The following tutorials highlight advanced functionality and provide in-depth material on ensemble APIs.

Tutorial Content
Propagating input features Propagate feature input features through layers
to allow several layers to see the same input.
Probabilistic ensemble learning Build layers that output class probabilities from each base
learner so that the next layer or meta estimator learns
from probability distributions.
Advanced Subsemble techniques Learn homogenous partitions of feature space
that maximize base learner’s performance on each partition.
General multi-layer ensemble learning How to build ensembles with different layer classes
Passing file paths as data input Avoid loading data into the parent process by specifying a
file path to a memmaped array or a csv file.
Ensemble model selection Build transformers that replicate layers in ensembles for
model selection of higher-order layers and / or meta learners.

We use the same preliminary settings as in the getting started section.

import numpy as np
from pandas import DataFrame
from sklearn.metrics import accuracy_score

seed = 2017
np.random.seed(seed)

idx = np.random.permutation(150)
X = data.data[idx]
y = data.target[idx]


Propagating input features¶

When stacking several layers of base learners, the variance of the input will typically get smaller as learners get better and better at predicting the output and the remaining errors become increasingly difficult to correct for. This multicolinearity can significantly limit the ability of the ensemble to improve upon the best score of the subsequent layer as there is too little variation in predictions for the ensemble to learn useful combinations. One way to increase this variation is to propagate features from the original input and / or earlier layers. To achieve this in ML-Ensemble, we use the propagate_features attribute. To see how this works, let’s compare a three-layer ensemble with and without feature propagation.

from mlens.ensemble import SuperLearner
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.svm import SVC

def build_ensemble(incl_meta, propagate_features=None):
"""Return an ensemble."""
if propagate_features:
n = len(propagate_features)
propagate_features_1 = propagate_features
propagate_features_2 = [i for i in range(n)]
else:
propagate_features_1 = propagate_features_2 = None

estimators = [RandomForestClassifier(random_state=seed), SVC()]

ensemble = SuperLearner()

if incl_meta:
return ensemble


Without feature propagation, the meta learner will learn from the predictions of the penultimate layers:

base = build_ensemble(False)
base.fit(X, y)
pred = base.predict(X)[:5]
print("Input to meta learner :\n %r" % pred)


Out:

Input to meta learner :
array([[ 2.,  2.],
[ 2.,  2.],
[ 2.,  2.],
[ 1.,  1.],
[ 1.,  1.]], dtype=float32)


When we propagate features, some (or all) of the input seen by one layer is passed along to the next layer. For instance, we can propagate some or all of the input array through our two intermediate layers to the meta learner input of the meta learner:

base = build_ensemble(False, [1, 3])
base.fit(X, y)
pred = base.predict(X)[:5]
print("Input to meta learner :\n %r" % pred)


Out:

Input to meta learner :
array([[ 3.20000005,  2.29999995,  2.        ,  2.        ],
[ 3.20000005,  2.29999995,  2.        ,  2.        ],
[ 3.        ,  2.0999999 ,  2.        ,  2.        ],
[ 3.20000005,  1.5       ,  1.        ,  1.        ],
[ 2.79999995,  1.39999998,  1.        ,  1.        ]], dtype=float32)


In this scenario, the meta learner will see noth the predictions made by the penultimate layer, as well as the second and fourth feature of the original input. By propagating features, the issue of multicolinearity in deep ensembles can be mitigated. In particular, it can give the meta learner greater opportunity to identify neighborhoods in the original feature space where base learners struggle. We can get an idea of how feature propagation works with our toy example. First, we need a simple ensemble evaluation routine. In our case, propagating the original features through two layers of the same library of base learners gives a dramatic increase in performance on the test set:

def evaluate_ensemble(propagate_features):
"""Wrapper for ensemble evaluation."""
ens = build_ensemble(True, propagate_features)
ens.fit(X[:75], y[:75])
pred = ens.predict(X[75:])
return accuracy_score(pred, y[75:])

score_no_prep = evaluate_ensemble(None)
score_prep = evaluate_ensemble([0, 1, 2, 3])
print("Test set score no feature propagation  : %.3f" % score_no_prep)
print("Test set score with feature propagation: %.3f" % score_prep)


