Metadata-Version: 2.1
Name: calibrated_explanations
Version: 0.5.0
Summary: Extract calibrated explanations from machine learning models.
Author-email: Helena Löfström <helena.lofstrom@ju.se>, Tuwe Löfström <tuwe.lofstrom@ju.se>
Project-URL: Homepage, https://github.com/Moffran/calibrated_explanations
Project-URL: Bug Tracker, https://github.com/Moffran/calibrated_explanations/issues
Classifier: Development Status :: 3 - Alpha
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: BSD License
Classifier: Operating System :: OS Independent
Requires-Python: >=3.8
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: crepes
Requires-Dist: venn-abers
Requires-Dist: ipython
Requires-Dist: lime
Requires-Dist: matplotlib
Requires-Dist: numpy
Requires-Dist: pandas
Requires-Dist: scikit-learn

# Calibrated Explanations ([Documentation](https://calibrated-explanations.readthedocs.io/en/latest/?badge=latest))
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**Calibrated Explanations** is an explanation method for machine learning designed to enhance both the interpretability of model predictions and the quantification of uncertainty. In many real-world applications, understanding how confident a model is about its predictions is just as important as the predictions themselves. This framework provides calibrated explanations for both predictions and feature importance by quantifying **aleatoric** and **epistemic uncertainty** — two types of uncertainty that offer critical insights into both data and model reliability.

- **Aleatoric uncertainty** represents the noise inherent in the data. It affects the spread of probability distributions (for probabilistic outcomes) and predictions (for regression). This uncertainty is **irreducible** because it reflects limitations in the data generation process itself. Incorporating calibration ensures accurate aleatoric uncertainty.
  
- **Epistemic uncertainty** arises from the model's lack of knowledge due to limited training data or insufficient complexity. It affects the model’s confidence in its output when it encounters unfamiliar or out-of-distribution data. Unlike aleatoric uncertainty, epistemic uncertainty is **reducible** — it can be minimized by gathering more data, improving the model architecture, or refining features.

By providing estimates for both aleatoric and epistemic uncertainty, **Calibrated Explanations** offers a more comprehensive understanding of predictions, both in terms of accuracy and confidence. This is particularly valuable in high-stakes environments where model reliability and interpretability are essential, such as in healthcare, finance, and autonomous systems.

For an in-depth guide on how to start using Calibrated Explanations, refer to the [Getting Started](#getting-started) section below.

### Core Features:
- **Calibrated Prediction Confidence**: Obtain well-calibrated uncertainty estimates for predictions, helping users make informed decisions based on the model’s confidence.
- **Uncertainty-Aware Feature Importance**: Understand not only which features are important but also how uncertain the model is about the contribution of those features.
- **Support for Various Tasks**: The framework supports classification, regression, and probabilistic regression, making it adaptable to a wide range of machine learning problems.

The ability to quantify both aleatoric and epistemic uncertainty provides practitioners with actionable insights into the reliability of predictions and explanations, fostering **appropriate trust** ([read paper](https://scholar.google.com/citations?view_op=view_citation&hl=sv&user=reKgRBwAAAAJ&citation_for_view=reKgRBwAAAAJ:Se3iqnhoufwC)) and transparency in machine learning models. 

### Distinctive Characteristics of Calibrated Explanations

Calibrated Explanations offers a range of features designed to enhance both the interpretability and reliability of machine learning models. These characteristics can be summarized as follows:

* **Fast, reliable, stable, and robust feature importance explanations** for:
  - **Binary classification models** ([Read paper](https://doi.org/10.1016/j.eswa.2024.123154)).
  - **Multi-class classification models** ([Read paper](https://raw.githubusercontent.com/mlresearch/v230/main/assets/lofstrom24a/lofstrom24a.pdf), [Slides](https://copa-conference.com/presentations/Lofstrom.pdf)).
  - **Regression models** ([Read paper](https://arxiv.org/abs/2308.16245)), including:
    - **Probabilistic explanations**: Provides the probability that the target exceeds a user-defined threshold.
    - **Difficulty-adaptable explanations**: Adjust explanations based on conformal normalization for varying levels of data difficulty.

* **Aleatoric and epistemic uncertainty estimates**: These estimates are provided by **Venn-Abers** for probabilistic explanations and by **Conformal Predictive Systems** for regression tasks. Both these techniques are grounded in solid theoretical foundations, leveraging **conformal prediction** and **Venn prediction** to ensure reliability and robustness in uncertainty quantification.

* **Calibration of the underlying model**: Ensures that predictions accurately reflect reality, improving trust in model outputs.

* **Comprehensive uncertainty quantification**:
  - **Prediction uncertainty**: Quantifies both aleatoric and epistemic uncertainties for the model’s predictions.
  - **Feature importance uncertainty**: Measures uncertainty in feature importance scores, helping to assess the reliability of each feature's contribution.

