	dense_batch	compute(…)	compute_input	compute_result

Mathematical formulation

Refer to Developer Guide: Objective function.

Programming Interface

All types and functions in this section are declared in the oneapi::dal::objective_function namespace and be available via inclusion of the oneapi/dal/algo/objective_function.hpp header file.

Result options

classresult_option_id

Public Methods

constexprresult_option_id()=default

constexprresult_option_id(constresult_option_id_base&base)

Descriptor

template<typenameFloat=float,typenameMethod=method::by_default,typenameTask=task::by_default,typenameObjective=logloss_objective::descriptor<Float>>classdescriptor

Template Parameters

Float – The floating-point type that the algorithm uses for intermediate computations. Can be float or double.
Method – Tag-type that specifies an implementation of algorithm. Can be method::dense_batch.
Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.
Objective – The descriptor of the objective function to computate. Can be logloss_objective::descriptor.

Constructors

descriptor()

Creates a new instance of the class with the default property values.

descriptor(constobjective_t&obj)

Creates a new instance of the class with the given obj property value.

Properties

constobjective_t&objective

Choose objective function for calculations.

Getter & Setter: const objective_t & get_objective()
auto & set_objective(const objective_t &obj)

result_option_idresult_options

Choose which results should be computed and returned.

Getter & Setter: result_option_id get_result_options() const
auto & set_result_options(const result_option_id &value)

Method tags

structdense_batch

Tag-type that denotes computational method.

usingby_default=dense_batch

Alias tag-type for the computational method.

Task tags

structcompute

Tag-type that parameterizes entities that are used to compute statistics.

usingby_default=compute

Alias tag-type for compute task.

Compute compute(...)

Input

template<typenameTask=task::by_default>classcompute_input

Template Parameters: Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.

Constructors

compute_input(consttable&data, consttable&parameters, consttable&responses)

Creates a new instance of the class with the given data, parameters and responses property valuea.

Properties

consttable&responses

An $n \times 1$ table with the correct class labels. Default value: table{}.

Getter & Setter: const table & get_responses() const
auto & set_responses(const table &value)

consttable&parameters

An $p + 1 \times 1$ table with the model weights. Default value: table{}.

Getter & Setter: const table & get_parameters() const
auto & set_parameters(const table &value)

consttable&data

An $n \times p$ table with the training data, where each row stores one feature vector. Default value: table{}.

Getter & Setter: const table & get_data() const
auto & set_data(const table &value)

Result

template<typenameTask=task::by_default>classcompute_result

Template Parameters: Task – Tag-type that specifies the type of the problem to solve. Can be task::compute.

Constructors

compute_result()

Creates a new instance of the class with the default property values.

Properties

consttable&hessian

The matrix of size $p + 1 \times p + 1$ with the objective function hessian. Default value: table{}.

Getter & Setter: const table & get_hessian() const
auto & set_hessian(const table &value)

consttable&value

The matrix of size $1 \times 1$ with the objective function value. Default value: table{}.

Getter & Setter: const table & get_value() const
auto & set_value(const table &value)

consttable&gradient

The matrix of size $p + 1 \times 1$ with the objective function gradient. Default value: table{}.

Getter & Setter: const table & get_gradient() const
auto & set_gradient(const table &value)

constresult_option_id&result_options

Result options that indicates availability of the properties. Default value: default_result_options<Task>.

Getter & Setter: const result_option_id & get_result_options() const
auto & set_result_options(const result_option_id &value)

Operation

template<typenameDescriptor>objective_function::compute_resultcompute(constDescriptor&desc, constobjective_function::compute_input&input)

Parameters

desc – objective_function algorithm descriptor objective_function::descriptor
input – Input for objective_function computation. Contains data, parameters and responses

Preconditions: input.data.has_data  ==  true
input.parameters.has_data  ==  true
input.responses.has_data  ==  true
input.data.row_count  ==  input.responses.row_count
input.data.column_count  +  1  ==  input.parameters.row_count
input.responses.column_count  ==  1
input.parameters.column_count  ==  1
Postconditions: result.value.row_count  ==  1
result.value.column_count  ==  1
result.gradient.row_count  ==  input.data.column_count  +  1
result.gradient.column_count  ==  1
result.hessian.row_count  ==  input.data.column_count  +  1
result.hessian.column_count  ==  input.data.column_count  +  1

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Intel® oneAPI Data Analytics Library Developer Guide and Reference

Objective function

Mathematical formulation

Programming Interface