mlens.ensemble.super_learner module

ML-ENSEMBLE

author:Sebastian Flennerhag
copyright:2017
licence:MIT

Super Learner class. Fully integrable with Scikit-learn.

class mlens.ensemble.super_learner.SuperLearner(folds=2, shuffle=False, random_state=None, scorer=None, raise_on_exception=True, array_check=2, verbose=False, n_jobs=-1, backend=None, layers=None)[source]

Bases: mlens.ensemble.base.BaseEnsemble

Super Learner class.

The Super Learner (also known as the Stacking Ensemble)is an supervised ensemble algorithm that uses K-fold estimation to map a training set \((X, y)\) into a prediction set \((Z, y)\), where the predictions in \(Z\) are constructed using K-Fold splits of \(X\) to ensure \(Z\) reflects test errors, and that applies a user-specified meta learner to predict \(y\) from \(Z\). The algorithm in sudo code follows:

  1. Specify a library \(L\) of base learners
  2. Fit all base learners on \(X\) and store the fitted estimators.
  3. Split \(X\) into \(K\) folds, fit every learner in \(L\) on the training set and predict test set. Repeat until all folds have been predicted.
  4. Construct a matrix \(Z\) by stacking the predictions per fold.
  5. Fit the meta learner on \(Z\) and store the learner

The ensemble can be used for prediction by mapping a new test set \(T\) into a prediction set \(Z'\) using the learners fitted in (2), and then mapping \(Z'\) to \(y'\) using the fitted meta learner from (5).

The Super Learner does asymptotically as well as (up to a constant) an Oracle selector. For the theory behind the Super Learner, see [1] and [2] as well as references therein.

Stacking K-fold predictions to cover an entire training set is a time consuming method and can be prohibitively costly for large datasets. With large data, other ensembles that fits an ensemble on subsets can achieve similar performance at a fraction of the training time. However, when data is noisy or of high variance, the SuperLearner ensure all information is used during fitting.

References

[1]van der Laan, Mark J.; Polley, Eric C.; and Hubbard, Alan E., “Super Learner” (July 2007). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 222. http://biostats.bepress.com/ucbbiostat/paper222
[2]Polley, Eric C. and van der Laan, Mark J., “Super Learner In Prediction” (May 2010). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 266. http://biostats.bepress.com/ucbbiostat/paper266

Notes

This implementation uses the agnostic meta learner approach, where the user supplies the meta learner to be used. For the original Super Learner algorithm (i.e. learn the best linear combination of the base learners), the user can specify a linear regression as the meta learner.

See also

BlendEnsemble, Subsemble

Parameters:
  • folds (int (default = 2)) – number of folds to use during fitting. Note: this parameter can be specified on a layer-specific basis in the add method.
  • shuffle (bool (default = True)) – whether to shuffle data before generating folds.
  • random_state (int (default = None)) – random seed if shuffling inputs.
  • scorer (object (default = None)) – scoring function. If a function is provided, base estimators will be scored on the training set assembled for fitting the meta estimator. Since those predictions are out-of-sample, the scores represent valid test scores. The scorer should be a function that accepts an array of true values and an array of predictions: score = f(y_true, y_pred).
  • raise_on_exception (bool (default = True)) – whether to issue warnings on soft exceptions or raise error. Examples include lack of layers, bad inputs, and failed fit of an estimator in a layer. If set to False, warnings are issued instead but estimation continues unless exception is fatal. Note that this can result in unexpected behavior unless the exception is anticipated.
  • array_check (int (default = 2)) –

    level of strictness in checking input arrays.

    • array_check = 0 will not check X or y
    • array_check = 1 will check X and y for inconsistencies and warn when format looks suspicious, but retain original format.
    • array_check = 2 will impose Scikit-learn array checks, which converts X and y to numpy arrays and raises an error if conversion fails.
  • verbose (int or bool (default = False)) –

    level of verbosity.

    • verbose = 0 silent (same as verbose = False)
    • verbose = 1 messages at start and finish (same as verbose = True)
    • verbose = 2 messages for each layer

    If verbose >= 50 prints to sys.stdout, else sys.stderr. For verbosity in the layers themselves, use fit_params.

  • n_jobs (int (default = -1)) – number of CPU cores to use for fitting and prediction.
  • backend (str or object (default = 'threading')) – backend infrastructure to use during call to mlens.externals.joblib.Parallel. See Joblib for further documentation. To set global backend, set mlens.config.BACKEND.
scores_

dict – if scorer was passed to instance, scores_ contains dictionary with cross-validated scores assembled during fit call. The fold structure used for scoring is determined by folds.