* **Proximity-based rules for straightforward interpretation**: Generates rules that are easily interpretable by relating instance values to feature importance weights.

* **Alternative explanations with uncertainty quantification**: Provides explanations for how predicted outcomes would change if specific input features were modified, including uncertainty estimates for these alternative outcomes.

* **Conjunctional rules**: Provides feature importance explanations for interactions between multiple features, highlighting joint contributions (discussed in detail in the [regression paper](https://arxiv.org/abs/2308.16245)).

* **Conditional rules for contextual explanations**: Allows users to create explanations conditioned on specific criteria, enabling better handling of e.g. fairness and bias constraints ([Read paper](https://doi.org/10.1007/978-3-031-63787-2_17)). Using conformal terminology, this means that Mondrian categories are supported. 
  
### Example Explanation
Below is an example of a probabilistic alternative explanation for an instance from the California Housing regression dataset, with a threshold set at 180,000. The light red area in the background represents the calibrated probability interval for the prediction being below the threshold, as determined by the underlying model using a Conformal Predictive System to generate a probability estimate and Venn-Abers to generate epistemic uncertainty.

The darker red bars for each rule (seen to the left) show the probability intervals provided by Venn-Abers, indicating how the likelihood of the outcome changes when specific feature values (seen to the right) are modified according to the rule conditions.
<p align="center">
  <a href="https://calibrated-explanations.readthedocs.io/en/latest/?badge=latest">
    <img src="https://github.com/Moffran/calibrated_explanations/blob/main/docs/images/counterfactual_probabilistic_house_regression.jpg" alt="Probabilistic alternative explanation for California Housing">
  </a>
</p>

## Getting started
The [notebooks folder](https://github.com/Moffran/calibrated_explanations/tree/main/notebooks) contains a number of notebooks illustrating different use cases for `calibrated-explanations`. The [quickstart_wrap](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/quickstart_wrap.ipynb), using the `WrapCalibratedExplainer` class, is similar to this Getting Started, including plots and output.

The notebooks listed below are using the `CalibratedExplainer` class. They showcase a number of different use cases, as indicated by their names:
* [quickstart](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/quickstart.ipynb) - similar to this Getting Started, but without a wrapper class.
* [demo_binary_classification](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_binary_classification.ipynb) - with examples for binary classification 
* [demo_multiclass](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_multiclass_glass.ipynb) - with examples for multi-class classification
* [demo_regression](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_regression.ipynb) - with examples for regression
* [demo_probabilistic_regression](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_probabilistic_regression.ipynb) - with examples for regression with thresholds
* [demo_under_the_hood](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_under_the_hood.ipynb) - illustrating how to access the information composing the explanations

### Classification
Let us illustrate how we may use `calibrated_explanations` to generate explanations from a classifier trained on a dataset from
[www.openml.org](https://www.openml.org), which we first split into a
training and a test set using `train_test_split` from
[sklearn](https://scikit-learn.org), and then further split the
training set into a proper training set and a calibration set:


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

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

X = dataset.data.values.astype(float)
y = (dataset.target.values == 'True').astype(int)

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,
                                                            test_size=0.25)

```

We now create our wrapper object, using a `RandomForestClassifier` as learner. 


```python
from sklearn.ensemble import RandomForestClassifier
from calibrated_explanations import WrapCalibratedExplainer, __version__

print(f"calibrated_explanations {__version__}")

classifier = WrapCalibratedExplainer(RandomForestClassifier())
display(classifier)
```

We now fit our model using the proper training set.


```python
classifier.fit(X_prop_train, y_prop_train)
display(classifier)
```

The `WrapCalibratedExplainer` class has a `predict` and a `predict_proba` method that returns the predictions and probability estimates of the underlying classifier. If the model is not yet calibrated, then the underlying models `predict` and `predict_proba` methods are used. If the model is calibrated, then the `predict` and `predict_proba` method of the calibration model is used.


```python
print('Uncalibrated prediction (probability estimates):')
print(f'{classifier.predict(X_test)} ({classifier.predict_proba(X_test)})')
```

Before we can generate explanations, we need to calibrate our model using the calibration set. 


```python
classifier.calibrate(X_cal, y_cal)
display(classifier)
```

Once the model is calibrated, the `predict` and `predict_proba` methods produce calibrated predictions and probability estimates.


```python
proba, (low, high) = classifier.predict_proba(X_test, uq_interval=True)
print('Calibrated prediction (probability estimates):')
print(f'{classifier.predict(X_test)} ({proba})')
print('Calibrated uncertainty interval for the positive class:')
print([(low[i], high[i]) for i in range(len(low))])
```

#### Factual Explanations
Let us explain a test instance using our `WrapCalibratedExplainer` object. The method used to get factual explanations is `explain_factual`. 


```python
factual_explanations = classifier.explain_factual(X_test)
display(classifier)
```

Once we have the explanations, we can plot all of them using the `plot` function. 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` function can be called, submitting the index of the test instance to plot.


