How and When to Use a Calibrated Classification Model with scikit-learn

Last Updated on September 25, 2019

Instead of predicting class values directly for a classification problem, it can be convenient to predict the probability of an observation belonging to each possible class.

Predicting probabilities allows some flexibility including deciding how to interpret the probabilities, presenting predictions with uncertainty, and providing more nuanced ways to evaluate the skill of the model.

Predicted probabilities that match the expected distribution of probabilities for each class are referred to as calibrated. The problem is, not all machine learning models are capable of predicting calibrated probabilities.

There are methods to both diagnose how calibrated predicted probabilities are and to better calibrate the predicted probabilities with the observed distribution of each class. Often, this can lead to better quality predictions, depending on how the skill of the model is evaluated.

In this tutorial, you will discover the importance of calibrating predicted probabilities and how to diagnose and improve the calibration of models used for probabilistic classification.

After completing this tutorial, you will know:

• Nonlinear machine learning algorithms often predict uncalibrated class probabilities.
• Reliability diagrams can be used to diagnose the calibration of a model, and methods can be used to better calibrate predictions for a problem.
• How to develop reliability diagrams and calibrate classification models in Python with scikit-learn.

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How and When to Use a Calibrated Classification Model with scikit-learn
Photo by Nigel Howe, some rights reserved.

Tutorial Overview

This tutorial is divided into four parts; they are:

1. Predicting Probabilities
2. Calibration of Predictions
3. How to Calibrate Probabilities in Python
4. Worked Example of Calibrating SVM Probabilities

Predicting Probabilities

A classification predictive modeling problem requires predicting or forecasting a label for a given observation.

An alternative to predicting the label directly, a model may predict the probability of an observation belonging to each possible class label.

This provides some flexibility both in the way predictions are interpreted and presented (choice of threshold and prediction uncertainty) and in the way the model is evaluated.

Although a model may be able to predict probabilities, the distribution and behavior of the probabilities may not match the expected distribution of observed probabilities in the training data.

This is especially common with complex nonlinear machine learning algorithms that do not directly make probabilistic predictions and instead use approximations.

The distribution of the probabilities can be adjusted to better match the expected distribution observed in the data. This adjustment is referred to as calibration, as in the calibration of the model or the calibration of the distribution of class probabilities.

[…] we desire that the estimated class probabilities are reflective of the true underlying probability of the sample. That is, the predicted class probability (or probability-like value) needs to be well-calibrated. To be well-calibrated, the probabilities must effectively reflect the true likelihood of the event of interest.

— Page 249, Applied Predictive Modeling, 2013.

Calibration of Predictions

There are two concerns in calibrating probabilities; they are diagnosing the calibration of predicted probabilities and the calibration process itself.

Reliability Diagrams (Calibration Curves)

A reliability diagram is a line plot of the relative frequency of what was observed (y-axis) versus the predicted probability frequency  (x-axis).

Reliability diagrams are common aids for illustrating the properties of probabilistic forecast systems. They consist of a plot of the observed relative frequency against the predicted probability, providing a quick visual intercomparison when tuning probabilistic forecast systems, as well as documenting the performance of the final product

Specifically, the predicted probabilities are divided up into a fixed number of buckets along the x-axis. The number of events (class=1) are then counted for each bin (e.g. the relative observed frequency). Finally, the counts are normalized. The results are then plotted as a line plot.

These plots are commonly referred to as ‘reliability‘ diagrams in forecast literature, although may also be called ‘calibration‘ plots or curves as they summarize how well the forecast probabilities are calibrated.

The better calibrated or more reliable a forecast, the closer the points will appear along the main diagonal from the bottom left to the top right of the plot.

The position of the points or the curve relative to the diagonal can help to interpret the probabilities; for example:

• Below the diagonal: The model has over-forecast; the probabilities are too large.
• Above the diagonal: The model has under-forecast; the probabilities are too small.

Probabilities, by definition, are continuous, so we expect some separation from the line, often shown as an S-shaped curve showing pessimistic tendencies over-forecasting low probabilities and under-forecasting high probabilities.

Reliability diagrams provide a diagnostic to check whether the forecast value Xi is reliable. Roughly speaking, a probability forecast is reliable if the event actually happens with an observed relative frequency consistent with the forecast value.

The reliability diagram can help to understand the relative calibration of the forecasts from different predictive models.

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Probability Calibration

The predictions made by a predictive model can be calibrated.

Calibrated predictions may (or may not) result in an improved calibration on a reliability diagram.

Some algorithms are fit in such a way that their predicted probabilities are already calibrated. Without going into details why, logistic regression is one such example.

Other algorithms do not directly produce predictions of probabilities, and instead a prediction of probabilities must be approximated. Some examples include neural networks, support vector machines, and decision trees.

The predicted probabilities from these methods will likely be uncalibrated and may benefit from being modified via calibration.

Calibration of prediction probabilities is a rescaling operation that is applied after the predictions have been made by a predictive model.

