# Calibrate or select a machine learning algorithm¶

## Calibration¶

Calibration of a machine learning algorithm.

A machine learning algorithm depends on hyper-parameters, e.g. the number of clusters for a clustering algorithm, the regularization constant for a regression model, the kernel for a Gaussian process regression, … Its ability to generalize the information learned during the training stage, and thus to avoid over-fitting, which is an over-reliance on the learning data set, depends on the values of these hyper-parameters. Thus, the hyper-parameters minimizing the learning quality measure are rarely those minimizing the generalization one. Classically, the generalization one decreases before growing again as the model becomes more complex, while the learning error keeps decreasing. This phenomenon is called the curse of dimensionality.

In this module, the MLAlgoCalibration class aims to calibrate the hyper-parameters in order to minimize this measure of the generalization quality over a calibration parameter space. This class relies on the MLAlgoAssessor class which is a discipline (MDODiscipline) built from a machine learning algorithm (MLAlgo), a dataset (Dataset), a quality measure (MLQualityMeasure) and various options for the data scaling, the quality measure and the machine learning algorithm. The inputs of this discipline are hyper-parameters of the machine learning algorithm while the output is the quality criterion.

class gemseo.mlearning.core.calibration.MLAlgoAssessor(algo, dataset, parameters, measure, measure_options=None, transformer=mappingproxy({}), **algo_options)[source]

Discipline assessing the quality of a machine learning algorithm.

This quality depends on the values of parameters to calibrate with the MLAlgoCalibration.

Parameters:
• algo (str) – The name of a machine learning algorithm.

• dataset (Dataset) – A learning dataset.

• parameters (Iterable[str]) – The parameters of the machine learning algorithm to calibrate.

• measure (type[MLQualityMeasure]) – A measure to assess the machine learning algorithm.

• measure_options (MeasureOptionsType | None) – The options of the quality measure. If “multioutput” is missing, it is added with False as value. If None, do not use quality measure options.

• transformer (TransformerType) –

The strategies to transform the variables. The values are instances of Transformer while the keys are the names of either the variables or the groups of variables, e.g. "inputs" or "outputs" in the case of the regression algorithms. If a group is specified, the Transformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

• **algo_options (MLAlgoParameterType) – The options of the machine learning algorithm.

Raises:

ValueError – If the measure option “multioutput” is True.

classmethod activate_time_stamps()

Activate the time stamps.

For storing start and end times of execution and linearizations.

Return type:

None

Add the inputs against which to differentiate the outputs.

If the discipline grammar type is MDODiscipline.JSON_GRAMMAR_TYPE and an input is either a non-numeric array or not an array, it will be ignored. If an input is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.SIMPLE_GRAMMAR_TYPE and an input is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

Parameters:

inputs (Iterable[str] | None) – The input variables against which to differentiate the outputs. If None, all the inputs of the discipline are used.

Raises:

ValueError – When the inputs wrt which differentiate the discipline are not inputs of the latter.

Return type:

None

Add the outputs to be differentiated.

If the discipline grammar type is MDODiscipline.JSON_GRAMMAR_TYPE and an output is either a non-numeric array or not an array, it will be ignored. If an output is declared as an array but the type of its items is not defined, it is assumed as a numeric array.

If the discipline grammar type is MDODiscipline.SIMPLE_GRAMMAR_TYPE and an output is not an array, it will be ignored. Keep in mind that in this case the array subtype is not checked.

Parameters:

outputs (Iterable[str] | None) – The output variables to be differentiated. If None, all the outputs of the discipline are used.

Raises:

ValueError – When the outputs to differentiate are not discipline outputs.

Return type:

None

Add a namespace prefix to an existing input grammar element.

The updated input grammar element name will be namespace + namespaces_separator + name.

Parameters:
• name (str) – The element name to rename.

• namespace (str) – The name of the namespace.

Add a namespace prefix to an existing output grammar element.

The updated output grammar element name will be namespace + namespaces_separator + name.

Parameters:
• name (str) – The element name to rename.

