# Supervised learning¶

This module contains the base class for the supervised machine learning algorithms.

Supervised machine learning is a task of learning relationships between input and output variables based on an input-output dataset. One usually distinguishes between two types of supervised machine learning algorithms, based on the nature of the outputs. For a continuous output variable, a regression is performed, while for a discrete output variable, a classification is performed.

Given a set of input variables $$x \in \mathbb{R}^{n_{\text{samples}}\times n_{\text{inputs}}}$$ and a set of output variables $$y\in \mathbb{K}^{n_{\text{samples}}\times n_{\text{outputs}}}$$, where $$n_{\text{inputs}}$$ is the dimension of the input variable, $$n_{\text{outputs}}$$ is the dimension of the output variable, $$n_{\text{samples}}$$ is the number of training samples and $$\mathbb{K}$$ is either $$\mathbb{R}$$ or $$\mathbb{N}$$ for regression and classification tasks respectively, a supervised learning algorithm seeks to find a function $$f: \mathbb{R}^{n_{\text{inputs}}} \to \mathbb{K}^{n_{\text{outputs}}}$$ such that $$y=f(x)$$.

In addition, we often want to impose some additional constraints on the function $$f$$, mainly to ensure that it has a generalization capacity beyond the training data, i.e. it is able to correctly predict output values of new input values. This is called regularization. Assuming $$f$$ is parametrized by a set of parameters $$\theta$$, and denoting $$f_\theta$$ the parametrized function, one typically seeks to minimize a function of the form

$\mu(y, f_\theta(x)) + \Omega(\theta),$

where $$\mu$$ is a distance-like measure, typically a mean squared error, a cross entropy in the case of a regression, or a probability to be maximized in the case of a classification, and $$\Omega$$ is a regularization term that limits the parameters from over-fitting, typically some norm of its argument.

The supervised module implements this concept through the MLSupervisedAlgo class based on a Dataset.

Classes:

 MLSupervisedAlgo(data[, transformer, …]) Supervised machine learning algorithm.
class gemseo.mlearning.core.supervised.MLSupervisedAlgo(data, transformer={'inputs': <gemseo.mlearning.transform.scaler.min_max_scaler.MinMaxScaler object>}, input_names=None, output_names=None, **parameters)[source]

Supervised machine learning algorithm.

Inheriting classes shall overload the MLSupervisedAlgo._fit() and MLSupervisedAlgo._predict() methods.

Attributes
• learning_set (Dataset) – The learning dataset.

• parameters (Dict[str,MLAlgoParameterType]) – The parameters of the machine learning algorithm.

• transformer (Dict[str,Transformer]) – 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 None, do not transform the variables.

• algo (Any) – The interfaced machine learning algorithm.

• input_names (List[str]) – The names of the input variables.

• output_names (List[str]) – The names of the output variables.

• input_space_center (Dict[str,ndarray]) – The center of the input space.

Parameters
• input_names (Optional[Iterable[str]]) – The names of the input variables. If None, consider all input variables mentioned in the learning dataset.

• output_names (Optional[Iterable[str]]) – The names of the output variables. If None, consider all input variables mentioned in the learning dataset.

• data (Dataset) –

• transformer (TransformerType) –

• parameters (MLAlgoParameterType) –

Return type

None

Classes:

 Decorators for supervised algorithms.

Attributes:

 input_data The input data matrix. input_shape The dimension of the input variables before applying the transformers. is_trained Return whether the algorithm is trained. output_data The output data matrix. output_shape The dimension of the output variables before applying the transformers.

Methods:

 learn([samples]) Train the machine learning algorithm from the learning dataset. load_algo(directory) Load a machine learning algorithm from a directory. predict(input_data, *args, **kwargs) Evaluate ‘predict’ with either array or dictionary-based input data. save([directory, path, save_learning_set]) Save the machine learning algorithm.
class DataFormatters[source]

Decorators for supervised algorithms.