There are two popular approaches to calibrating probabilities; they are the Platt Scaling and Isotonic Regression.

Platt Scaling is simpler and is suitable for reliability diagrams with the S-shape. Isotonic Regression is more complex, requires a lot more data (otherwise it may overfit), but can support reliability diagrams with different shapes (is nonparametric).

Platt Scaling is most effective when the distortion in the predicted probabilities is sigmoid-shaped. Isotonic Regression is a more powerful calibration method that can correct any monotonic distortion. Unfortunately, this extra power comes at a price. A learning curve analysis shows that Isotonic Regression is more prone to overfitting, and thus performs worse than Platt Scaling, when data is scarce.

Note, and this is really important: better calibrated probabilities may or may not lead to better class-based or probability-based predictions. It really depends on the specific metric used to evaluate predictions.

In fact, some empirical results suggest that the algorithms that can benefit the more from calibrating predicted probabilities include SVMs, bagged decision trees, and random forests.

[…] after calibration the best methods are boosted trees, random forests and SVMs.

How to Calibrate Probabilities in Python

The scikit-learn machine learning library allows you to both diagnose the probability calibration of a classifier and calibrate a classifier that can predict probabilities.

Diagnose Calibration

You can diagnose the calibration of a classifier by creating a reliability diagram of the actual probabilities versus the predicted probabilities on a test set.

In scikit-learn, this is called a calibration curve.

This can be implemented by first calculating the calibration_curve() function. This function takes the true class values for a dataset and the predicted probabilities for the main class (class=1). The function returns the true probabilities for each bin and the predicted probabilities for each bin. The number of bins can be specified via the n_bins argument and default to 5.

For example, below is a code snippet showing the API usage:

Calibrate Classifier

A classifier can be calibrated in scikit-learn using the CalibratedClassifierCV class.

There are two ways to use this class: prefit and cross-validation.

You can fit a model on a training dataset and calibrate this prefit model using a hold out validation dataset.

For example, below is a code snippet showing the API usage:

Alternately, the CalibratedClassifierCV can fit multiple copies of the model using k-fold cross-validation and calibrate the probabilities predicted by these models using the hold out set. Predictions are made using each of the trained models.

For example, below is a code snippet showing the API usage:

The CalibratedClassifierCV class supports two types of probability calibration; specifically, the parametric ‘sigmoid‘ method (Platt’s method) and the nonparametric ‘isotonic‘ method which can be specified via the ‘method‘ argument.

Worked Example of Calibrating SVM Probabilities

We can make the discussion of calibration concrete with some worked examples.

In these examples, we will fit a support vector machine (SVM) to a noisy binary classification problem and use the model to predict probabilities, then review the calibration using a reliability diagram and calibrate the classifier and review the result.

SVM is a good candidate model to calibrate because it does not natively predict probabilities, meaning the probabilities are often uncalibrated.

A note on SVM: probabilities can be predicted by calling the decision_function() function on the fit model instead of the usual predict_proba() function. The probabilities are not normalized, but can be normalized when calling the calibration_curve() function by setting the ‘normalize‘ argument to ‘True‘.

The example below fits an SVM model on the test problem, predicted probabilities, and plots the calibration of the probabilities as a reliability diagram,

Running the example creates a reliability diagram showing the calibration of the SVMs predicted probabilities (solid line) compared to a perfectly calibrated model along the diagonal of the plot (dashed line.)

We can see the expected S-shaped curve of a conservative forecast.

Uncalibrated SVM Reliability Diagram

We can update the example to fit the SVM via the CalibratedClassifierCV class using 5-fold cross-validation, using the holdout sets to calibrate the predicted probabilities.

The complete example is listed below.

Running the example creates a reliability diagram for the calibrated probabilities.

The shape of the calibrated probabilities is different, hugging the diagonal line much better, although still under-forecasting in the upper quadrant.

Visually, the plot suggests a better calibrated model.

Calibrated SVM Reliability Diagram

We can make the contrast between the two models more obvious by including both reliability diagrams on the same plot.

The complete example is listed below.

Running the example creates a single reliability diagram showing both the calibrated (orange) and uncalibrated (blue) probabilities.

It is not really an apples-to-apples comparison as the predictions made by the calibrated model are in fact a combination of five submodels.

Nevertheless, we do see a marked difference in the reliability of the calibrated probabilities (very likely caused by the calibration process).

Calibrated and Uncalibrated SVM Reliability Diagram

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

Summary

In this tutorial, you discovered the importance of calibrating predicted probabilities and how to diagnose and improve the calibration of models used for probabilistic classification.

Specifically, you learned:

• Nonlinear machine learning algorithms often predict uncalibrated class probabilities.
• Reliability diagrams can be used to diagnose the calibration of a model, and methods can be used to better calibrate predictions for a problem.
• How to develop reliability diagrams and calibrate classification models in Python with scikit-learn.

