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
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
.
- 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()
andMLSupervisedAlgo._predict()
methods.- Parameters
data (Dataset) – The learning dataset.
transformer (Mapping[str, TransformerType] | None) –
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, theTransformer
will be applied to all the variables of this group. If None, do not transform the variables.By default it is set to {‘inputs’: <gemseo.mlearning.transform.scaler.min_max_scaler.MinMaxScaler object at 0x7fdc216a1760>}.
input_names (Iterable[str] | None) –
The names of the input variables. If
None
, consider all the input variables of the learning dataset.By default it is set to None.
output_names (Iterable[str] | None) –
The names of the output variables. If
None
, consider all the output variables of the learning dataset.By default it is set to None.
**parameters (MLAlgoParameterType) – The parameters of the machine learning algorithm.
- Raises
ValueError – When both the variable and the group it belongs to have a transformer.
- Return type
None
- class DataFormatters[source]
Decorators for supervised algorithms.
- 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, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[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, Mapping[str, numpy.ndarray]]], Union[numpy.ndarray, Mapping[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
- 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]
- learn(samples=None, fit_transformers=True)
Train the machine learning algorithm from the learning dataset.
- load_algo(directory)
Load a machine learning algorithm from a directory.
- Parameters
directory (str | Path) – The path to the directory where the machine learning algorithm is saved.
- Return type
None
- 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, Mapping[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, Mapping[str, numpy.ndarray]]
- save(directory=None, path='.', save_learning_set=False)
Save the machine learning algorithm.
- Parameters
directory (str | None) –
The name of the directory to save the algorithm.
By default it is set to None.
path (str | Path) –
The path to parent directory where to create the directory.
By default it is set to ..
save_learning_set (bool) –
Whether to save the learning set or get rid of it to lighten the saved files.
By default it is set to False.
- Returns
The path to the directory where the algorithm is saved.
- Return type
- property input_data: numpy.ndarray
The input data matrix.
- property input_dimension: int
The input space dimension.
- property is_trained: bool
Return whether the algorithm is trained.
- property learning_samples_indices: Sequence[int]
The indices of the learning samples used for the training.
- property output_data: numpy.ndarray
The output data matrix.
- property output_dimension: int
The output space dimension.