• namespace (str) – The name of the namespace.

Add an observer for the status.

Add an observer for the status to be notified when self changes of status.

Parameters:

obs (Any) – The observer to add.

Return type:

None

auto_get_grammar_file(is_input=True, name=None, comp_dir=None)

Use a naming convention to associate a grammar file to the discipline.

Search in the directory comp_dir for either an input grammar file named name + "_input.json" or an output grammar file named name + "_output.json".

Parameters:
• is_input (bool) –

Whether to search for an input or output grammar file.

By default it is set to True.

• name (str | None) – The name to be searched in the file names. If None, use the name of the discipline class.

• comp_dir (str | Path | None) – The directory in which to search the grammar file. If None, use the GRAMMAR_DIRECTORY if any, or the directory of the discipline class module.

Returns:

The grammar file path.

Return type:

str

check_input_data(input_data, raise_exception=True)

Check the input data validity.

Parameters:
• input_data (dict[str, Any]) – The input data needed to execute the discipline according to the discipline input grammar.

• raise_exception (bool) –

Whether to raise on error.

By default it is set to True.

Return type:

None

check_jacobian(input_data=None, derr_approx='finite_differences', step=1e-07, threshold=1e-08, linearization_mode='auto', inputs=None, outputs=None, parallel=False, n_processes=2, use_threading=False, wait_time_between_fork=0, auto_set_step=False, plot_result=False, file_path='jacobian_errors.pdf', show=False, fig_size_x=10, fig_size_y=10, reference_jacobian_path=None, save_reference_jacobian=False, indices=None)

Check if the analytical Jacobian is correct with respect to a reference one.

If reference_jacobian_path is not None and save_reference_jacobian is True, compute the reference Jacobian with the approximation method and save it in reference_jacobian_path.

If reference_jacobian_path is not None and save_reference_jacobian is False, do not compute the reference Jacobian but read it from reference_jacobian_path.

If reference_jacobian_path is None, compute the reference Jacobian without saving it.

Parameters:
• input_data (dict[str, ndarray] | None) – The input data needed to execute the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.

• derr_approx (str) –

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to “finite_differences”.

• threshold (float) –

The acceptance threshold for the Jacobian error.

By default it is set to 1e-08.

• linearization_mode (str) –

the mode of linearization: direct, adjoint or automated switch depending on dimensions of inputs and outputs (Default value = ‘auto’)

By default it is set to “auto”.

• inputs (Iterable[str] | None) – The names of the inputs wrt which to differentiate the outputs.

• outputs (Iterable[str] | None) – The names of the outputs to be differentiated.

• step (float) –

The differentiation step.

By default it is set to 1e-07.

• parallel (bool) –

Whether to differentiate the discipline in parallel.

By default it is set to False.

• n_processes (int) –

The maximum simultaneous number of threads, if use_threading is True, or processes otherwise, used to parallelize the execution.

By default it is set to 2.

Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.

By default it is set to False.

• wait_time_between_fork (float) –

The time waited between two forks of the process / thread.

By default it is set to 0.

• auto_set_step (bool) –

Whether to compute the optimal step for a forward first order finite differences gradient approximation.

By default it is set to False.

• plot_result (bool) –

Whether to plot the result of the validation (computed vs approximated Jacobians).

By default it is set to False.

• file_path (str | Path) –

The path to the output file if plot_result is True.

By default it is set to “jacobian_errors.pdf”.

• show (bool) –

Whether to open the figure.

By default it is set to False.

• fig_size_x (float) –

The x-size of the figure in inches.

By default it is set to 10.

• fig_size_y (float) –

The y-size of the figure in inches.

By default it is set to 10.

• reference_jacobian_path (str | Path | None) – The path of the reference Jacobian file.

• save_reference_jacobian (bool) –

Whether to save the reference Jacobian.

By default it is set to False.