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131 Responses to How and When to Use a Calibrated Classification Model with scikit-learn

1. Elie Kawerk September 3, 2018 at 11:34 pm #

I wish you include the last 2 tutorials in “Machine learning mastery with Python”.

• Jason Brownlee September 4, 2018 at 6:06 am #

Thanks. They may be a little advanced for that beginner book.

2. Mark Littlewood September 4, 2018 at 1:30 am #

Thanks for this, very interesting but on my Gradient Descent Boosting UK horse racing ratings it did not improve performance sadly

• Jason Brownlee September 4, 2018 at 6:10 am #

Thanks, nice one for trying!

• Mark Littlewood March 18, 2020 at 10:15 pm #

Correction actually I was taking the code for creating the calibration plot from another example and I was setting normalize to True. For horse racing you really want to take the probabilities as is and when I did this the probabilities were pretty well calibrated without adjustment

• Mark Littlewood March 18, 2020 at 10:17 pm #

Is there a Python Sklearn function the measures the fit of the calibration curve ie a kind of MSE on the curve

3. Ratiba September 7, 2018 at 6:47 am #

Thanks, very useful.

4. Raj September 10, 2018 at 2:40 pm #

In reliability plot, how to plot observed values on y-axis bins. For eg: what can be possible value for a 0.2 bin on y-axis. May be a detailed illustration of the reliability plot will be helpful. Thank you.

• Jason Brownlee September 11, 2018 at 6:25 am #

Good question, I would expect that the calculated bins will be accessible some how, I don’t have an example.

5. Joe F October 31, 2018 at 8:53 pm #

This is a great article – could you explain a but more about how to calibrate with an oversampled dataset (which will have produced incorrect probabilities) – should you adjust the probabilities to account for the oversampling yourself, before calibration, or after, or should you just use the weights parameter within the fit() function ? Any thoughts?

• Jason Brownlee November 1, 2018 at 6:06 am #

You could fit with an oversampled dataset, but calibrate with an un-touched validation dataset.

6. M K November 9, 2018 at 6:32 am #

Yet another cool contribution of yours to ML community, as usual!

Could you please indicate how this approach may be used with a random forest as a classifier — as RF doesn’t output a decision function as SVC.

Many thanks.

• Jason Brownlee November 9, 2018 at 1:58 pm #

You can use the calibration method directly.

Perhaps I don’t understand the problem you’re having?

7. M K November 9, 2018 at 6:48 am #

Hi, again.

Please disregard my previous question — it seems that returning predict_proba(testX)[:, 1] in the function uncalibrated (when using a random forest) resolves my issue.

Thanks,

M.

8. Jen K. March 22, 2019 at 6:07 am #

Hi Jason,

Would it be possible to use CalibratedClassifierCV to calibrate a non scikit learn model? For example, how would I go about calibrating a classifier written in tensorflow?

Thanks,
Jen

• Jason Brownlee March 22, 2019 at 8:43 am #

Perhaps, but you may need to wrap the model to look like a sklearn classifier (like we can do in Keras).

9. Andres M. March 29, 2019 at 6:45 am #

Hi Jason , thanks for making such detailed explanation! I’ve been reading about these issues as I am trying to look for the best way of comparing different classifiers performances, and it is very common to use the ROC curve and the AUC. However, as you posted here, “not all machine learning models are capable of predicting calibrated probabilities”, so i guess it only make sense to speak about probabilities and thresholds for some classifiers only. But most of the models in sklearn either have the .predict_prob() method or the .decision_function() one, so i would like to know which specific models are we talking about here. I don’t see what it means to choose the threshole for a model that doesn’t return a decision function (like in a decision tree for example), but it does have a predict_prob() method nevertheless.

In simple words, which classifiers can I compare using the ROC and callibrate the probabilities?

• Jason Brownlee March 29, 2019 at 8:49 am #

Simple models are built on a probabilistic model, such as logistic regression, whereas many nonlinear methods don’t operate that way.

One approach might be to treat models separately with and without calibration, throw them all in the mix and see what performs best in your comparison. The calibration won’t hurt probabilistic models like logistic regression and will help non-probabilistic models.

10. cs student April 21, 2019 at 5:19 pm #

Could you please elaborate more on how can this be extended to multi-class problems?

• Jason Brownlee April 22, 2019 at 6:17 am #

Is there a specific aspect that you’re having trouble with?

• Ahmad December 12, 2019 at 3:34 am #

Hi Janson, when I try to run on multi-class, the calibration_curve is throwing error as “bad input shape.

“fop_uncalibrated, mpv_uncalibrated = calibration_curve(testy, yhat_uncalibrated, n_bins=10, normalize=True)”

testy size is [59, 8], np_utils categorical data.
yhat_uncalibrated size is [59, 8], which is “model.decision_function(testX)” output.

• Jason Brownlee December 12, 2019 at 6:29 am #

Yes, the implementation is for binary classification only as far as I recall.

