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Extract calibrated explanations from machine learning models.

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Calibrated Explanations (Documentation)

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calibrated-explanations is a Python package for the local feature importance explanation method called Calibrated Explanations, supporting both classification and regression. The proposed method is based on Venn-Abers (classification & regression) and Conformal Predictive Systems (regression) and has the following characteristics:

  • Fast, reliable, stable and robust feature importance explanations for:
    • Binary classification models
    • Multi-class classification models
    • Regression models
      • Including probabilistic explanations of the probability that the target exceeds a user-defined threshold
      • With difficulty adaptable explanations (conformal normalization)
  • Calibration of the underlying model to ensure that predictions reflect reality.
  • Uncertainty quantification of the prediction from the underlying model and the feature importance weights.
  • Rules with straightforward interpretation in relation to instance values and feature weights.
  • Possibility to generate counterfactual rules with uncertainty quantification of the expected predictions.
  • Conjunctional rules conveying feature importance for the interaction of included features.
  • Conditional rules, allowing users the ability to create contextual explanations to handle e.g. bias and fairness constraints.

Below is an example of a probabilistic counterfactual explanation for an instance of the regression dataset California Housing (with the threshold 180 000). The light red area in the background is representing the calibrated probability interval (for the prediction being below the threshold) of the underlying model, as indicated by a Conformal Predictive System and calibrated through Venn-Abers. The darker red bars for each rule show the probability intervals that Venn-Abers indicate for an instance changing a feature value in accordance with the rule condition.

Probabilistic counterfactual explanation for California Housing

Table 1 summarizes the characteristics of Calibrated Explanations.

Characteristics of Calibrated Explanantions

Getting started

The notebooks folder contains a number of notebooks illustrating different use cases for calibrated-explanations. The following are commented and should be a good start:


Let us illustrate how we may use calibrated-explanations to generate explanations from a classifier trained on a dataset from, which we first split into a training and a test set using train_test_split from sklearn, and then further split the training set into a proper training set and a calibration set:

from sklearn.datasets import fetch_openml
from sklearn.model_selection import train_test_split

dataset = fetch_openml(name="wine", version=7, as_frame=True)

X =
y = ( == 'True').astype(int)

feature_names = dataset.feature_names

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=2, stratify=y)

X_prop_train, X_cal, y_prop_train, y_cal = train_test_split(X_train, y_train,

We now fit a model on our data.

from sklearn.ensemble import RandomForestClassifier

rf = RandomForestClassifier(n_jobs=-1), y_prop_train)

Factual Explanations

Lets extract explanations for our test set using the calibrated-explanations package by importing CalibratedExplainer from calibrated_explanations.

from calibrated_explanations import CalibratedExplainer, __version__

explainer = CalibratedExplainer(rf, X_cal, y_cal, feature_names=feature_names)

factual_explanations = explainer.explain_factual(X_test)

Once we have the explanations, we can plot all of them using plot_all. Default, a regular plot, without uncertainty intervals included, is created. To include uncertainty intervals, change the parameter uncertainty=True. To plot only a single instance, the plot_explanation function can be called, submitting the index of the test instance to plot. You can also add and remove conjunctive rules.


factual_explanations.plot_explanation(0, uncertainty=True)


Counterfactual Explanations

An alternative to factual rules is to extract counterfactual rules. explain_counterfactual can be called to get counterfactual rules with an appropriate discretizer automatically assigned.

counterfactual_explanations = explainer.explain_counterfactual(X_test)

Counterfactuals are also visualized using the plot_all. Plotting an individual counterfactual explanation is done using plot_explanation, submitting the index of the test instance to plot. Adding or removing conjunctions is done as before.


Individual explanations can also be plotted using plot_explanation.


Support for multiclass

calibrated-explanations supports multiclass which is demonstrated in demo_multiclass. That notebook also demonstrates how both feature names and target and categorical labels can be added to improve the interpretability.


Extracting explanations for regression is very similar to how it is done for classification.

dataset = fetch_openml(name="house_sales", version=3)

X =
y =

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=1)

X_prop_train, X_cal, y_prop_train, y_cal = train_test_split(X_train, y_train,

Let us now fit a RandomForestRegressor from sklearn to the proper training set:

from sklearn.ensemble import RandomForestRegressor

rf = RandomForestRegressor(), y_prop_train)

Factual Explanations

Define a CalibratedExplainer object using the new model and data. The mode parameter must be explicitly set to regression. Regular and uncertainty plots work in the same way as for classification.

explainer = CalibratedExplainer(rf, X_cal, y_cal, mode='regression')

factual_explanations = explainer.explain_factual(X_test)



Default, the confidence interval is set to a symmetric interval of 90% (defined as low_high_percentiles=(5,95)). The intervals can cover any user specified interval, including one-sided intervals. To define a one-sided upper-bounded 90% interval, set low_high_percentiles=(-np.inf,90), and to define a one-sided lower-bounded 95% interval, set low_high_percentiles=(5,np.inf). Percentiles can also be set to any other values in the range (0,100) (exclusive), and intervals do not have to be symmetric.

lower_bounded_explanations = explainer.explain_factual(X_test, low_high_percentiles=(5,np.inf))
asymmetric_explanations = explainer.explain_factual(X_test, low_high_percentiles=(5,75))

Counterfactual Explanations

The explain_counterfactual will work exactly the same as for classification. Counterfactual plots work in the same way as for classification.

counterfactual_explanations = explainer.explain_counterfactual(X_test)



The parameter low_high_percentiles works in the same way as for factual explanations.

