MRCpy.DWGCS

class MRCpy.DWGCS(loss='0-1', deterministic=True, random_state=None, fit_intercept=False, D=4, sigma_=None, B=1000, solver='adam', alpha=0.01, stepsize='decay', mini_batch_size=None, max_iters=None, phi='linear', **phi_kwargs)

Double-Weighting General Covariate Shift

The class DWGCS implements the method Double-Weighting for General Covariate Shift (DWGCS) proposed in [1]. It is designed for supervised classification under covariate shift.

DW-GCS provides adaptatition to covariate shift when a set of training samples and a set of unlabeled samples from the testing distribution are available at learning, without any prior knowledge about the supports of the training and testing distribution.

It implements 0-1 and log loss, and it can be used with multiple feature mappings.

See also

For more information about DWGCS, one can refer to the following paper:

[1] `Segovia-Martín, J. I., Mazuelas, S., & Liu, A. (2023). Double-Weighting for Covariate Shift Adaptation. International Conference on Machine Learning (ICML) 2023.

@InProceedings{SegMazLiu:23, title = {Double-Weighting for Covariate Shift Adaptation}, author = {Segovia-Mart{‘i}n, Jos{‘e} I.

and Mazuelas, Santiago and Liu, Anqi},

booktitle = {Proceedings of the 40th

International Conference on Machine Learning},

pages = {30439–30457}, year = {2023}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23–29 Jul}, publisher = {PMLR}, }

lossstr {‘0-1’, ‘log’}, default = ‘0-1’

Type of loss function to use for the risk minimization. 0-1 loss quantifies the probability of classification error at a certain example for a certain rule. Log-loss quantifies the minus log-likelihood at a certain example for a certain rule.

deterministicbool, default = True

Whether the prediction of the labels should be done in a deterministic way (given a fixed random_state in the case of using random Fourier or random ReLU features).

random_stateint, RandomState instance, default = None

Random seed used when ‘fourier’ and ‘relu’ options for feature mappings are used to produce the random weights.

fit_interceptbool, default = False

Whether to calculate the intercept for MRCs If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered).

Dint, default = 4

Hyperparameter that balances the trade-off between error in expectation estimates and confidence of the classification.

Bint, default = 1000

Parameter that bound the maximum value of the weights beta associated to the training samples.

solver{‘cvx’, ‘grad’, ‘adam’}, default = ’adam’

Method to use in solving the optimization problem. Default is ‘cvx’. To choose a solver, you might want to consider the following aspects:

’cvx’

Solves the optimization problem using the CVXPY library. Obtains an accurate solution while requiring more time than the other methods. Note that the library uses the GUROBI solver in CVXpy for which one might need to request for a license. A free license can be requested here

’grad’

Solves the optimization using stochastic gradient descent. The parameters max_iters, stepsize and mini_batch_size determine the number of iterations, the learning rate and the batch size for gradient computation respectively. Note that the implementation uses nesterov’s gradient descent in case of ReLU and threshold features, and the above parameters do no affect the optimization in this case.

’adam’

Solves the optimization using stochastic gradient descent with adam (adam optimizer). The parameters max_iters, alpha and mini_batch_size determine the number of iterations, the learning rate and the batch size for gradient computation respectively. Note that the implementation uses nesterov’s gradient descent in case of ReLU and threshold features, and the above parameters do no affect the optimization in this case.

alphafloat, default = 0.001

Learning rate for ’adam’ solver.

mini_batch_sizeint, default = 1 or 32

The size of the batch to be used for computing the gradient in case of stochastic gradient descent and adam optimizer. In case of stochastic gradient descent, the default is 1, and in case of adam optimizer, the default is 32.

max_itersint, default = 100000 or 5000 or 2000

The maximum number of iterations to use in case of ’grad’ or ’adam’ solver. The default value is 100000 for ’grad’ solver and 5000 for ’adam’ solver and 2000 for nesterov’s gradient descent.

phistr or BasePhi instance, default = ‘linear’

Type of feature mapping function to use for mapping the input data. The currenlty available feature mapping methods are ‘fourier’, ‘relu’, 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.

‘relu’

It uses Rectified Linear Unit (ReLU) features. See class RandomReLUPhi.