• Ahmad December 12, 2019 at 4:58 pm #

Okay, thank you for the information. If I want to implement it for multi-class how can I do that. Can you suggest a way

• Jason Brownlee December 13, 2019 at 5:54 am #

Sorry, I don’t have an example. I cannot give you off the cuff advice.

11. Blanca September 4, 2019 at 12:55 am #

Hi!
Thanks so much for this post, it’s been extremely useful!
I’ve been running a random forest and applying the calibration as you suggest here, but now the size of the dataset is increasing and I might need to shift to Spark. Do you know if there is a way of doing the calibration on Spark?
Thanks!

• Jason Brownlee September 4, 2019 at 6:01 am #

Sorry, I don’t know about Spark.

• Blanca September 4, 2019 at 5:39 pm #

Thanks! =)

12. Nemo October 3, 2019 at 4:40 am #

Hello.

Can calibration change relative position of predictions for some objects? I mean, if predicted probability for object1 is greater than that for object2 before calibration, but it is contrariwise after.

If not, does it mean that calibration doesn’t affect ROC-AUC score?

Thank you!

• Jason Brownlee October 3, 2019 at 6:54 am #

It often does not, but it may, e.g. for probabilities around the threshold.

I would expect the ROC to change after calibration!

13. Samarth Dhawan October 6, 2019 at 5:33 pm #

Hi, How can I do a gridseach along with CaliberatedClassifierCV to tune my parameters?

• Jason Brownlee October 7, 2019 at 8:28 am #

I’m not sure, perhaps try using the CalibrateClassifier without the CV as part of a pipeline inside a gridsearchcv?

• Tom Weichle June 4, 2021 at 3:38 am #

Hi Jason, I’m wondering if you happen to think about this issue further related to performing a GridSearch for tuning parameters and then calibrating afterwards. It’s an interesting problem and I haven’t come across much discussion related to this.

• Jason Brownlee June 4, 2021 at 7:06 am #

Ideally, calibration would be part of the modeling pipeline and evalutaed within the test harness.

14. Mohammad October 22, 2019 at 12:39 am #

Awesome 🙂

15. Marina Drus November 2, 2019 at 5:58 am #

Very well explained! Thank you!

16. Elias December 11, 2019 at 12:31 am #

Is it really necessary to use CalibratedClassifierCV within a SVC?

I think you get a 5 fold CV calibration using sv = SVC(probabilities=True). Right?

• Jason Brownlee December 11, 2019 at 7:00 am #

It will use cv to estimate the corrected probabilities, not to evaluate the model.

• Elias December 11, 2019 at 9:22 pm #

Thank you!

So would you recommend using CalibratedClassifierCV instead or does it depend on the use casw?

• Jason Brownlee December 12, 2019 at 6:21 am #

I generally use it in practice.

17. Ahmad December 12, 2019 at 3:30 am #

Hi Jason,
Can you please explain me about generating calibration_curve on multi class classifier probabilities.

• Jason Brownlee December 12, 2019 at 6:29 am #

Sorry, I don’t have an example. It might not make sense, I have only seen it for binary classes (I think).

• Aykut Özdemir October 4, 2021 at 6:57 pm #

What you have to do is to use an one-vs-all-approach to transform your multi-class problem into many binary problems (for each class). After that you are able to create a calibration curve for every class seperately. So what I did was to use CalibratedClassifierCV to calibrate my classifier. In the next step you an OneVsRestClassifier with your previously calibrated classifier. After fitting the OneVsRestClassifier provides a field named base_estimators and with each of them you can create a calibration curve, since all of these represent a binary classifier (for each class resprectively). See the explanation at https://scikit-learn.org/stable/modules/calibration.html#multiclass-support and especially https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.13.7457&rep=rep1&type=pdf

hope this helps

• Adrian Tam October 6, 2021 at 10:17 am #

Thanks for sharing. That seems reasonable.

18. Abhilash Menon January 8, 2020 at 2:15 am #

Hi Jason, Thanks for all your help! I am working on a pet project of mine and I have been ranking instances in the positive class in the decreasing order of their probabilities generated by XGBoost. From your article, I can see that calibration is basically rescaling. This was my understanding as well. However, I find that the order of candidates is changing as well once I choose to sort based on calibrated class probabilities. For example:: 0.94 became 0.91 and 0.85 became 0.95 after calibration. This changes the order of instances (ranking). In some cases, the probabilities dropped by 0.2 which is a margin.
If the underlying mechanism for calibration is Logistic regression on probs generated by the model to predict the actual outcome why does it not scale and cause this change in order? Please correct me if I have made any wrong assumptions here. Thanks!

Note: the calibration method I used was sigmoid.

• Jason Brownlee January 8, 2020 at 8:28 am #

Yes, think of it as a non-linear mapping from uncalibrated probs to calibrated probs.

E.g. one probability distribution function to another.

