Stacking Ensemble Machine Learning With Python

Last Updated on August 17, 2020

Stacking or Stacked Generalization is an ensemble machine learning algorithm.

It uses a meta-learning algorithm to learn how to best combine the predictions from two or more base machine learning algorithms.

The benefit of stacking is that it can harness the capabilities of a range of well-performing models on a classification or regression task and make predictions that have better performance than any single model in the ensemble.

In this tutorial, you will discover the stacked generalization ensemble or stacking in Python.

After completing this tutorial, you will know:

  • Stacking is an ensemble machine learning algorithm that learns how to best combine the predictions from multiple well-performing machine learning models.
  • The scikit-learn library provides a standard implementation of the stacking ensemble in Python.
  • How to use stacking ensembles for regression and classification predictive modeling.

Let’s get started.

  • Updated Aug/2020: Improved code examples, added more references.
Stacking Ensemble Machine Learning With Python

Stacking Ensemble Machine Learning With Python
Photo by lamoix, some rights reserved.

Tutorial Overview

This tutorial is divided into four parts; they are:

  1. Stacked Generalization
  2. Stacking Scikit-Learn API
  3. Stacking for Classification
  4. Stacking for Regression

Stacked Generalization

Stacked Generalization or “Stacking” for short is an ensemble machine learning algorithm.

It involves combining the predictions from multiple machine learning models on the same dataset, like bagging and boosting.

Stacking addresses the question:

  • Given multiple machine learning models that are skillful on a problem, but in different ways, how do you choose which model to use (trust)?

The approach to this question is to use another machine learning model that learns when to use or trust each model in the ensemble.

  • Unlike bagging, in stacking, the models are typically different (e.g. not all decision trees) and fit on the same dataset (e.g. instead of samples of the training dataset).
  • Unlike boosting, in stacking, a single model is used to learn how to best combine the predictions from the contributing models (e.g. instead of a sequence of models that correct the predictions of prior models).

The architecture of a stacking model involves two or more base models, often referred to as level-0 models, and a meta-model that combines the predictions of the base models, referred to as a level-1 model.

  • Level-0 Models (Base-Models): Models fit on the training data and whose predictions are compiled.
  • Level-1 Model (Meta-Model): Model that learns how to best combine the predictions of the base models.

The meta-model is trained on the predictions made by base models on out-of-sample data. That is, data not used to train the base models is fed to the base models, predictions are made, and these predictions, along with the expected outputs, provide the input and output pairs of the training dataset used to fit the meta-model.

The outputs from the base models used as input to the meta-model may be real value in the case of regression, and probability values, probability like values, or class labels in the case of classification.

The most common approach to preparing the training dataset for the meta-model is via k-fold cross-validation of the base models, where the out-of-fold predictions are used as the basis for the training dataset for the meta-model.

The training data for the meta-model may also include the inputs to the base models, e.g. input elements of the training data. This can provide an additional context to the meta-model as to how to best combine the predictions from the meta-model.

Once the training dataset is prepared for the meta-model, the meta-model can be trained in isolation on this dataset, and the base-models can be trained on the entire original training dataset.

Stacking is appropriate when multiple different machine learning models have skill on a dataset, but have skill in different ways. Another way to say this is that the predictions made by the models or the errors in predictions made by the models are uncorrelated or have a low correlation.

Base-models are often complex and diverse. As such, it is often a good idea to use a range of models that make very different assumptions about how to solve the predictive modeling task, such as linear models, decision trees, support vector machines, neural networks, and more. Other ensemble algorithms may also be used as base-models, such as random forests.

  • Base-Models: Use a diverse range of models that make different assumptions about the prediction task.

The meta-model is often simple, providing a smooth interpretation of the predictions made by the base models. As such, linear models are often used as the meta-model, such as linear regression for regression tasks (predicting a numeric value) and logistic regression for classification tasks (predicting a class label). Although this is common, it is not required.

  • Regression Meta-Model: Linear Regression.
  • Classification Meta-Model: Logistic Regression.

The use of a simple linear model as the meta-model often gives stacking the colloquial name “blending.” As in the prediction is a weighted average or blending of the predictions made by the base models.