• indices (Iterable[int] | None) – The indices of the inputs and outputs for the different sub-Jacobian matrices, formatted as {variable_name: variable_components} where variable_components can be either an integer, e.g. 2 a sequence of integers, e.g. [0, 3], a slice, e.g. slice(0,3), the ellipsis symbol () or None, which is the same as ellipsis. If a variable name is missing, consider all its components. If None, consider all the components of all the inputs and outputs.

Returns:

Whether the analytical Jacobian is correct with respect to the reference one.

check_output_data(raise_exception=True)

Check the output data validity.

Parameters:

raise_exception (bool) –

Whether to raise an exception when the data is invalid.

By default it is set to True.

Return type:

None

classmethod deactivate_time_stamps()

Deactivate the time stamps.

For storing start and end times of execution and linearizations.

Return type:

None

static deserialize(file_path)

Deserialize a discipline from a file.

Parameters:

file_path (str | Path) – The path to the file containing the discipline.

Returns:

The discipline instance.

Return type:

MDODiscipline

execute(input_data=None)

Execute the discipline.

This method executes the discipline:

Parameters:

input_data (Mapping[str, Any] | None) – The input data needed to execute the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.

Returns:

The discipline local data after execution.

Raises:

RuntimeError – When residual_variables are declared but self.run_solves_residuals is False. This is not suported yet.

Return type:

dict[str, Any]

get_all_inputs()

Return the local input data as a list.

The order is given by MDODiscipline.get_input_data_names().

Returns:

The local input data.

Return type:

list[Any]

get_all_outputs()

Return the local output data as a list.

The order is given by MDODiscipline.get_output_data_names().

Returns:

The local output data.

Return type:

list[Any]

get_attributes_to_serialize()

Define the names of the attributes to be serialized.

Returns:

The names of the attributes to be serialized.

Return type:

list[str]

static get_data_list_from_dict(keys, data_dict)

Filter the dict from a list of keys or a single key.

If keys is a string, then the method return the value associated to the key. If keys is a list of strings, then the method returns a generator of value corresponding to the keys which can be iterated.

Parameters:
• keys (str | Iterable) – One or several names.

• data_dict (dict[str, Any]) – The mapping from which to get the data.

Returns:

Either a data or a generator of data.

Return type:

Any | Generator[Any]

get_disciplines_in_dataflow_chain()

Return the disciplines that must be shown as blocks in the XDSM.

By default, only the discipline itself is shown. This function can be differently implemented for any type of inherited discipline.

Returns:

The disciplines shown in the XDSM chain.

Return type:
get_expected_dataflow()

Return the expected data exchange sequence.

This method is used for the XDSM representation.

The default expected data exchange sequence is an empty list.

MDOFormulation.get_expected_dataflow

Returns:

The data exchange arcs.

Return type:
get_expected_workflow()

Return the expected execution sequence.

This method is used for the XDSM representation.

The default expected execution sequence is the execution of the discipline itself.

MDOFormulation.get_expected_workflow

Returns:

The expected execution sequence.

Return type:

SerialExecSequence

get_input_data(with_namespaces=True)

Return the local input data as a dictionary.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the input names, if any.

By default it is set to True.

Returns:

The local input data.

Return type:

dict[str, Any]

get_input_data_names(with_namespaces=True)

Return the names of the input variables.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the input names, if any.

By default it is set to True.

Returns:

The names of the input variables.

Return type:

list[str]

get_input_output_data_names(with_namespaces=True)

Return the names of the input and output variables.

Args:
with_namespaces: Whether to keep the namespace prefix of the

output names, if any.

Returns:

The name of the input and output variables.

Return type:

list[str]

get_inputs_asarray()

Return the local output data as a large NumPy array.

The order is the one of MDODiscipline.get_all_outputs().

Returns:

The local output data.

Return type:

ndarray

get_inputs_by_name(data_names)

Return the local data associated with input variables.

Parameters:

data_names (Iterable[str]) – The names of the input variables.

Returns:

The local data for the given input variables.

Raises:

ValueError – When a variable is not an input of the discipline.

Return type:

list[Any]

get_local_data_by_name(data_names)

Return the local data of the discipline associated with variables names.