• Pepe September 5, 2020 at 5:51 am #

Hey man, same doubt.

Take a look here:
https://scikit-learn.org/stable/modules/calibration.html#calibration

CalibratedClassifierCV uses a cross-validation approach to fit both the classifier and the regressor. For each of the k (trainset, testset) couple, a classifier is trained on the train set, and its predictions on the test set are used to fit a regressor. We end up with k (classifier, regressor) couples where each regressor maps the output of its corresponding classifier into [0, 1]. Each couple is exposed in the calibrated_classifiers_ attribute, where each entry is a calibrated classifier with a predict_proba method that outputs calibrated probabilities.

->>>The output of predict_proba for the main CalibratedClassifierCV instance corresponds to the AVERAGE of the predicted probabilities of the k estimators in the calibrated_classifiers_ list.

The output of predict is the class that has the highest probability.

• Jason Brownlee September 5, 2020 at 6:54 am #

Thanks for sharing.

• John September 5, 2020 at 7:55 am #

mmmm it should not be the case as you are averaging monotonically functions. It may occur because some observations, which were close (e.g. 0.0021 and 0.002), may get “squished” together, being rounded. The ranking, the AUC, should be almost the same

19. Vera February 19, 2020 at 8:55 pm #

Hi Jason!

I’m a bit confused and maybe you can help me.
When I use a different strategy for calibration, the predictions of the model change. I was trying different methods (platt, isotonic, prefit, cv) just to get an idea of what is going on. But I found my predictions change everytime. I am working with text data, classifying 25 classes.

Best,
Vera

• Jason Brownlee February 20, 2020 at 6:11 am #

Yes. Perhaps pick a metric and optimize it via CV or a hold out validation set.

20. Gledson February 20, 2020 at 1:32 am #

Hello, I would like to know if it is possible to perform the calibration with more than two classes? If so, how to do it?

Thanks

• Jason Brownlee February 20, 2020 at 6:16 am #

It may be possible. I don’t have a tutorial on the topic, sorry.

21. Riz March 13, 2020 at 7:35 am #

How do we finalize the model? Usually, after we are happy with the a model, we fit it on all of the data. Is that the same with calibration? Thanks!

• Jason Brownlee March 13, 2020 at 8:23 am #

Yes, but you will need a validation set or a CV procedure for the final model to calibrate.

22. Riz March 13, 2020 at 9:02 am #

So if I understand correctly, using the example below, the model is finalized in step 3 and then can be used to predict new data (step 4)?

1) model=RandomForestClassifier()
2) calibrated=CalibratedClassifierCV(model, method=’sigmoid’, cv=5)
3) calibrated.fit(X_train,y_train)
4)calibrated_probs = calibrated.predict_proba(X)[:,1]

23. riz April 25, 2020 at 1:59 pm #

Is saving/loading the calibratedclassifiercv the same as any other model? I have tried saving and loading the calibrated and running predictions, but they end up being way off from when the model is originally created, thanks!

• Jason Brownlee April 26, 2020 at 6:03 am #

Yes, I believe so.

Sorry to hear that you are having trouble. Perhaps try posting your code and error to stackoverflow?

24. Som Dubey May 27, 2020 at 4:57 pm #

This is great for reading and can be useful for predictions in classifier. I believe i will now always would like to do this exercise to see how my predictions are compared to calibrated ones. Thanks a lot sir.

25. mathswoman July 3, 2020 at 7:46 pm #

sorry i don’t get what you mean by : Below the diagonal: The model has over-forecast; the probabilities are too large.
Above the diagonal: The model has under-forecast; the probabilities are too small. surely if the curve is below the line then we are under foreceasting?? e..g given probability of 0.5, a perfect classifier will predict 0.5 of population will be posotives. however if our model is saying given probabliluty 0.5 the proportion is actually 0.4 then we are underestimating the positives?

26. mathswoman July 10, 2020 at 4:40 pm #

ok, say i fit a classifier using my training data (from grid search e.g. xgboost). i then run calibration calling ‘prefit’ variable, and this fit this calibrated classifier on training data – why can i not do this? — apparently you cannot

• Jason Brownlee July 11, 2020 at 6:02 am #

Why can’t you do it? I have not tried, I’m curious.

Perhaps just fit the model again with the chosen hyperparameters and calibration?

27. mathswoman July 13, 2020 at 8:50 pm #

because accoridng to the documentation the data must be disjoint from the one used for training.

• Jason Brownlee July 14, 2020 at 6:19 am #

Yes, perhaps prepare a hold out dataset, or split some data off from train – e.g. manually.

28. Maryam August 22, 2020 at 2:42 am #

Dear Jason,
Thank you for the useful tutorial.
I would like to know what the difference is between “confidence calibration” and “joint calibration”?

Thank you in advance to consider our requirements.

Best
Maryam

• Jason Brownlee August 22, 2020 at 6:19 am #

Thanks for the suggestion.

Where did you hear these terms?