The super learner may be considered a specialized type of stacking.

Stacking is designed to improve modeling performance, although is not guaranteed to result in an improvement in all cases.

Achieving an improvement in performance depends on the complexity of the problem and whether it is sufficiently well represented by the training data and complex enough that there is more to learn by combining predictions. It is also dependent upon the choice of base models and whether they are sufficiently skillful and sufficiently uncorrelated in their predictions (or errors).

If a base-model performs as well as or better than the stacking ensemble, the base model should be used instead, given its lower complexity (e.g. it’s simpler to describe, train and maintain).

Stacking Scikit-Learn API

Stacking can be implemented from scratch, although this can be challenging for beginners.

For an example of implementing stacking from scratch in Python, see the tutorial:

For an example of implementing stacking from scratch for deep learning, see the tutorial:

The scikit-learn Python machine learning library provides an implementation of stacking for machine learning.

It is available in version 0.22 of the library and higher.

First, confirm that you are using a modern version of the library by running the following script:

Running the script will print your version of scikit-learn.

Your version should be the same or higher. If not, you must upgrade your version of the scikit-learn library.

Stacking is provided via the StackingRegressor and StackingClassifier classes.

Both models operate the same way and take the same arguments. Using the model requires that you specify a list of estimators (level-0 models), and a final estimator (level-1 or meta-model).

A list of level-0 models or base models is provided via the “estimators” argument. This is a Python list where each element in the list is a tuple with the name of the model and the configured model instance.

For example, below defines two level-0 models:

Each model in the list may also be a Pipeline, including any data preparation required by the model prior to fitting the model on the training dataset. For example:

The level-1 model or meta-model is provided via the “final_estimator” argument. By default, this is set to LinearRegression for regression and LogisticRegression for classification, and these are sensible defaults that you probably do not want to change.

The dataset for the meta-model is prepared using cross-validation. By default, 5-fold cross-validation is used, although this can be changed via the “cv” argument and set to either a number (e.g. 10 for 10-fold cross-validation) or a cross-validation object (e.g. StratifiedKFold).

Sometimes, better performance can be achieved if the dataset prepared for the meta-model also includes inputs to the level-0 models, e.g. the input training data. This can be achieved by setting the “passthrough” argument to True and is not enabled by default.

Now that we are familiar with the stacking API in scikit-learn, let’s look at some worked examples.

Stacking for Classification

In this section, we will look at using stacking for a classification problem.

First, we can use the make_classification() function to create a synthetic binary classification problem with 1,000 examples and 20 input features.

The complete example is listed below.

Running the example creates the dataset and summarizes the shape of the input and output components.

Next, we can evaluate a suite of different machine learning models on the dataset.

Specifically, we will evaluate the following five algorithms:

  • Logistic Regression.
  • k-Nearest Neighbors.
  • Decision Tree.
  • Support Vector Machine.
  • Naive Bayes.

Each algorithm will be evaluated using default model hyperparameters. The function get_models() below creates the models we wish to evaluate.

Each model will be evaluated using repeated k-fold cross-validation.

The evaluate_model() function below takes a model instance and returns a list of scores from three repeats of stratified 10-fold cross-validation.

We can then report the mean performance of each algorithm and also create a box and whisker plot to compare the distribution of accuracy scores for each algorithm.

Tying this together, the complete example is listed below.

Running the example first reports the mean and standard deviation accuracy for each model.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

We can see that in this case, SVM performs the best with about 95.7 percent mean accuracy.

A box-and-whisker plot is then created comparing the distribution accuracy scores for each model, allowing us to clearly see that KNN and SVM perform better on average than LR, CART, and Bayes.

Box Plot of Standalone Model Accuracies for Binary Classification

Box Plot of Standalone Model Accuracies for Binary Classification

Here we have five different algorithms that perform well, presumably in different ways on this dataset.

Next, we can try to combine these five models into a single ensemble model using stacking.

We can use a logistic regression model to learn how to best combine the predictions from each of the separate five models.

The get_stacking() function below defines the StackingClassifier model by first defining a list of tuples for the five base models, then defining the logistic regression meta-model to combine the predictions from the base models using 5-fold cross-validation.