Methods:

 format_dict(predict) Make an array-based function be called with a dictionary of NumPy arrays. format_input_output(predict) Make a function robust to type, array shape and data transformation. format_samples(predict) Make a 2D NumPy array-based function work with 1D NumPy array. format_transform([transform_inputs, …]) Force a function to transform its input and/or output variables.
classmethod format_dict(predict)[source]

Make an array-based function be called with a dictionary of NumPy arrays.

Parameters

predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a NumPy array in input and returns a NumPy array.

Returns

A function making the function ‘predict’ work with either a NumPy data array or a dictionary of NumPy data arrays indexed by variables names. The evaluation will have the same type as the input data.

Return type

Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_input_output(predict)[source]

Make a function robust to type, array shape and data transformation.

Parameters

predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function of interest to be called.

Returns

A function calling the function of interest ‘predict’, while guaranteeing consistency in terms of data type and array shape, and applying input and/or output data transformation if required.

Return type

Callable[[Union[numpy.ndarray, Dict[str, numpy.ndarray]]], Union[numpy.ndarray, Dict[str, numpy.ndarray]]]

classmethod format_samples(predict)[source]

Make a 2D NumPy array-based function work with 1D NumPy array.

Parameters

predict (Callable[[numpy.ndarray], numpy.ndarray]) – The function to be called; it takes a 2D NumPy array in input and returns a 2D NumPy array. The first dimension represents the samples while the second one represents the components of the variables.

Returns

A function making the function ‘predict’ work with either a 1D NumPy array or a 2D NumPy array. The evaluation will have the same dimension as the input data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

classmethod format_transform(transform_inputs=True, transform_outputs=True)[source]

Force a function to transform its input and/or output variables.

Parameters
• transform_inputs (bool) – If True, apply the transformers to the input variables.

• transform_outputs (bool) – If True, apply the transformers to the output variables.

Returns

A function evaluating a function of interest, after transforming its input data and/or before transforming its output data.

Return type

Callable[[numpy.ndarray], numpy.ndarray]

property input_data

The input data matrix.

property input_shape

The dimension of the input variables before applying the transformers.

property is_trained

Return whether the algorithm is trained.

learn(samples=None)[source]

Train the machine learning algorithm from the learning dataset.

Parameters

samples (Optional[List[int]]) – The indices of the learning samples. If None, use the whole learning dataset.

Raises

NotImplementedError – If an output transformer modifies both the input and the output variables, e.g. PLS.

Return type

None

Load a machine learning algorithm from a directory.

Parameters

directory (str) – The path to the directory where the machine learning algorithm is saved.

Return type

None

property output_data

The output data matrix.

property output_shape

The dimension of the output variables before applying the transformers.

predict(input_data, *args, **kwargs)[source]

Evaluate ‘predict’ with either array or dictionary-based input data.

Firstly, the pre-processing stage converts the input data to a NumPy data array, if these data are expressed as a dictionary of NumPy data arrays.

Then, the processing evaluates the function ‘predict’ from this NumPy input data array.

Lastly, the post-processing transforms the output data to a dictionary of output NumPy data array if the input data were passed as a dictionary of NumPy data arrays.

Parameters
• input_data (Union[numpy.ndarray, Dict[str, numpy.ndarray]]) – The input data.

• *args – The positional arguments of the function ‘predict’.

• **kwargs – The keyword arguments of the function ‘predict’.

Returns

The output data with the same type as the input one.

Return type

Union[numpy.ndarray, Dict[str, numpy.ndarray]]

save(directory=None, path='.', save_learning_set=False)

Save the machine learning algorithm.

Parameters
• directory (Optional[str]) – The name of the directory to save the algorithm.

• path (str) – The path to parent directory where to create the directory.

• save_learning_set (bool) – If False, do not save the learning set to lighten the saved files.

Returns

The path to the directory where the algorithm is saved.

Return type

str