Probabilistic Regression Explanations

It is possible to create probabilistic explanations for regression, providing the probability that the target value is below the provided threshold (which is 180 000 in the examples below). All methods are the same as for normal regression and classification, except that the explain_factual and explain_counterfactual methods need the additional threshold value (here 180 000).

factual_explanations = explainer.explain_factual(X_test, 180000)



counterfactual_explanations = explainer.explain_counterfactual(X_test, 180000)


Additional Regression Use Cases

Regression offers many more options and to learn more about them, see the demo_regression or the demo_probabilistic_regression notebooks.


Known Limitations

The implementation currently only support numerical input. Use the utils.transform_to_numeric (released in version v0.3.1) to transform a DataFrame with text data into numerical form and at the same time extracting categorical_features, categorical_labels, target_labels (if text labels) and mappings (used to apply the same mappings to new data) to be used as input to the CalibratedExplainer. The algorithm does not currently support image data.



calibrated-explanations is implemented in Python, so you need a Python environment.

Install calibrated-explanations from PyPI:

pip install calibrated-explanations

or from conda-forge:

conda install -c conda-forge calibrated-explanations

or by following further instructions at conda-forge.

The dependencies are:



Contributions are welcome. Please send bug reports, feature requests or pull requests through the project page on GitHub. You can find a detailed guide for contributions in



For documentation, see


Further reading and citing

The calibrated-explanations method for classification is introduced in the paper:

The extensions for regression are introduced in the paper:

The paper that originated the idea of calibrated-explanations is:

If you use calibrated-explanations for a scientific publication, you are kindly requested to cite one of the papers above.

Bibtex entry for the original paper:

	title = 	{Calibrated explanations: With uncertainty information and counterfactuals},
	journal = 	{Expert Systems with Applications},
	pages = 	{123154},
	year = 		{2024},
	issn = 		{0957-4174},
	doi = 		{},
	url = 		{},
	author = 	{Helena Löfström and Tuwe Löfström and Ulf Johansson and Cecilia Sönströd},
	keywords = 	{Explainable AI, Feature importance, Calibrated explanations, Venn-Abers, Uncertainty quantification, Counterfactual explanations},
	abstract = 	{While local explanations for AI models can offer insights into individual predictions, such as feature importance, they are plagued by issues like instability. The unreliability of feature weights, often skewed due to poorly calibrated ML models, deepens these challenges. Moreover, the critical aspect of feature importance uncertainty remains mostly unaddressed in Explainable AI (XAI). The novel feature importance explanation method presented in this paper, called Calibrated Explanations (CE), is designed to tackle these issues head-on. Built on the foundation of Venn-Abers, CE not only calibrates the underlying model but also delivers reliable feature importance explanations with an exact definition of the feature weights. CE goes beyond conventional solutions by addressing output uncertainty. It accomplishes this by providing uncertainty quantification for both feature weights and the model’s probability estimates. Additionally, CE is model-agnostic, featuring easily comprehensible conditional rules and the ability to generate counterfactual explanations with embedded uncertainty quantification. Results from an evaluation with 25 benchmark datasets underscore the efficacy of CE, making it stand as a fast, reliable, stable, and robust solution.}

Bibtex entry for the regression paper:

      title = 	      	{Calibrated Explanations for Regression},
      author =          {L\"ofstr\"om, Tuwe and L\"ofstr\"om, Helena and Johansson, Ulf and S\"onstr\"od, Cecilia and Matela, Rudy},
      year =            {2023},
      eprint =          {2308.16245},
      archivePrefix =   {arXiv},
      primaryClass =    {cs.LG}

To cite this software, use the following bibtex entry:

	author = 	{Löfström, Helena and Löfström, Tuwe and Johansson, Ulf and Sönströd, Cecilia and Matela, Rudy},
	license = 	{BSD-3-Clause},
	title = 	{Calibrated Explanations},
	url = 		{},
	version = 	{v0.3.3},
	month = 	May,
	year = 		{2024}



This research is funded by the Swedish Knowledge Foundation together with industrial partners supporting the research and education environment on Knowledge Intensive Product Realization SPARK at Jönköping University, Sweden, through projects: AFAIR grant no. 20200223 and PREMACOP grant no. 20220187. Helena Löfström was a PhD student in the Industrial Graduate School in Digital Retailing (INSiDR) at the University of Borås, funded by the Swedish Knowledge Foundation, grant no. 20160035.

Rudy Matela has been our git guru and has helped us with the release process.

We have used both the ConformalPredictiveSystem and DifficultyEstimator classes from Henrik Boströms crepes package to provide support for regression.

We have used the VennAbers class from Ivan Petejs venn-abers package to provide support for probabilistic explanations (both classification and probabilistic regression).

We have used code from Marco Tulio Correia Ribeiros lime package for the Discretizer class.

The check_is_fitted and safe_instance functions in calibrated_explanations.utils are copied from sklearn and shap.


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