We can include the stacking ensemble in the list of models to evaluate, along with the standalone models.

Our expectation is that the stacking ensemble will perform better than any single base model.

This is not always the case and if it is not the case, then the base model should be used in favor of the ensemble model.

The complete example of evaluating the stacking ensemble model alongside the standalone models is listed below.

Running the example first reports the performance of each model. This includes the performance of each base model, then the stacking ensemble.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

In this case, we can see that the stacking ensemble appears to perform better than any single model on average, achieving an accuracy of about 96.4 percent.

A box plot is created showing the distribution of model classification accuracies.

Here, we can see that the mean and median accuracy for the stacking model sits slightly higher than the SVM model.

Box Plot of Standalone and Stacking Model Accuracies for Binary Classification

Box Plot of Standalone and Stacking Model Accuracies for Binary Classification

If we choose a stacking ensemble as our final model, we can fit and use it to make predictions on new data just like any other model.

First, the stacking ensemble is fit on all available data, then the predict() function can be called to make predictions on new data.

The example below demonstrates this on our binary classification dataset.

Running the example fits the stacking ensemble model on the entire dataset and is then used to make a prediction on a new row of data, as we might when using the model in an application.

Stacking for Regression

In this section, we will look at using stacking for a regression problem.

First, we can use the make_regression() function to create a synthetic regression problem with 1,000 examples and 20 input features.

The complete example is listed below.

Running the example creates the dataset and summarizes the shape of the input and output components.

Next, we can evaluate a suite of different machine learning models on the dataset.

Specifically, we will evaluate the following three algorithms:

  • k-Nearest Neighbors.
  • Decision Tree.
  • Support Vector Regression.

Note: The test dataset can be trivially solved using a linear regression model as the dataset was created using a linear model under the covers. As such, we will leave this model out of the example so we can demonstrate the benefit of the stacking ensemble method.

Each algorithm will be evaluated using the default model hyperparameters. The function get_models() below creates the models we wish to evaluate.

Each model will be evaluated using repeated k-fold cross-validation. The evaluate_model() function below takes a model instance and returns a list of scores from three repeats of 10-fold cross-validation.

We can then report the mean performance of each algorithm and also create a box and whisker plot to compare the distribution of accuracy scores for each algorithm.

In this case, model performance will be reported using the mean absolute error (MAE). The scikit-learn library inverts the sign on this error to make it maximizing, from -infinity to 0 for the best score.

Tying this together, the complete example is listed below.

Running the example first reports the mean and standard deviation MAE for each model.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

We can see that in this case, KNN performs the best with a mean negative MAE of about -100.

A box-and-whisker plot is then created comparing the distribution negative MAE scores for each model.

Box Plot of Standalone Model Negative Mean Absolute Error for Regression

Box Plot of Standalone Model Negative Mean Absolute Error for Regression

Here we have three different algorithms that perform well, presumably in different ways on this dataset.

Next, we can try to combine these three models into a single ensemble model using stacking.

We can use a linear regression model to learn how to best combine the predictions from each of the separate three models.

The get_stacking() function below defines the StackingRegressor model by first defining a list of tuples for the three base models, then defining the linear regression meta-model to combine the predictions from the base models using 5-fold cross-validation.

We can include the stacking ensemble in the list of models to evaluate, along with the standalone models.

Our expectation is that the stacking ensemble will perform better than any single base model.

This is not always the case, and if it is not the case, then the base model should be used in favor of the ensemble model.

The complete example of evaluating the stacking ensemble model alongside the standalone models is listed below.

Running the example first reports the performance of each model. This includes the performance of each base model, then the stacking ensemble.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

In this case, we can see that the stacking ensemble appears to perform better than any single model on average, achieving a mean negative MAE of about -56.

A box plot is created showing the distribution of model error scores. Here, we can see that the mean and median scores for the stacking model sit much higher than any individual model.

Box Plot of Standalone and Stacking Model Negative Mean Absolute Error for Regression

Box Plot of Standalone and Stacking Model Negative Mean Absolute Error for Regression

If we choose a stacking ensemble as our final model, we can fit and use it to make predictions on new data just like any other model.