Parameters:

data_names (Iterable[str]) – The names of the variables.

Returns:

The local data associated with the variables names.

Raises:

ValueError – When a name is not a discipline input name.

Return type:

Generator[Any]

get_output_data(with_namespaces=True)

Return the local output data as a dictionary.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the output names, if any.

By default it is set to True.

Returns:

The local output data.

Return type:

dict[str, Any]

get_output_data_names(with_namespaces=True)

Return the names of the output variables.

Parameters:

with_namespaces

Whether to keep the namespace prefix of the output names, if any.

By default it is set to True.

Returns:

The names of the output variables.

Return type:

list[str]

get_outputs_asarray()

Return the local input data as a large NumPy array.

The order is the one of MDODiscipline.get_all_inputs().

Returns:

The local input data.

Return type:

ndarray

get_outputs_by_name(data_names)

Return the local data associated with output variables.

Parameters:

data_names (Iterable[str]) – The names of the output variables.

Returns:

The local data for the given output variables.

Raises:

ValueError – When a variable is not an output of the discipline.

Return type:

list[Any]

get_sub_disciplines(recursive=False)

Determine the sub-disciplines.

This method lists the sub-disciplines’ disciplines. It will list up to one level of disciplines contained inside another one unless the recursive argument is set to True.

Parameters:

recursive (bool) –

If True, the method will look inside any discipline that has other disciplines inside until it reaches a discipline without sub-disciplines, in this case the return value will not include any discipline that has sub-disciplines. If False, the method will list up to one level of disciplines contained inside another one, in this case the return value may include disciplines that contain sub-disciplines.

By default it is set to False.

Returns:

The sub-disciplines.

Return type:
is_all_inputs_existing(data_names)

Test if several variables are discipline inputs.

Parameters:

data_names (Iterable[str]) – The names of the variables.

Returns:

Whether all the variables are discipline inputs.

Return type:

bool

is_all_outputs_existing(data_names)

Test if several variables are discipline outputs.

Parameters:

data_names (Iterable[str]) – The names of the variables.

Returns:

Whether all the variables are discipline outputs.

Return type:

bool

is_input_existing(data_name)

Test if a variable is a discipline input.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline input.

Return type:

bool

is_output_existing(data_name)

Test if a variable is a discipline output.

Parameters:

data_name (str) – The name of the variable.

Returns:

Whether the variable is a discipline output.

Return type:

bool

static is_scenario()

Whether the discipline is a scenario.

Return type:

bool

linearize(input_data=None, force_all=False, force_no_exec=False)

Execute the linearized version of the code.

Parameters:
• input_data (dict[str, Any] | None) – The input data needed to linearize the discipline according to the discipline input grammar. If None, use the MDODiscipline.default_inputs.

• force_all (bool) –

If False, MDODiscipline._differentiated_inputs and MDODiscipline._differentiated_outputs are used to filter the differentiated variables. otherwise, all outputs are differentiated wrt all inputs.

By default it is set to False.

• force_no_exec (bool) –

If True, the discipline is not re-executed, cache is loaded anyway.

By default it is set to False.

Returns:

The Jacobian of the discipline.

Return type:

dict[str, dict[str, ndarray]]

notify_status_observers()

Notify all status observers that the status has changed.

Return type:

None

remove_status_observer(obs)

Remove an observer for the status.

Parameters:

obs (Any) – The observer to remove.

Return type:

None

reset_statuses_for_run()

Set all the statuses to MDODiscipline.STATUS_PENDING.

Raises:

ValueError – When the discipline cannot be run because of its status.

Return type:

None

serialize(file_path)

Serialize the discipline and store it in a file.

Parameters:

file_path (str | Path) – The path to the file to store the discipline.

Return type:

None

set_cache_policy(cache_type='SimpleCache', cache_tolerance=0.0, cache_hdf_file=None, cache_hdf_node_name=None, is_memory_shared=True)

Set the type of cache to use and the tolerance level.

This method defines when the output data have to be cached according to the distance between the corresponding input data and the input data already cached for which output data are also cached.

