conformal.regression

Regression module contains methods for conformal regression.

Conformal regressors predict a range of values (not always a single value) under a given significance level (error rate). Every regressors works in combination with a nonconformity measure and on average predicts the correct value with the given error rate. Lower error rates result in narrower ranges of predicted values.

Structure:

• ConformalRegressor

  • Inductive (InductiveRegressor)
  • Cross (CrossRegressor)

class conformal.regression.PredictionRegr(lo, hi)

Bases: object

Conformal regression prediction object, which is produced by the ConformalRegressor.predict() method.

lo

Lowest value of the predicted range.

Type:float

hi

Highest value of the predicted range.

Type:float

Examples

>>> train, test = next(LOOSampler(Table('housing')))
>>> ccr = CrossRegressor(AbsError(LinearRegressionLearner()), 5, train)
>>> prediction = ccr.predict(test[0], 0.1)
>>> print(prediction.width())

__init__(lo, hi)

Initialize the prediction.

Parameters:

• lo (float) – Lowest value of the predicted range.
• hi (float) – Highest value of the predicted range.

range()

Predicted range: lo, hi.

verdict(ref)

Conformal regression prediction is correct when the actual value appears in the predicted range.

Parameters:ref – Reference/actual value Returns:True if the prediction is correct.

width()

Width of the predicted range: hi - lo.

class conformal.regression.ConformalRegressor(nc_measure)

Bases: orangecontrib.conformal.base.ConformalPredictor

Base class for conformal regression.

__init__(nc_measure)

Verify that the nonconformity measure can be used for regression.

predict(example, eps)

Compute a regression prediction object for a given example and significance level.

Function determines what is the eps-th lowest nonconformity score and computes the range of values that would result in a lower or equal nonconformity. This inverse of the nonconformity score is computed by the nonconformity measure’s cp.nonconformity.RegrNC.predict() function.

Parameters:

• example (Instance) – Orange row instance.
• eps (float) – Default significance level (error rate).

Returns:

Regression prediction object.

Return type:

PredictionRegr

__call__(example, eps)

Compute predicted range for a given example and significance level.

Parameters:

• example (Instance) – Orange row instance.
• eps (float) – Significance level (error rate).

Returns:

Predicted range as a pair (PredictionRegr.lo, PredictionRegr.hi)

class conformal.regression.TransductiveRegressor(nc_measure)

Bases: conformal.regression.ConformalRegressor

Transductive regression. TODO

class conformal.regression.InductiveRegressor(nc_measure, train=None, calibrate=None)

Bases: conformal.regression.ConformalRegressor

Inductive regression.

alpha

Nonconformity scores of the calibration instances. Computed by the fit() method. Must be sorted in increasing order.

Examples

>>> train, test = next(LOOSampler(Table('housing')))
>>> train, calibrate = next(RandomSampler(train, 2, 1))
>>> icr = InductiveRegressor(AbsError(LinearRegressionLearner()), train, calibrate)
>>> print(icr(test[0], 0.1))

__init__(nc_measure, train=None, calibrate=None)

Initialize inductive regressor with a nonconformity measure, training set and calibration set. If present, fit the conformal regressor to the training set and compute the nonconformity scores of calibration set.

Parameters:

• nc_measure (RegrNC) – Regression nonconformity measure.
• train (Optional[Table]) – Table of examples used as a training set.
• calibrate (Optional[Table]) – Table of examples used as a calibration set.

fit(train, calibrate)

Fit the conformal regressor to the training set, compute and store sorted nonconformity scores (alpha) on the calibration set and store the domain.

Parameters:

• train (Optional[Table]) – Table of examples used as a training set.
• calibrate (Optional[Table]) – Table of examples used as a calibration set.

class conformal.regression.CrossRegressor(nc_measure, k, train=None)

Bases: conformal.regression.InductiveRegressor

Cross regression.

Examples

>>> train, test = next(LOOSampler(Table('housing')))
>>> ccr = CrossRegressor(AbsError(LinearRegressionLearner()), 4, train)
>>> print(ccr(test[0], 0.1))

__init__(nc_measure, k, train=None)

Initialize cross regressor with a nonconformity measure, number of folds and training set. If present, fit the conformal regressor to the training set.

Parameters:

• nc_measure (RegrNC) – Regression nonconformity measure.
• k (int) – Number of folds.
• train (Optional[Table]) – Table of examples used as a training set.

fit(train)

Fit the cross regressor to the training set. Split the training set into k folds for use as training and calibration set with an inductive regressor. Concatenate the computed nonconformity scores and store them (InductiveRegressor.alpha).

Parameters:train (Table) – Table of examples used as a training set.

class conformal.regression.LOORegressor(nc_measure, train=None)

Bases: conformal.regression.CrossRegressor

Leave-one-out regressor is a cross conformal regressor with the number of folds equal to the size of the training set.

Examples

>>> train, test = next(LOOSampler(Table('housing')))
>>> ccr = LOORegressor(AbsError(LinearRegressionLearner()), train)
>>> print(ccr(test[0], 0.1))

__init__(nc_measure, train=None)

Initialize cross regressor with a nonconformity measure, number of folds and training set. If present, fit the conformal regressor to the training set.

Parameters:

• nc_measure (RegrNC) – Regression nonconformity measure.
• k (int) – Number of folds.
• train (Optional[Table]) – Table of examples used as a training set.

fit(train)

Fit the cross regressor to the training set. Split the training set into k folds for use as training and calibration set with an inductive regressor. Concatenate the computed nonconformity scores and store them (InductiveRegressor.alpha).

Parameters:train (Table) – Table of examples used as a training set.