First, the stacking ensemble is fit on all available data, then the predict() function can be called to make predictions on new data.

The example below demonstrates this on our regression dataset.

Running the example fits the stacking ensemble model on the entire dataset and is then used to make a prediction on a new row of data, as we might when using the model in an application.

Further Reading

This section provides more resources on the topic if you are looking to go deeper.

Related Tutorials

Papers

Books

APIs

Articles

Summary

In this tutorial, you discovered the stacked generalization ensemble or stacking in Python.

Specifically, you learned:

  • Stacking is an ensemble machine learning algorithm that learns how to best combine the predictions from multiple well-performing machine learning models.
  • The scikit-learn library provides a standard implementation of the stacking ensemble in Python.
  • How to use stacking ensembles for regression and classification predictive modeling.

Do you have any questions?
Ask your questions in the comments below and I will do my best to answer.

44 Responses to Stacking Ensemble Machine Learning With Python

  1. Fawaz Mokbal April 10, 2020 at 6:58 am #

    Thanks for this great explanation.
    I have a question, how can I pass a specific type of data (e.g. specific class) to a specific algorithm, where each model learns from its particular data. then gathering all models (stacking) to predict
    best regards,

    • Jason Brownlee April 10, 2020 at 8:38 am #

      You can fit different models perhaps manually, then use another model to combine the predictions. E.g. all maually.

  2. Francisco April 10, 2020 at 7:12 am #

    Hi Jason, thanks for the blog and all the information in a digested form, I am a beginner in all aspects and I can really see the advantages of using the method of stacking. I am yet to start doing my first project but before that I plan on reading as much as possible from your articles.

    Thank you and be safe, I hope to learn as much as posible from you.

    Cheers from Mexico!!

  3. ppalmes April 10, 2020 at 9:24 am #

    that’s a lot of coding which can be reduce into just several lines of code n AutoMLPipeline: https://github.com/IBM/AutoMLPipeline.jl

  4. Akshay April 10, 2020 at 9:42 am #

    Great article, Jason! Keep these coming. Thanks!

  5. Tolga Karahan April 10, 2020 at 9:29 pm #

    Thanks for sharing. I suppose when cv=n argument provided to the StackingClassifier, it implicitly trains base models on training data and then trains StackingClassifier with predictions of base models on out-of-sample data right?

  6. Yaniv Rotaru May 1, 2020 at 9:08 pm #

    Thanks a lot for the info! though I have a question:
    I have tried your stacking for classification on the given dataset, I took the first 800 samples for training and produced the box plot, however, when I test each model’s accuracy results on the 200 test samples the stacking model doesn’t provide the best results, do you have an explanation for this?

    • Jason Brownlee May 2, 2020 at 5:44 am #

      Yes, stacking is not guaranteed to outperform base models.

      This is why we must use controlled experiments as the basis for model selection.

  7. Siva Sai May 16, 2020 at 5:11 am #

    Hi Jason Brownlee, your articles really helped a lot many times.
    In a paragraph you stated that ” That is, data not used to train the base models is fed to the base models, predictions are made, and these predictions, along with the expected outputs, provide the input and output pairs of the training dataset used to fit the meta-model.”

    Here what do you mean by expected outputs ??

    • Jason Brownlee May 16, 2020 at 6:24 am #

      I’m happy to hear that!

      Expected outputs are target values in the dataset.

      • Siva Sai May 16, 2020 at 3:23 pm #

        So you mean that during model.fit(x_train,y_train) (training phase), the meta-model will not learn anything, only at the time of model.score(x_test,y_test) (testing phase),the meta-model trains on the test inputs and predicted values/labels made by base estimator.

        Is my understand correct ?

        • Jason Brownlee May 17, 2020 at 6:27 am #

          No, I don’t quite follow your summary.

          The stacking model is fit during the call to fit(). The call to cross_val_score() will fit and evaluate k models which internally involves calls to fit().

  8. farukgogh May 19, 2020 at 1:04 am #

    hi Jason, thank you for your great tutorials!