The cache can be either a SimpleCache recording the last execution or a cache storing all executions, e.g. MemoryFullCache and HDF5Cache. Caching data can be either in-memory, e.g. SimpleCache and MemoryFullCache, or on the disk, e.g. HDF5Cache.

The attribute CacheFactory.caches provides the available caches types.

Parameters:
• cache_type (str) –

The type of cache.

By default it is set to “SimpleCache”.

• cache_tolerance (float) –

The maximum relative norm of the difference between two input arrays to consider that two input arrays are equal.

By default it is set to 0.0.

• cache_hdf_file (str | Path | None) – The path to the HDF file to store the data; this argument is mandatory when the MDODiscipline.HDF5_CACHE policy is used.

• cache_hdf_node_name (str | None) – The name of the HDF file node to store the discipline data. If None, MDODiscipline.name is used.

• is_memory_shared (bool) –

Whether to store the data with a shared memory dictionary, which makes the cache compatible with multiprocessing.

By default it is set to True.

Return type:

None

set_disciplines_statuses(status)

Set the sub-disciplines statuses.

To be implemented in subclasses.

Parameters:

status (str) – The status.

Return type:

None

Set the Jacobian approximation method.

Sets the linearization mode to approx_method, sets the parameters of the approximation for further use when calling MDODiscipline.linearize().

Parameters:
• jac_approx_type (str) –

The approximation method, either “complex_step” or “finite_differences”.

By default it is set to “finite_differences”.

• jax_approx_step (float) –

The differentiation step.

By default it is set to 1e-07.

• jac_approx_n_processes (int) –

The maximum simultaneous number of threads, if jac_approx_use_threading is True, or processes otherwise, used to parallelize the execution.

By default it is set to 1.

Whether to use threads instead of processes to parallelize the execution; multiprocessing will copy (serialize) all the disciplines, while threading will share all the memory This is important to note if you want to execute the same discipline multiple times, you shall use multiprocessing.

By default it is set to False.

• jac_approx_wait_time (float) –

The time waited between two forks of the process / thread.

By default it is set to 0.

Return type:

None

set_optimal_fd_step(outputs=None, inputs=None, force_all=False, print_errors=False, numerical_error=2.220446049250313e-16)

Compute the optimal finite-difference step.

Compute the optimal step for a forward first order finite differences gradient approximation. Requires a first evaluation of the perturbed functions values. The optimal step is reached when the truncation error (cut in the Taylor development), and the numerical cancellation errors (round-off when doing f(x+step)-f(x)) are approximately equal.

Warning

This calls the discipline execution twice per input variables.

https://en.wikipedia.org/wiki/Numerical_differentiation and “Numerical Algorithms and Digital Representation”, Knut Morken , Chapter 11, “Numerical Differentiation”

Parameters:
• inputs (Iterable[str] | None) – The inputs wrt which the outputs are linearized. If None, use the MDODiscipline._differentiated_inputs.

• outputs (Iterable[str] | None) – The outputs to be linearized. If None, use the MDODiscipline._differentiated_outputs.

• force_all (bool) –

Whether to consider all the inputs and outputs of the discipline;

By default it is set to False.

• print_errors (bool) –

Whether to display the estimated errors.

By default it is set to False.

• numerical_error (float) –

The numerical error associated to the calculation of f. By default, this is the machine epsilon (appx 1e-16), but can be higher when the calculation of f requires a numerical resolution.

By default it is set to 2.220446049250313e-16.

Returns:

The estimated errors of truncation and cancellation error.

Raises:

ValueError – When the Jacobian approximation method has not been set.

store_local_data(**kwargs)

Store discipline data in local data.