**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 - DWGCS(loss='log', phi='fourier', n_components=300)

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

Methods

DWKMM(xTr, xTe)	Obtain training and testing weights.
compute_lambda(xTe, tau_, n_classes)	Compute deviation in the mean estimate tau using the given testing instances.
compute_phi(X)	Compute the feature mapping corresponding to instances given for learning the classifiers and prediction.
compute_tau(xTr, yTr)	Compute mean estimate tau using the given training instances.
error(X, Y)	Return the mean error obtained for the given test data and labels.
fit(xTr, yTr[, xTe])	Fit the MRC model.
get_params([deep])	Get parameters for this estimator.
get_upper_bound()	Returns the upper bound on the expected loss for the fitted classifier.
minimax_risk(X, tau_, lambda_, n_classes)	Solves the marginally constrained minimax risk optimization problem for different types of loss (0-1 and log loss).
predict(X)	Predicts classes for new instances using a fitted model.
predict_proba(X)	Computes conditional probabilities corresponding to each class for the given unlabeled instances.
psi(mu, phi)	Function to compute the psi function in the objective using the given solution mu and the feature mapping corresponding to a single instance.
score(X, y[, sample_weight])	Return the mean accuracy on the given test data and labels.
set_params(**params)	Set the parameters of this estimator.

DWKMM(xTr, xTe)

Obtain training and testing weights.

Computes the weights associated to the training and testing samples solving the DW-KMM problem.

Parameters

xTrarray-like of shape (n_samples, n_dimensions)

Training instances used in

• Computing the training weights beta and testing weights alpha.

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

xTrarray-like of shape (n_samples, n_dimensions)

Testing instances used in

• Computing the training weights beta and testing weights alpha.

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

Returns

self

Weights self.beta_ and self.alpha_

__init__(loss='0-1', deterministic=True, random_state=None, fit_intercept=False, D=4, sigma_=None, B=1000, solver='adam', alpha=0.01, stepsize='decay', mini_batch_size=None, max_iters=None, phi='linear', **phi_kwargs)

compute_lambda(xTe, tau_, n_classes)

Compute deviation in the mean estimate tau using the given testing instances.

Parameters

xTearray-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)

The mean estimates for the expectations of feature mappings.

n_classesint

Number of labels in the dataset.

Returns

lambda_

Confidence vector

compute_phi(X)

Compute the feature mapping corresponding to instances given for learning the classifiers and prediction.

Parameters

Xarray-like of shape (n_samples, n_dimensions)

Instances to be converted to features.

Returns

phi_alpha

Feature mapping weighted by alpha

compute_tau(xTr, yTr)

Compute mean estimate tau using the given training instances.

Parameters

xTrarray-like of shape (n_samples, n_dimensions)

Training instances used for solving the minimax risk optimization problem.

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

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

Returns

tau_

Mean expectation estimate

error(X, Y)

Return the mean error obtained for the given test data and labels.

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.

Returns

errorfloat

Mean error of the learned MRC classifier

fit(xTr, yTr, xTe=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

xTrarray-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.

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

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

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

These instances 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_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.

get_upper_bound()

Returns the upper bound on the expected loss for the fitted classifier.

Returns

upper_boundfloat

Upper bound of the expected loss for the fitted classifier.

minimax_risk(X, tau_, lambda_, n_classes)

Solves the marginally constrained minimax risk optimization problem for different types of loss (0-1 and log loss). When use_cvx=False, it uses SGD optimization for linear and random fourier feature mappings and nesterov subgradient approach for the rest.

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)

The mean estimates for the expectations of feature mappings.

lambda_array-like of shape (n_features * n_classes)

The 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)

Predicts 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.

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)

Computes conditional probabilities corresponding to each class for the given unlabeled instances.

Parameters

Xarray-like of shape (n_samples, n_dimensions)

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

Returns

hy_xarray-like of shape (n_samples, n_classes)

The conditional probabilities (p(y|x)) corresponding to each class.

psi(mu, phi)

Function to compute the psi function in the objective using the given solution mu and the feature mapping corresponding to a single instance.

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_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.

Examples using MRCpy.DWGCS

Example: Use of DWGCS (Double-Weighting General Covariate Shift) for Covariate Shift Adaptation

Example: Use of DWGCS (Double-Weighting General Covariate Shift) for Covariate Shift Adaptation