    I want to use CalibratedClassifier in Level0 estimators, then stacking them. I tried this one but not sure. Is it true?

    model1=XGBClassifier()
    model2=…..

    calibrated1 = CalibratedClassifierCV(model1, cv=5)
    calibrated1.fit(X_train, y_train)
    calibrated2 = ….
    calibrated2.fit(….)

    estimators = [(‘xgb’, calibrated1),(‘…’, calibrated2)]

    clf = StackingClassifier(estimators=estimators, final_estimator=LogisticRegression())

    • Jason Brownlee May 19, 2020 at 6:08 am #

      Thanks.

      Calibrating level0 classifiers does not make sense to me, sorry. You might have to use some trial and error to make it work.

  9. Xiao June 9, 2020 at 7:15 pm #

    Hi,Jason!Thanks for your sharing. I used this tutorial for my binary classification task.I have 1000 image samples,and each sample has 4000 dimmensions that extrcted by CNN. However, the stacking result is lower than lr or bayes classifier, and also the super learning in your another tutorial. Could you tell me the reason? Hope for your reply.Many thanks!

    • Jason Brownlee June 10, 2020 at 6:11 am #

      Answering “why” questions it too hard/intractable.

      Often the best we can do is use controlled experiments and present results to support decision of what model or modeling pipeline works well/best.

  10. Vinayak July 10, 2020 at 12:50 am #

    Thanks for the wonderful tutorial.

    I see in this tutorial each base learner evaluated using default model hyperparameters. In real time, can I implement the base learner with hyperparameters tuning so I might get a better accuracy from meta-model?

    Can we use boosting and bagging classifiers in level 0 or as base learners?

    • Jason Brownlee July 10, 2020 at 6:01 am #

      Thanks!

      Yes, tuning is a good idea.

      You can use ensembles as base models if you like.

  11. Vinayak July 10, 2020 at 7:00 pm #

    Thank you.

    1. From below piece of code which you used in this tutorial, I believe we are getting accuracy on Test data set, please confirm?

    # evaluate a given model using cross-validation
    def evaluate_model(model):
    cv = RepeatedKFold(n_splits=10, n_repeats=3, random_state=1)
    scores = cross_val_score(model, X, y, scoring=’neg_mean_absolute_error’, cv=cv, n_jobs=-1, error_score=’raise’)
    return scores

    2. I am working on a classification problem and please find my different classification algorithm results below.

    Method Train Acuracy Test Acuracy
    0 Logistic Regression 0.8504762 0.8426966
    1 KNN 0.9330952 0.9550562
    2 Naive Bayes 0.7882540 0.7640449
    3 SVM 0.9573810 0.9775281
    4 Decision Tree 1.0000000 0.9438202
    5 Random Forest 0.9477778 0.9550562
    6 Stacking 1.0000000 0.9775281

    Base learners – 0 to 5, Meta model – 6

    If you look at Stacking classifier, it is completely over-fit on training data and I don’t think this is best model to consider, is that right?

    Note: I tried removing Decision tree from my base learners list because it’s over-fit on training data and but still I get below results from stacking classifier.So again this is not best model, is that right?

    Accuracy of Training data set: 1.0000 %
    Accuracy of Test data set: 0.9888 %

    Perhaps I will go for SVM as my final model.

    • Jason Brownlee July 11, 2020 at 6:09 am #

      There is no train/test sets. Instead, we are using repeated k-fold cross-validation to estimate model performance.

      Not sure I would agree it is overfit. You can focus on hold out set performance to select a model.

  12. Vinayak July 11, 2020 at 2:52 pm #

    Sorry, could you please clarify what is “hold out set performance”?

    Also, please answer below question.

    1. From below piece of code which you used in this tutorial, I believe we are getting accuracy on Test data set, please confirm?

    # evaluate a given model using cross-validation
    def evaluate_model(model):
    cv = RepeatedKFold(n_splits=10, n_repeats=3, random_state=1)
    scores = cross_val_score(model, X, y, scoring=’neg_mean_absolute_error’, cv=cv, n_jobs=-1, error_score=’raise’)
    return scores

  13. Alex August 12, 2020 at 5:24 pm #

    Hello,

    First of all, great guide. I found it really useful.