Examples

Instantiate ensembles with no preprocessing: use list of estimators

>>> from mlens.ensemble import SuperLearner
>>> from mlens.metrics.metrics import rmse
>>> from sklearn.datasets import load_boston
>>> from sklearn.linear_model import Lasso
>>> from sklearn.svm import SVR
>>>
>>> X, y = load_boston(True)
>>>
>>> ensemble = SuperLearner()
>>> ensemble.add([SVR(), ('can name some or all est', Lasso())])
>>> ensemble.add_meta(SVR())
>>>
>>> ensemble.fit(X, y)
>>> preds = ensemble.predict(X)
>>> rmse(y, preds)
6.955358...

Instantiate ensembles with different preprocessing pipelines through dicts.

>>> from mlens.ensemble import SuperLearner
>>> from mlens.metrics.metrics import rmse
>>> from sklearn.datasets import load_boston
>>> from sklearn. preprocessing import MinMaxScaler, StandardScaler
>>> from sklearn.linear_model import Lasso
>>> from sklearn.svm import SVR
>>>
>>> X, y = load_boston(True)
>>>
>>> preprocessing_cases = {'mm': [MinMaxScaler()],
...                        'sc': [StandardScaler()]}
>>>
>>> estimators_per_case = {'mm': [SVR()],
...                        'sc': [('can name some or all ests', Lasso())]}
>>>
>>> ensemble = SuperLearner()
>>> ensemble.add(estimators_per_case, preprocessing_cases).add(SVR(),
...                                                            meta=True)
>>>
>>> ensemble.fit(X, y)
>>> preds = ensemble.predict(X)
>>> rmse(y, preds)
7.841329...
add(estimators, preprocessing=None, folds=None, proba=False, meta=False, propagate_features=None, **kwargs)[source]

Add layer to ensemble.

Parameters:
  • estimators (dict of lists or list or instance) –

    estimators constituting the layer. If preprocessing is none and the layer is meant to be the meta estimator, it is permissible to pass a single instantiated estimator. If preprocessing is None or list, estimators should be a list. The list can either contain estimator instances, named tuples of estimator instances, or a combination of both.

    option_1 = [estimator_1, estimator_2]
option_2 = [("est-1", estimator_1), ("est-2", estimator_2)]
option_3 = [estimator_1, ("est-2", estimator_2)]

    If different preprocessing pipelines are desired, a dictionary that maps estimators to preprocessing pipelines must be passed. The names of the estimator dictionary must correspond to the names of the estimator dictionary.

    preprocessing_cases = {"case-1": [trans_1, trans_2],
                       "case-2": [alt_trans_1, alt_trans_2]}

estimators = {"case-1": [est_a, est_b],
              "case-2": [est_c, est_d]}

    The lists for each dictionary entry can be any of option_1, option_2 and option_3.

  • preprocessing (dict of lists or list, optional (default = None)) –

    preprocessing pipelines for given layer. If the same preprocessing applies to all estimators, preprocessing should be a list of transformer instances. The list can contain the instances directly, named tuples of transformers, or a combination of both.

    option_1 = [transformer_1, transformer_2]
option_2 = [("trans-1", transformer_1),
            ("trans-2", transformer_2)]
option_3 = [transformer_1, ("trans-2", transformer_2)]

    If different preprocessing pipelines are desired, a dictionary that maps preprocessing pipelines must be passed. The names of the preprocessing dictionary must correspond to the names of the estimator dictionary.

    preprocessing_cases = {"case-1": [trans_1, trans_2],
                       "case-2": [alt_trans_1, alt_trans_2]}

estimators = {"case-1": [est_a, est_b],
              "case-2": [est_c, est_d]}

    The lists for each dictionary entry can be any of option_1, option_2 and option_3.

  • folds (int, optional) – Use if a different number of folds is desired than what the ensemble was instantiated with.
  • proba (bool) – whether layer should predict class probabilities. Note: setting proba=True will attempt to call an the estimators predict_proba method.
  • propagate_features (list, optional) – List of column indexes to propagate from the input of the layer to the output of the layer. Propagated features are concatenated and stored in the leftmost columns of the output matrix. The propagate_features list should define a slice of the numpy array containing the input data, e.g. [0, 1] to propagate the first two columns of the input matrix to the output matrix.
  • meta (bool (default = False)) – indicator if the layer added is the final meta estimator. This will prevent folded or blended fits of the estimators and only fit them once on the full input data.
  • **kwargs (optional) – optional keyword arguments.
Returns:

self – ensemble instance with layer instantiated.
Return type:

instance
add_meta(estimator, **kwargs)[source]

Meta Learner.

Meta learner to be used for final predictions.

Parameters:
  • estimator (instance) – estimator instance.
  • **kwargs (optional) – optional keyword arguments.