29. Maryam August 29, 2020 at 6:36 am #

Dear Jason,
I am grateful for your quick response.
I would like to search for bayesian deep learning and uncertainty and in these papers I have faced some definition about calibration that I could not understand:

1- Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning
2-On Calibration of Modern Neural Networks

would you mind explaining how to apply calibration in detail?

Maryam

• Jason Brownlee August 29, 2020 at 8:07 am #

Thanks for the suggestion, perhaps in the future.

30. Bruno Barre September 12, 2020 at 9:22 pm #

Hi, I would like to have your opinion to a question/idea I just asked on the “Cross Validated” site, about a global measure for calibration. Here is the link https://stats.stackexchange.com/questions/487179/calibration-measure-for-classification-with-linear-slope .

31. Gunther November 9, 2020 at 8:50 am #

Thanks for the tutorial, very helpful! One question: Suppose I first split my data into a test set and a train set. Then I do random search with k-fold cross validation to find the best hyperparameters or algorithm, and then fit the best one with the entire training set. Finally, I would then like to calibrate my model (i.e., using the prefit method). For that I would need another holdout set completely independent of the others, right (what you call valX, valY above, so train to train the classifier, val for calibration, and test as the final test set). Or is there another less data-intensive way? Like using the same data as used for training the classifier for doing the calibration through applying k-fold cross validation to the calibrator?

• Jason Brownlee November 9, 2020 at 1:14 pm #

Yes, you can use CV to determine the calibration for the model as well using the entire dataset. This is the default approach in sklearn.

• Gunther November 9, 2020 at 9:54 pm #

Thank you Jason, thought so. What shook my confidence is the following sentence in the sklearn user guide:

“It is up to the user make sure that the data used for fitting the classifier is disjoint from the data used for fitting the regressor.” (scikit-learn.org/stable/modules/calibration.html)

which seems to suggest otherwise. Do you know why that is?

• Gunther November 9, 2020 at 10:52 pm #

Maybe to clarify what I mean: My point is that if I want to *prefit* my classifier and only then apply CalibratedClassifierCV to fit only the regressor, then I need to store my train/test split(s) from training the classifier and hand them over to the cv argument of CalibratedClassifierCV. Because otherwise the splits will be different and the regressor will be fit on data on the classifier has been fit on. (this is independent of using kfold with k>1 or simply k=1)

I came to this conclusion because I understood the sklearn documentation like so:

CalibratedClassifier(my_clf, cv = 5) –> For each train/test split, my_clf is fit on train set and the regressor is fit based on my_clf.predict_proba(test_set). The decisive thing is that within each fold train data is disjoint from test data.

CalibratedClassifier(my_clf, cv = ‘prefit’) –> Does not perform CV. Just fits the regressor based on whatever data is passed.

• Gunther November 10, 2020 at 12:02 am #

Phased more succinctly still: I cannot use *all* data to fit one classifier (my_clf), and then use CalibratedClassifierCV(my_clf, cv = ‘prefit), simply because there is no data left that my_clf has not seen.

In other words, CalibratedClassifierCV can use k-fold CV in the way it does only because it later outputs an average of predictions of the k models it has fitted, but never an output of a model that has been fitted on all data at once.

• Jason Brownlee November 10, 2020 at 6:44 am #

Yes.

• Jason Brownlee November 10, 2020 at 6:44 am #

Right. Prefit means no cv and you would calibrate using data not seen during training (ideally)

• Jason Brownlee November 10, 2020 at 6:41 am #

Hmm, not off hand.

Calibrating on a separate dataset would be nice/wise if you have the data to spare. We rarely do.

• Gunther December 6, 2020 at 3:19 am #

Hey Jason,
though late I just wanted to say thank you for responding to my extensive posts!
So, thanks! 🙂

• Jason Brownlee December 6, 2020 at 7:09 am #

You’re welcome.

32. Farid Alizadeh November 24, 2020 at 4:06 am #

I am teaching a masters level machine learning class and was looking for a quick way to implement AIC/BIC for linear and logistic regression in Python’s Scikit-learn module. I came across your page. Question: Is there an error in the formulas for the AIC/BIC for linear regression? The mean square error (divided by sigma^2) is already the log-likelihood. Why are you taking its log again? Also, the second term must be multiplied by the estimated sigma. I would rewrite the function as follows:

def calculate_aic(n, mse, num_params, sigma):
aic = n * mse + 2 * num_params * sigma
return aic

Ditto for BIC.

33. Deyan December 9, 2020 at 9:44 am #

Thank you for the post! Perhaps this has been answered already, but more simply:

Can you use the same validation set you use for hyperparameter tuning, for calibration as well (assuming you split into train/val/test)?

• Jason Brownlee December 9, 2020 at 9:46 am #

Yes, but ideally it would be better to use separate datasets – if you can spare the data.