Out:

Test set score no feature propagation  : 0.667
Test set score with feature propagation: 0.987


By combining feature propagation with the Subset transformer, you can propagate the feature through several layers without any of the base estimators in those layers seeing the propagated features. This can be desirable if you want to propagate the input features to the meta learner without intermediate base learners always having access to the original input data. In this case, we specify propagation as above, but add a preprocessing pipeline to intermediate layers:

from mlens.preprocessing import Subset

estimators = [RandomForestClassifier(random_state=seed), SVC()]
ensemble = SuperLearner()

# Initial layer, propagate as before

# Intermediate layer, keep propagating, but add a preprocessing
# pipeline that selects a subset of the input
preprocessing=[Subset([2, 3])],
propagate_features=[0, 1])


In the above example, the two first features of the original input data will be propagated through both layers, but the second layer will not be trained on it. Instead, it will only see the predictions made by the base learners in the first layer.

ensemble.fit(X, y)
n = list(ensemble.layer_2.learners[0].learner)[0].estimator.feature_importances_.shape[0]
m = ensemble.predict(X).shape[1]
print("Num features seen by estimators in intermediate layer: %i" % n)
print("Num features in the output array of the intermediate layer: %i" % m)


Out:

Num features seen by estimators in intermediate layer: 2
Num features in the output array of the intermediate layer: 4


Probabilistic ensemble learning¶

When the target to predict is a class label, it can often be beneficial to let higher-order layers or the meta learner learn from class probabilities, as opposed to the predicted class. Scikit-learn classifiers can return a matrix that, for each observation in the test set, gives the probability that the observation belongs to the a given class. While we are ultimately interested in class membership, this information is much richer that just feeding the predicted class to the meta learner. In essence, using class probabilities allow the meta learner to weigh in not just the predicted class label (the highest probability), but also with what confidence each estimator makes the prediction, and how estimators consider the alternative. First, let us set a benchmark ensemble performance when learning is by predicted class membership.

from mlens.ensemble import BlendEnsemble
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.svm import SVC

def build_ensemble(proba, **kwargs):
"""Return an ensemble."""
estimators = [RandomForestClassifier(random_state=seed),
SVC(probability=proba)]

ensemble = BlendEnsemble(**kwargs)
ensemble.add(estimators, proba=proba)   # Specify 'proba' here

return ensemble


As in the ensemble guide, we fit on the first half, and test on the remainder.

ensemble = build_ensemble(proba=False)
ensemble.fit(X[:75], y[:75])
preds = ensemble.predict(X[75:])
print("Accuracy:\n%r" % accuracy_score(preds, y[75:]))


Out:

Accuracy:
0.66666666666666663


Now, to enable probabilistic learning, we set proba=True in the add method for all layers except the final meta learner layer.

ensemble = build_ensemble(proba=True)
ensemble.fit(X[:75], y[:75])
preds = ensemble.predict(X[75:])
print("\nAccuracy:\n%r" % accuracy_score(preds, y[75:]))


Out:

Accuracy:
0.95999999999999996


In this case, using probabilities has a drastic effect on predictive performance, increasing some 40 percentage points. For an applied example see the ensemble used to beat the Scikit-learn MNIST benchmark.

Subsembles leverages the idea that neighborhoods of feature space have a specific local structure. When we fit an estimator across all feature space, it is very hard to capture several such local properties. Subsembles partition the feature space and fits each base learner to each partitions, thereby allow base learners to optimize locally. Instead, the task of generalizing across neighborhoods is left to the meta learner. This strategy can be very powerful when the local structure first needs to be extracted, before an estimator can learn to generalize. Suppose you want to learn the probability distribution of some variable $$y$$. Often, the true distribution is multi-modal, which is an extremely hard problem. In fact, most machine learning algorithms, especially with convex optimization objectives, are ill equipped to solve this problem. Subsembles can overcome this issue allowing base estimators to fit one mode of the distribution at a time, which yields a better representation of the distribution and greatly facilitates the learning problem of the meta learner.