Parameters:

**kwargs (Any) – The data to be stored in MDODiscipline.local_data.

Return type:

None

GRAMMAR_DIRECTORY: ClassVar[str | None] = None

The directory in which to search for the grammar files if not the class one.

activate_cache: bool = True

Whether to cache the discipline evaluations by default.

activate_counters: ClassVar[bool] = True

Whether to activate the counters (execution time, calls and linearizations).

activate_input_data_check: ClassVar[bool] = True

Whether to check the input data respect the input grammar.

activate_output_data_check: ClassVar[bool] = True

Whether to check the output data respect the output grammar.

algo: str

The name of a machine learning algorithm.

algos: list[MLAlgo]

The instances of the machine learning algorithm (one per execution of the machine learning algorithm assessor).

cache: AbstractCache | None

The cache containing one or several executions of the discipline according to the cache policy.

property cache_tol: float

The cache input tolerance.

This is the tolerance for equality of the inputs in the cache. If norm(stored_input_data-input_data) <= cache_tol * norm(stored_input_data), the cached data for stored_input_data is returned when calling self.execute(input_data).

Raises:

ValueError – When the discipline does not have a cache.

data_processor: DataProcessor

A tool to pre- and post-process discipline data.

dataset: Dataset

The learning dataset.

property default_inputs: dict[str, Any]

The default inputs.

Raises:

TypeError – When the default inputs are not passed as a dictionary.

property disciplines: list[gemseo.core.discipline.MDODiscipline]

The sub-disciplines, if any.

exec_for_lin: bool

Whether the last execution was due to a linearization.

property exec_time: float | None

The cumulated execution time of the discipline.

This property is multiprocessing safe.

Raises:

RuntimeError – When the discipline counters are disabled.

property grammar_type: BaseGrammar

The type of grammar to be used for inputs and outputs declaration.

input_grammar: BaseGrammar

The input grammar.

jac: dict[str, dict[str, ndarray]]

The Jacobians of the outputs wrt inputs of the form {output: {input: matrix}}.

property linearization_mode: str

The linearization mode among MDODiscipline.AVAILABLE_MODES.

Raises:

ValueError – When the linearization mode is unknown.

property local_data: DisciplineData

The current input and output data.

measure: MLQualityMeasure

The measure to assess the machine learning algorithm.

measure_options: dict[str, int | Dataset]

The options of the quality measure.

property n_calls: int | None

The number of times the discipline was executed.

This property is multiprocessing safe.

Raises:

RuntimeError – When the discipline counters are disabled.

property n_calls_linearize: int | None

The number of times the discipline was linearized.

This property is multiprocessing safe.

Raises:

RuntimeError – When the discipline counters are disabled.

name: str

The name of the discipline.

output_grammar: BaseGrammar

The output grammar.

parameters: list[str]

The parameters of the machine learning algorithm.

re_exec_policy: str

The policy to re-execute the same discipline.

residual_variables: Mapping[str, str]

The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.

run_solves_residuals: bool

If True, the run method shall solve the residuals.

property status: str

The status of the discipline.

transformer: TransformerType

The transformation strategy for data groups.

class gemseo.mlearning.core.calibration.MLAlgoCalibration(algo, dataset, parameters, calibration_space, measure, measure_options=None, transformer=mappingproxy({}), **algo_options)[source]

Calibration of a machine learning algorithm.

Parameters:
• algo (str) – The name of a machine learning algorithm.

• dataset (Dataset) – A learning dataset.

• parameters (Iterable[str]) – The parameters of the machine learning algorithm to calibrate.

• calibration_space (DesignSpace) – The space defining the calibration variables.

• measure (MLQualityMeasure) – A measure to assess the machine learning algorithm.

• measure_options (MeasureOptionsType | None) – The options of the quality measure. If None, do not use the quality measure options.

• transformer (TransformerType) –

The strategies to transform the variables. The values are instances of Transformer while the keys are the names of either the variables or the groups of variables, e.g. "inputs" or "outputs" in the case of the regression algorithms. If a group is specified, the Transformer will be applied to all the variables of this group. If IDENTITY, do not transform the variables.

By default it is set to {}.

• **algo_options (MLAlgoParameterType) – The options of the machine learning algorithm.

execute(input_data)[source]

Calibrate the machine learning algorithm from a driver.

The driver can be either a DOE or an optimizer.

