MRCpy.LCMRC

class MRCpy.LCMRC(s=0.3, loss='0-1', n_classes=2, alpha=None, eps=0.0001, phi='linear', use_closed_form=False, **phi_kwargs)

Marginally Constrained Cost Sensitive Minimax Risk Classifier.

The class LCMRC implements Marginally Constrained Cost Sensitive Minimax Risk Classifiers (MRC), an MRC that can use any loss defined by a loss matrix. It implements two kinds of prediction methods.

Parameters:

n_classesint

Number of different possible labels for an instance.

sfloat, default=0.3

Parameter that tunes the estimation of expected values of feature mapping function. It is used to calculate \(\boldsymbol{\lambda}\) (variance in the mean estimates for the expectations of the feature mappings) in the following way

\[\boldsymbol{\lambda} = s \cdot \text{std}(\Phi(X,Y)) / \sqrt{|X|}\]

where (X,Y) is the dataset of training samples and their labels respectively and \(\text{std}(\Phi(X,Y))\) stands for standard deviation of \(\phi(X,Y)\) in the supervised dataset (X,Y).

lossstr or array-like of shape (n_classes_classification, n_classes)

If a string, one of '0-1', 'ordinal', 'abstention', 'random', 'ordinal-squared'. Generates the corresponding loss matrix. If an array, it will be used as the transposed loss matrix.

alphafloat, optional

Penalty for abstention in that type of loss. Defaults to 1 / (n_classes + 1).

max_itersint, default=2000

Maximum number of iterations to use for finding the solution of optimization in the subgradient approach.

phistr or BasePhi instance, default=’linear’

Type of feature mapping function to use for mapping the input data. The currently available feature mapping methods are 'fourier' and 'linear'. The users can also implement their own feature mapping object (should be a BasePhi instance) and pass it to this argument. Note that when using 'fourier' feature mapping, training and testing instances are expected to be normalized. To implement a feature mapping, please go through the Feature Mappings section.

'linear'

It uses the identity feature map referred to as Linear feature map. See class BasePhi.

'fourier'

It uses Random Fourier Feature map. See class RandomFourierPhi.

epsfloat, default=1e-4

Threshold for comparing values. For instance, testing if two values are different is done as abs(value1 - value2) < eps instead of value1 == value2.

use_closed_formbool, default=False

If True, and if the loss matrix is squared, then it will use the closed form method for classification.

**phi_kwargsAdditional parameters for feature mappings.

Groups the multiple optional parameters for the corresponding feature mappings (phi).

For example in case of fourier features, the number of features is given by n_components parameter which can be passed as argument LCMRC(phi='fourier', n_components=500).

The list of arguments for each feature mappings class can be found in the corresponding documentation.

Methods

error(X, Y[, mean])	Return the error obtained for the given test
fit(X, Y[, X_])	Fit the MRC model.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
minimax_risk(X, tau_, lambda_, n_classes)	Solves the minimax risk problem for different the given loss matrix
predict(X)	Predict classes for new instances using a fitted model.
predict_proba(X)	Conditional probabilities corresponding to each class for each unlabeled input instance
score(X, y[, sample_weight])	Return the mean accuracy on the given test data and labels.
set_fit_request(*[, X_])	Request metadata passed to the fit method.
set_params(**params)	Set the parameters of this estimator.
set_score_request(*[, sample_weight])	Request metadata passed to the score method.

__init__(s=0.3, loss='0-1', n_classes=2, alpha=None, eps=0.0001, phi='linear', use_closed_form=False, **phi_kwargs)

Initialize self. See help(type(self)) for accurate signature.

error(X, Y, mean=True)

Return the error obtained for the given test

data and labels using the loss function given

Parameters:

Xarray-like of shape (n_samples, n_dimensions)

Test instances for which the labels are to be predicted by the MRC model.

Yarray-like of shape (n_samples, 1), default = None

Labels corresponding to the testing instances used to compute the error in the prediction.

mean: `Boolean`, defaults to `True`. If true, the method returns the mean error.

If false, the method returns an array with all the errors.

Returns:

errorfloat (if mean is True)

Mean error of the learned MRC classifier

OR

error: array-like of shape (n_samples) (if mean is False)

Array with the errors commited when classifying each instance

fit(X, Y, X_=None)

Fit the MRC model.

Computes the parameters required for the minimax risk optimization and then calls the minimax_risk function to solve the optimization.

Parameters:

Xarray-like of shape (n_samples, n_dimensions)

Training instances used in

• Calculating the expectation estimates that constrain the uncertainty set for the minimax risk classification

• Solving the minimax risk optimization problem.

n_samples is the number of training samples and n_dimensions is the number of features.

Yarray-like of shape (n_samples, 1), default=None

Labels corresponding to the training instances used only to compute the expectation estimates.

X_array-like of shape (n_samples2, n_dimensions), default=None

These instances are optional and when given, will be used in the minimax risk optimization. These extra instances are generally a smaller set and give an advantage in training time.

Returns:

self :

Fitted estimator

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

minimax_risk(X, tau_, lambda_, n_classes)

Solves the minimax risk problem for different the given loss matrix

Parameters:

Xarray-like of shape (n_samples, n_dimensions)

Training instances used for solving the minimax risk optimization problem.

tau_array-like of shape (n_features * n_classes)

Mean estimates for the expectations of feature mappings.

lambda_array-like of shape (n_features * n_classes)

Variance in the mean estimates for the expectations of the feature mappings.

n_classesint

Number of labels in the dataset.

Returns:

self :

Fitted estimator

predict(X)

Predict classes for new instances using a fitted model.

Returns the predicted classes for the given instances in X using the probabilities given by the function predict_proba. This method overwrites the parent’s class method so that non-square loss matrices are allowed.

Parameters:

Xarray-like of shape (n_samples, n_dimensions)

Test instances for which the labels are to be predicted by the MRC model.

Returns:

y_predarray-like of shape (n_samples,)

Predicted labels corresponding to the given instances.

predict_proba(X)

Conditional probabilities corresponding to each class for each unlabeled input instance

Parameters:

Xarray-like of shape (n_samples, n_dimensions)

Testing instances for which the prediction probabilities are calculated for each class.

Returns:

hy_xndarray of shape (n_samples, n_classes)

Probabilities \((p(y|x))\) corresponding to the predictions for each class.

score(X, y, sample_weight=None)

Return the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters:

Xarray-like of shape (n_samples, n_features)

Test samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True labels for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:

scorefloat

Mean accuracy of self.predict(X) w.r.t. y.

set_fit_request(*, X_: Union[bool, None, str] = '$UNCHANGED$') → MRCpy.lcmrc.LCMRC

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

X_str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for X_ parameter in fit.

Returns:

selfobject

The updated object.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_score_request(*, sample_weight: Union[bool, None, str] = '$UNCHANGED$') → MRCpy.lcmrc.LCMRC

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to score.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in score.

Returns:

selfobject

The updated object.