By default, the Subsemble class partitioning the dataset randomly. Note however that partitions are created on the data “as is”, so if the ordering of observations is not random, neither will the partitioning be. For this reason, it is recommended to shuffle the data (e.g. via the shuffle option at initialization). To build a subsemble with random partitions, the only parameter needed is the number of partitions when instantiating the Subsemble.

from mlens.ensemble import Subsemble
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC

def build_subsemble():
"""Build a subsemble with random partitions"""
sub = Subsemble(partitions=3, folds=2)
return sub

sub= build_subsemble()
sub.fit(X, y)
s = sub.predict(X[:10]).shape[1]
print("No. prediction features: %i " % s)


Out:

No. prediction features: 6


During training, the base learners are copied to each partition, so the output of each layer gets multiplied by the number of partitions. In this case, we have 2 base learners for 3 partitions, giving 6 prediction features.

By creating partitions, subsembles scale significantly better than the SuperLearner, but in contrast to BlendEnsemble, the full training data is leveraged during training. But randomly partitioning the data does however not exploit the full advantage of locality, since it is only by luck that we happen to create such partitions. A better way is to learn how to best partition the data. We can either use unsupervised algorithms to generate clusters, or supervised estimators and create partitions based on their predictions. In ML-Ensemble, this is achieved by passing an estimator as partition_estimator. This estimator can differ between layers.

Very few limitation are imposed on the estimator: you can specify whether you want to fit it before generating partitions, whether to use labels in the partitioning, and what method to call to generate the partitions. See ClusteredSubsetIndex for the full documentation. This level of generality does impose some responsibility on the user. In particular, it is up to the user to ensure that sensible partitions are created. Problems to watch out for is too small partitions (too many clusters, too uneven cluster sizes) and clusters with too little variation: for instance with only a single class label in the entire partition, base learners have nothing to learn. Let’s see how to do this in practice. For instance, we can use an unsupervised K-Means clustering estimator to partition the data, like so:

from sklearn.cluster import KMeans

def build_clustered_subsemble(estimator):
"""Build a subsemble with random partitions"""
sub = Subsemble(partitions=2,
partition_estimator=estimator,
folds=2, verbose=2)

return sub

sub = build_clustered_subsemble(KMeans(2))
sub.fit(X[:, [0, 1]], y)


Out:

Fitting 2 layers
Processing layer-1             done | 00:00:00
Processing layer-2             done | 00:00:00
Fit complete                        | 00:00:00


The Iris dataset can actually separate the classes perfectly with a KMeans estimator which leads to zero label variation in each partition. For that reason the above code fits the KMeans estimator on only the first two columns. But this approach is nota very good way of doing it since we loose the rest of the data when fitting the estimators too. Instead, we could customize the partitioning estimator to make the subset selection itself. For instance, we can use Scikit-learn’s sklearn.pipeline.Pipeline class to put a dimensionality reduction transformer before the partitioning estimator, such as a sklearn.decomposition.PCA, or the mlens.preprocessing.Subset transformer to drop some features before estimation. We then use this pipeline as a our partition estimator and fit the subsemble on all features.

from mlens.preprocessing import Subset
from sklearn.pipeline import make_pipeline

# This partition estimator is equivalent to the one used above
pe = make_pipeline(Subset([0, 1]), KMeans(2))
sub = build_clustered_subsemble(pe)

sub.fit(X, y)


Out:

Fitting 2 layers
Processing layer-1             done | 00:00:00
Processing layer-2             done | 00:00:00
Fit complete                        | 00:00:00


In general, you may need to wrap an estimator around a custom class to modify it’s output to generate good partitions. For instance, in regression problems, the output of a supervised estimator needs to be binarized to give a discrete number of partitions. Here’s minimalist way of wrapping a Scikit-learn estimator:

from sklearn.linear_model import LinearRegression

class MyClass(LinearRegression):

def __init__(self, **kwargs):
super(MyClass, self).__init__(**kwargs)

def fit(self, X, y):
"""Fit estimator."""
super(MyClass, self).fit(X, y)
return self

def predict(self, X):
"""Generate partition"""
p = super(MyClass, self).predict(X)
return 1 * (p > p.mean())