34. Yangla January 1, 2021 at 2:35 am #

Hi .I have a question:how can i calibrate and forecast parameters of a fractional epidemiological model using Trust Région Reflective algorithm with matlab or scilab.If possible can i have an example.Thank you.

• Jason Brownlee January 1, 2021 at 5:32 am #

Sorry, I don’t have any examples of the technique you describe or any examples in matlab.

35. Pourvali Mohsen January 5, 2021 at 8:38 pm #

Thank you for the very useful tutorial, I have a question, according to the following paper I assumed calibration of a model could be post-processing, fit a new model on the result of the uncalibrated model. my question is how we can calibrate BERT for example (actually, I got a bit confused about how a calibration process would be)

• Jason Brownlee January 6, 2021 at 6:27 am #

Yes, calibration can be a post-hoc processing of predicted probabilities.

Sorry, I don’t have experience in calibrating BERT probabilities, I don’t want to give you misleading off cuff advice.

36. Pourvali Mohsen January 5, 2021 at 8:39 pm #

sorry, I forgot to post the paper
https://arxiv.org/pdf/1706.04599.pdf

37. Marlon Lohrbach January 13, 2021 at 8:15 am #

Hey Jason,

right now I am struggling with calibrating the probabilities of my XGB Classifier. As I am using the xgb api I have to use xgb.DMatrix objects. So I don’t know how to use the CalibratedClassifier model now. Do you got any ideas or advices? A XGB.Classifier returns poorer results….M

• Jason Brownlee January 13, 2021 at 10:13 am #

Sorry to hear that.

I would expect XGBClassifier to give identical results to using the XGB API directly.

If this is not the case, perhaps there is a bug in the latest version of the library or a difference in the way you have configured both implementations?

• Marlon January 13, 2021 at 7:18 pm #

That is the weird part about it. I am using the exact same parameters and even the same seed. This problem was also discussed on stackoverflow with no result so I thought I ask you. Thank you!

38. Daniela January 16, 2021 at 1:55 am #

Hey Jason!
First of all, you for this tutorial. 😉
Can I use this approach for multiclass classification?Let me do just a quick explanation about my problem.
I have a classification pipeline that the output is the probability of that input be part of a class a, b, c…
Although I have more then 100 classes, I just return the top 3 classes with higher probabilities for each input and based on that I choose the winner.
I would like to calibrate these probabilities in order to give the most realistic value for each input.
So, based on your example, how could i adapt to my problem?
Thank you again for your help!

• Jason Brownlee January 16, 2021 at 6:56 am #

Good question, I’m not sure off the cuff I’ve not tried.

Perhaps experiment and see if it is directly applicable?

• Daniela January 16, 2021 at 7:42 am #

Hum, I got it. I read again the scikit-learn doc and in the end of probability calibration explanation I found something about multiclass using CalibratedClassifierCV calibrates for each class separately in a OneVsRestClassifier. I will try and let you know if worked 😉

39. Sepideh Doost March 7, 2021 at 4:16 am #

Hi Jason, thank you so much for such a great article. I’m applying calibration on a random forest and the calibrated result is worse than the uncalibrated result. I’m taking the log_loss score as well and that also shows the score goes down with calibration. Is that normal?

• Jason Brownlee March 7, 2021 at 5:14 am #

You’re welcome.

It can happy, perhaps try an alternate calibration method/config, or do not calibrate.

40. Solly March 31, 2021 at 5:25 pm #

Hi Jason, I really appreciate good job that you are doing.. but i have issue with calibration..i used the below steps but my calibration probabilities are worse than non-calibrated

1. I splited my data into train and test
2. I further split then train data from step 1 into train and validation sets
3. I downsampled the training data from step 2 above
4. I fitted my model with downsampled training data from step3
5. i calibrated my model with untouched validation data from step 2.

Do you have an idea of what the problem might be or did i make mistake from above steps?

• Jason Brownlee April 1, 2021 at 8:08 am #

Thanks!

The steps look good.

Perhaps repeat the process with k-fold cv and average the results.

41. sinta anjelina June 7, 2021 at 6:12 pm #

Hi sir, thank you for your explanation it’s awesome. i wanna ask about what is the difference of getting probabilities from SVC with calibrated classifier and SVC with additional parameter probability set to true? Is it actually using the same procedure? I get different result by using both way

• Jason Brownlee June 8, 2021 at 7:13 am #

Good question, I recommend checking the API documentation.

42. L July 2, 2021 at 8:47 am #

hi Jason, any guidance on the size of the validation hold out set (or, the ratios between the train, validate, test split) if you are using a prefit model?

• Jason Brownlee July 3, 2021 at 6:06 am #

Not really other than “suitably representative”.

43. Tanrada September 30, 2021 at 5:34 am #

Hi Jason, thank you for a very informative article. Could I please ask if I should only calibrate the model (using cross-validation) after I have already finished tuning the hyper-parameters of the classifier, is that correct? Or should I tune the hyperparameters of the model (e.g. SVM) while having CalibratedClassifierCV() wrapped around it? Thank you so much

• Adrian Tam October 1, 2021 at 12:16 pm #

Cross validation is to give a score to a model, so we can compare different models using that score as a metric. Therefore, you should have the hyperparameters fixed, then run CV.