    If I use predict_proba for the stacking classifier, will it use the probabilities for the whole data set for the level1 model? Or will it use only the ones from each test split in each cross validation run. Im not sure I am making a lot of sense. I am looking at this guide and the out of folds prediction part for ensemble and I want to understand if it is the same idea, or if it isnt, which one is preferable? Also, can both of them be integrated in a pipeline that also does feature selection?

    Im a bit new to machine learning and python in general.

    Thanks a lot!

    • Jason Brownlee August 13, 2020 at 6:07 am #

      Thank you.

      Regardless of predicting labels or probabilities, the meta model is fit on the out of fold predictions from the base models.

      Does that help?

      • Alex Bugeac August 16, 2020 at 1:38 am #

        Yes, thanks. So, tell me if I understand corectly because I want to be sure: in this guide the meta model is fitted on the out of fold predictions, just like in your other guide for out of folds. Im asking because in this guide you dont create the meta dataset like in that one. Is this being done by the stacking classifier?

        • Jason Brownlee August 16, 2020 at 5:56 am #

          Correct on both accounts.

          The sklearn hides the complexity away and makes this complex ensemble algorithm “routine”. I love it!

  14. Kaushik Dayalan August 22, 2020 at 1:54 am #

    Working on a multiclass classification problem and the dataset is imbalanced I have used SMOTE to over sample. Using xgboost I could achieve an f1 score of about 90.67 affer tuning as well. Would stacked classifiers along with xgboost help increase the f1 score.

  15. Salome August 22, 2020 at 9:45 am #

    Thank you Mr. Jason for your guide. I used the codes above to implement a stacking model on Titanic datasets. For the hyperparameter tunning I used GrisearchCV. How can I extract the best stacking model? How will I use it to predict outcome on the test set?
    Thank you.

    • Jason Brownlee August 22, 2020 at 1:33 pm #

      You’re welcome.

      Well done! The gridsearchcv will provide access to the best configuration as follows:

      You can then fit a new model using the printed configuration, fit your model on all available data and call predict() for new data.

      If making predictions is new for you, see this:
      https://machinelearningmastery.com/make-predictions-scikit-learn/

  16. Anthony The Koala August 30, 2020 at 1:38 am #

    Dear Dr Jason,
    Again many thanks for your tutorials.

    I understand the listing directly under the heading “The complete example of evaluating the stacking ensemble model alongside the standalone models is listed below”

    What I have learned from the model from the get_models() and get_stacking().
    * get_stacking is a model.
    * get_models gets a list of models. That includes the get_stacking which is a model.
    * I could use the code under “The complete example of evaluating the stacking ensemble model alongside the standalone models is listed below” to make a prediction.
    * So making the prediction can be done underneath the lines for the boxplot.

    Conclusion by following the example at “The complete example of evaluating the stacking ensemble model alongside the standalone models is listed below” we can understand that the get_stacked() is a stacked model consisting of level 0 models and level1 LR model.

    Thank you,
    Anthony from Sydney

  17. Liu Qi September 3, 2020 at 6:06 pm #

    Dear Dr Jason,
    Thanks for your explain about stacking. I have a question about it. Several days ago I did a experiment that made the best params for every base model and the default params for every base model. In my opinion, if every base model could achieve a better performance, so that the meta model would get a higher accuracy by the training data combined by the predictions generated the base models. But in fact, the result was a little worse. So could you help me to explain the complex phenomenon?
    Best regards,

    • Jason Brownlee September 4, 2020 at 6:26 am #

      This is common.

      The reason is highly tuned models are fragile to small changes.

  18. Neeraj Gaur September 9, 2020 at 4:23 pm #

    Hi Jason

    I found your script and explanation very helful and as I am new in the feild.
    Not really sure how to cite your script in my manuscript.

    Do i just cite it as any mormal website is cited or is there there some other method?

    Best,
    Neeraj Gaur

  19. elham October 14, 2020 at 12:51 am #

    Hello..
    How to obtain feature importance from a Stacking Ensemble?
    I tried but it was not possible.

    • Jason Brownlee October 14, 2020 at 6:20 am #

      Off hand, I don’t think stacking offers this capability.

  20. elham October 26, 2020 at 11:28 pm #

    How do you think I can do this?
    I am a beginner, please help me how to write the code

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