Importantly, your partition estimator should implement a get_params method to avoid unexpected errors. If you don’t, you may encounter a NotFittedError when calling predict. To summarize the functionality in one example, let’s implement a simple (but rather useless) partition estimator that splits the data in half based on the sum of the features.

class SimplePartitioner():

def __init__(self):
pass

def our_custom_function(self, X, y=None):
"""Split the data in half based on the sum of features"""
# Labels should be numerical
return 1 * (X.sum(axis=1) > X.sum(axis=1).mean())

def get_params(self, deep=False):
return {}

# Note that the number of partitions the estimator creates *must* match the
# partitions argument passed to the subsemble.

sub = Subsemble(partitions=2, folds=3, verbose=1)
partition_estimator=SimplePartitioner(),
fit_estimator=False,
attr="our_custom_function")

sub.fit(X, y)


Out:

Fitting 1 layers
Fit complete                        | 00:00:00


A final word of caution. When implementing custom estimators from scratch, some care needs to be taken if you plan on copying the Subsemble. It is advised that the estimator inherits the sklearn.base.BaseEstimator class to provide a Scikit-learn compatible interface. For further information, see the API Reference documentation of the Subsemble and mlens.base.indexer.ClusteredSubsetIndex.

For an example of using clustered subsemble, see the subsemble used to beat the Scikit-learn MNIST benchmark.

General multi-layer ensemble learning¶

To alternate between the type of layer with each add call, the SequentialEnsemble class can be used to specify what type of layer (i.e. stacked, blended, subsamle-style) to add. This is particularly powerful if facing a large dataset, as the first layer can use a fast approach such as blending, while subsequent layers fitted on the remaining data can use more computationally intensive approaches.

from mlens.ensemble import SequentialEnsemble

ensemble = SequentialEnsemble()

# The initial layer is a blended layer, same as a layer in the BlendEnsemble
[SVC(), RandomForestClassifier(random_state=seed)])

# The second layer is a stacked layer, same as a layer of the SuperLearner

# The third layer is a subsembled layer, same as a layer of the Subsemble

# The meta estimator is added as in any other ensemble


The below table maps the types of layers available in the SequentialEnsemble with the corresponding ensemble.

Ensemble equivalent SequentialEnsemble parameter
‘SuperLearner’ ‘stack’
‘BlendEnsemble’ ‘blend’
‘Subsemble’ ‘subsemble’

Once instantiated, the SequentialEnsemble behaves as expect:

preds = ensemble.fit(X[:75], y[:75]).predict(X[75:])
accuracy_score(preds, y[75:])


In this case, the multi-layer SequentialEnsemble with an initial blended layer and second stacked layer achieves similar performance as the BlendEnsemble with probabilistic learning. Note that we could have made any of the layers probabilistic by setting Proba=True.

Passing file paths as data input¶

With large datasets, it can be expensive to load the full data into memory as a numpy array. Since ML-Ensemle uses a memmaped cache, the need to keep the full array in memory can be entirely circumvented by passing a file path as entry to X and y. There are two important things to note when doing this.

First, ML-Ensemble delpoys Scikit-learn’s array checks, and passing a string will cause an error. To avoid this, the ensemble must be initialized with array_check=0, in which case there will be no checks on the array. The user should make certain that the the data is approprate for esitmation, by converting missing values and infinites to numerical representation, ensuring that all features are numerical, and remove any headers, index columns and footers.

Second, ML-Ensemble expects the file to be either a csv, an npy or mmap file and will treat these differently.

• If a path to a csv file is passed, the ensemble will first load the file into memory, then dump it into the cache, before discarding the file from memory by replacing it with a pointer to the memmaped file. The loading module used for the csv file is the numpy.loadtxt() function.
• If a path to a npy file is passed, a memmaped pointer to it will be loaded.
• If a path to a mmap file is passed, it will be used as the memmaped input array for estimation.
import os
import tempfile

# We create a temporary folder in the current working directory
temp = tempfile.TemporaryDirectory(dir=os.getcwd())

# Dump the X and y array in the temporary directory, here as csv files
fx = os.path.join(temp.name, 'X.csv')
fy = os.path.join(temp.name, 'y.csv')

np.savetxt(fx, X)
np.savetxt(fy, y)

# We can now fit any ensemble simply by passing the file pointers fx and
# fy. Remember to set array_check=0.
ensemble = build_ensemble(False, array_check=0)
ensemble.fit(fx, fy)
preds = ensemble.predict(fx)
print(preds[:10])


Out:

[ 2.  2.  2.  1.  1.  2.  2.  2.  2.  2.]