• Tanrada October 6, 2021 at 2:57 am #

I am still quite confused with how to organise my data for tuning the hyperparameters and calibrating the probabilities.

1) Currently, my data is split into training and held-out test set (not used at all).

2) With the training data, I did hyperparameter tuning using random forest & random search with cv=5.

3) After this is done, can I use the same training data, fixed my hyperparameters and calibrate the model using let say cv=3? This would mean the data used to tune hyper-parameters will be used as well.

4)Now if I wish to compare the performance of calibrated vs non-calibrated model, how should I go about it? Using training data again & set a new cv (maybe cv=5) to fit and test these two models?

5) And the final model will be e.g. the calibrated model trained on all training data (with no CV) to then use to make predictions on held-out test set.

Thank you so much!

• Adrian Tam October 6, 2021 at 11:26 am #

After step 2, you know what hyperparameters you want to use. Then you can discard the CV data you got before. Now you can (a) train your model, or (b) train and then calibrate the model. You’re comparing (a) and (b). You can run k-fold CV with the same old training data on methods (a) and (b) to compare. You may try to use scikit-learn’s k-fold CV function but for (b) there’s another CV behind the scene to do the calibration, hence the data really used for training is even less.

• Adrian Tam October 6, 2021 at 5:46 am #

Calibrate only after you finish the hyperparameters.

• Tanrada October 6, 2021 at 6:40 am #

I understand that point but I was wondering can I then use all my training data and use cross validation to calibrate the model? or the data that was used to tune the model cannot be used to calibrate the model?

44. Angel December 1, 2021 at 8:46 am #

Hi Jason. Thanks for the tutorial. I’m confusing when to apply this calibration to pre-trained classifiers. Here’s what I did regarding my own project.

1) I used tenfold cross-validation (via sklearn kFold) to evaluate the model performances of the RF, SVM, and XGB with fixed, pre-tuned parameters. Performance metrics over the sub-test data during each k was finally averaged to give the final evaluation and comparison.
2) Following tenfold cross-validation. I fit each model with the whole training data and used these models for prediction purposes. SVM, particularly, predicted instances with probabilities < 0.5 as positives.

My question is when should I apply this calibration step to provide prediction results with calibrated probabilities? Should I simply calibrate them after tenfold cross-validation? Which method should I use, prefit or CV? FYI, currently, I only have a training dataset, the one used for tenfold cross-validation, and a dataset only for prediction purpose. The independent dataset is not available. I'm really confused right now and wonder if I need to integrate the calibration step even into the existing tenfold cross-validation step. If so, how to go about it? Thanks for the help in advance.

• Adrian Tam December 2, 2021 at 2:36 am #

It should be done after step 2 because at there you have the classifier trained.

• Angel December 3, 2021 at 4:58 am #

Thanks for the reply. I read the code and instructions and have one concern. What If I don’t have a distinct hold-out validation set if I need to calibrate using the method of ‘prefit’? Like mentioned earlier, I fit the model with all the training data I got in step 2. Thanks for the advice in advance.

• Angel December 3, 2021 at 5:54 am #

Sorry to add more information. I guess I can stick to the step 1 for the tenfold cross-validation and evaluation. However, to calibrate the models for prediction purposes, I may use untrained models with fixed parameters and use cv = 10 and then fit all the training data I got. In this case, it fulfills both purposes of training and calibration. I read this in the top-rated answer from the post (https://stats.stackexchange.com/questions/263393/scikit-correct-way-to-calibrate-classifiers-with-calibratedclassifiercv). Hope this will do.

• Adrian Tam December 8, 2021 at 6:36 am #

That’s correct. Thanks for the pointer to the StackExchange question.

45. Dave January 2, 2022 at 6:57 am #

Hey, if I understand correct; the reason we don’t fit the model when we use like cv = 5 is that the calibratorCV does training model for any training fold then does the calibration on calibration fold. But when cv = prefit, it doesn’t do training, it takes the trained model as input and calibrates that model with our choosen validation set. Do you think that is the mechanism inside, because it was tough for me to grasp which line does what, i rationalized that way. I’d glad if u approve or disprove me, thanks for work.

46. Vinay March 31, 2022 at 5:42 pm #

Hi Jason,

Will calibration improve the accuracy of a model, for example from 0.68 to 0.75? As I read it only helps to maintain the values.

47. Andrew May 14, 2022 at 2:56 am #

Hi Jason, thanks for the article!

I’m still trying to wrap my head around the purpose of calibration. Do you have any situation you might want to find the calibration specifically? Is it like a score function?

Also, comparing it to the expected probability, we mean the dataset right? Or some knowledge about the domain

Thanks for the help.