Parameters:

input_data (Mapping[str, Union[str, int, Mapping[str, Union[int, float]]]]) – The driver properties.

Return type:

None

get_history(name)[source]

Return the history of a variable.

Parameters:

name (str) – The name of the variable.

Returns:

The history of the variable.

Return type:

ndarray

algo_assessor: MLAlgoAssessor

The assessor for the machine learning algorithm.

property algos: MLAlgo

The trained machine learning algorithms.

calibration_space: DesignSpace

The space defining the calibration variables.

dataset: Dataset

The learning dataset.

maximize_objective: bool

Whether to maximize the quality measure.

optimal_algorithm: MLAlgo

The optimal machine learning algorithm.

optimal_criterion: float

The optimal quality measure.

optimal_parameters: dict[str, numpy.ndarray]

The optimal parameters for the machine learning algorithm.

scenario: Scenario

The scenario used to calibrate the machine learning algorithm.

## Selection¶

This module contains a class to select a machine learning algorithm from a list.

Machine learning is used to find relations or underlying structures in data. There is however no algorithm that is universally better than the others for an arbitrary problem. As for optimization, there is no free lunch for machine learning [Wol96].

Provided a quality measure, one can thus compare the performances of different machine learning algorithms.

This process can be easily performed using the class MLAlgoSelection.

A machine learning algorithm is built using a set of (hyper)parameters, before the learning takes place. In order to choose the best hyperparameters, a simple grid search over different values may be sufficient. The MLAlgoSelection does this. It can also perform a more advanced form of optimization than a simple grid search over predefined values, using the class MLAlgoCalibration.

class gemseo.mlearning.core.selection.MLAlgoSelection(dataset, measure, eval_method='learn', samples=None, **measure_options)[source]

Machine learning algorithm selector.

Parameters:
• dataset (Dataset) – The learning dataset.

• measure (str | MLQualityMeasure) – The name of a quality measure to measure the quality of the machine learning algorithms.

• eval_method (str) –

The name of the method to evaluate the quality measure.

By default it is set to “learn”.

• samples (Sequence[int] | None) – The indices of the learning samples to consider. Other indices are neither used for training nor for testing. If None, use all the samples.

• **measure_options (MeasureOptionType) – The options for the method to evaluate the quality measure. The option ‘multioutput’ will be set to False.

Raises:

ValueError – If the unsupported “multioutput” option is enabled.

Add a machine learning algorithm candidate.

Parameters:
• name (str) – The name of a machine learning algorithm.

• calib_space (DesignSpace | None) – The design space defining the parameters to be calibrated with a MLAlgoCalibration. If None, do not perform calibration.

• calib_algo (ScenarioInputDataType | None) – The name and the parameters of the optimization algorithm, e.g. {“algo”: “fullfact”, “n_samples”: 10}. If None, do not perform calibration.

• **option_lists – The parameters for the machine learning algorithm candidate. Each parameter has to be enclosed within a list. The list may contain different values to try out for the given parameter, or only one.

Return type:

None

Examples

>>> selector.add_candidate(
>>>     "LinearRegressor",
>>>     penalty_level=[0, 0.1, 1, 10, 20],
>>>     l2_penalty_ratio=[0, 0.5, 1],
>>>     fit_intercept=[True],
>>> )

select(return_quality=False)[source]

Select the best model.

The model is chosen through a grid search over candidates and their options, as well as an eventual optimization over the parameters in the calibration space.

Parameters:

return_quality (bool) –

Whether to return the quality of the best model.

By default it is set to False.

Returns:

The best model and its quality if required.

Return type:
candidates: list[tuple[MLAlgo, float]]

The candidate machine learning algorithms, after possible calibration, and their quality measures.

dataset: Dataset

The learning dataset.

factory: MLAlgoFactory

The factory used for the instantiation of machine learning algorithms.

measure: str

The name of a quality measure to measure the quality of the machine learning algorithms.

measure_options: dict[str, int | Dataset]

The options for the method to evaluate the quality measure.

## Examples¶

See the examples about classification and selection.