If you are following the examples on your machine, don’t forget to remove the temporary directory.

try:
temp.cleanup()
del temp
except OSError:
# This can fail on Windows
pass


Ensemble model selection¶

Ensembles benefit from a diversity of base learners, but often it is not clear how to parametrize the base learners. In fact, combining base learners with lower predictive power can often yield a superior ensemble. This hinges on the errors made by the base learners being relatively uncorrelated, thus allowing a meta estimator to learn how to overcome each model’s weakness. But with highly correlated errors, there is little for the ensemble to learn from.

To fully exploit the learning capacity in an ensemble, it is beneficial to conduct careful hyper parameter tuning, treating the base learner’s parameters as the parameters of the ensemble. By far the most critical part of the ensemble is the meta learner, but selecting an appropriate meta learner can be an ardous task if the entire ensemble has to be evaluated each time.

The task can be made considerably easier by treating the lower layers of an ensemble as preprocessing pipeline, and performing model selection on higher-order layers or meta learners. To use an ensemble for this purpose, set the model_selection parameter to True before fitting. This will modify how the transform method behaves, to ensure predict is called on test folds.

Warning

Remember to turn model selection off when done.

from mlens.model_selection import Evaluator

from mlens.metrics import make_scorer
from scipy.stats import uniform, randint

# Set up two competing ensemble bases as preprocessing transformers:
# one stacked ensemble base with proba and one without
base_learners = [RandomForestClassifier(random_state=seed),
SVC(probability=True)]

proba_transformer = SequentialEnsemble(
'blend', base_learners, proba=True)
class_transformer = SequentialEnsemble(
'blend', base_learners, proba=False)

# Set up a preprocessing mapping
# Each pipeline in this map is fitted once on each fold before
# evaluating candidate meta learners.
preprocessing = {'proba': [('layer-1', proba_transformer)],
'class': [('layer-1', class_transformer)]}

# Set up candidate meta learners
# We can specify a dictionary if we wish to try different candidates on
# different cases, or a list if all estimators should be run on all
# preprocessing pipelines (as in this example)
meta_learners = [SVC(), ('rf', RandomForestClassifier(random_state=seed))]

# Set parameter mapping
# Here, we differentiate distributions between cases for the random forest
params = {'svc': {'C': uniform(0, 10)},
'class.rf': {'max_depth': randint(2, 10)},
'proba.rf': {'max_depth': randint(2, 10),
'max_features': uniform(0.5, 0.5)}
}

scorer = make_scorer(accuracy_score)
evaluator = Evaluator(scorer=scorer, random_state=seed, cv=2)

evaluator.fit(X, y, meta_learners, params, preprocessing=preprocessing, n_iter=2)


We can now compare the performance of the best fit for each candidate meta learner.

print("Results:\n%s" % evaluator.results)


Out:

Results:
test_score-m  test_score-s  train_score-m  train_score-s  fit_time-m  fit_time-s  pred_time-m  pred_time-s                                                 params
class  rf            0.947         0.013          0.946          0.000       1.050       0.193        0.091        0.069                                       {'max_depth': 5}
class  svc           0.947         0.013          0.946          0.000       0.680       0.194        0.028        0.020                             {'C': 0.20960225406117416}
proba  rf            0.933         0.027          1.000          0.000       0.930       0.086        0.028        0.018  {'max_depth': 5, 'max_features': 0.51048011270305871}
proba  svc           0.960         0.000          0.973          0.000       0.606       0.089        0.043        0.042                              {'C': 7.6707016468248774}
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Total running time of the script: ( 0 minutes 18.291 seconds)

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