```python
factual_explanations.plot()
factual_explanations.plot(uncertainty=True)

factual_explanations.plot(0, uncertainty=True)
```

You can also add and remove conjunctive rules.


```python
factual_explanations.add_conjunctions().plot(0)
factual_explanations.plot(0, uncertainty=True)
factual_explanations.remove_conjunctions().plot(0, uncertainty=True)
```

#### Explore Alternative Explanations
An alternative to factual rules is to extract alternative rules, which is done using the `explore_alternatives` function. Alternative explanations provides insights on how predicted outcomes would change if specific input features were modified, including uncertainty estimates for these alternative outcomes.


```python
alternative_explanations = classifier.explore_alternatives(X_test)
display(classifier)
```

Alternatives are also visualized using the `plot` function. Plotting an individual alternative explanation is done using `plot`, submitting the index to plot. Adding or removing conjunctions is done as before. 


```python
alternative_explanations.plot()
alternative_explanations.add_conjunctions().plot()

alternative_explanations.plot(0)
```

`calibrated_explanations` supports multiclass which is demonstrated in [demo_multiclass](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_multiclass_glass.ipynb). That notebook also demonstrates how both feature names and target and categorical labels can be added to improve the interpretability. 

### Regression
Extracting explanations for regression is very similar to how it is done for classification. First we load and divide the dataset. The target is divided by 1000, meaning that the target is in thousands of dollars. 


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

X = dataset.data.values.astype(float)
y = dataset.target.values/1000

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=2, random_state=42)

X_prop_train, X_cal, y_prop_train, y_cal = train_test_split(X_train, y_train,
                                                            test_size=200)
```

We now create our wrapper object, using a `RandomForestRegressor` as learner. 


```python
from sklearn.ensemble import RandomForestRegressor

regressor = WrapCalibratedExplainer(RandomForestRegressor())
display(regressor)
```

We now fit our model using the proper training set.


```python
regressor.fit(X_prop_train, y_prop_train)
display(regressor)
```

The `WrapCalibratedExplainer` class has a `predict` method that returns the predictions and probability estimates of the underlying classifier. If the model is not yet calibrated, then the underlying models `predict` method is used. If the model is calibrated, then the `predict` method of the calibration model is used.


```python
print('Uncalibrated model prediction:')
print(regressor.predict(X_test))
```

Before we can generate explanations, we need to calibrate our model using the calibration set. 


```python
regressor.calibrate(X_cal, y_cal)
display(regressor)
```

We can easily add a difficulty estimator by assigning a `DifficultyEstimator` to the `difficulty_estimator` attribute when calibrating the model.


```python
from crepes.extras import DifficultyEstimator

de = DifficultyEstimator().fit(X=X_prop_train, learner=regressor.learner, scaler=True)
regressor.calibrate(X_cal, y_cal, difficulty_estimator=de)
display(regressor)
```

A `DifficultyEstimator` can also be assigned to an already calibrated model using the `set_difficult_estimator` method. Using `set_difficult_estimator(None)` removes any previously assigned `DifficultyEstimator`. 

Once the model is calibrated, the `predict` method produce calibrated predictions with uncertainties. The default confidence is 90 per cent, which can be altered using the `low_high_percentiles` parameter. 


```python
prediction, (low, high) = regressor.predict(X_test, uq_interval=True) # default low_high_percentiles=(5, 95)
print('Calibrated prediction:')
print(prediction)
print('Calibrated uncertainty interval:')
print([(low[i], high[i]) for i in range(len(low))])
```

You can also get the probability of the prediction being below a certain threshold using `predict_proba` by assigning the `threshold` parameter.


```python
prediction = regressor.predict(X_test, threshold=200)
print('Calibrated probabilistic prediction:')
print(prediction)

proba, (low, high) = regressor.predict_proba(X_test, uq_interval=True, threshold=200)
print('Calibrated probabilistic probability estimate [y_hat > threshold, y_hat <= threshold]:')
print(proba)
print('Calibrated probabilistic uncertainty interval for y_hat <= threshold:')
print([(low[i], high[i]) for i in range(len(low))])
```

#### Factual Explanations
Let us explain a test instance using our `WrapCalibratedExplainer` object. The method used to get factual explanations is `explain_factual`. 


```python
factual_explanations = regressor.explain_factual(X_test) # default low_high_percentiles=(5, 95)
display(regressor)
```

Regression also offer both regular and uncertainty plots for factual explanations with or without conjunctive rules, in almost exactly the same way as for classification. 


```python
factual_explanations.plot()
factual_explanations.plot(uncertainty=True)

factual_explanations.add_conjunctions().plot(uncertainty=True)
```

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. 


```python
lower_bounded_explanations = regressor.explain_factual(X_test, low_high_percentiles=(5,np.inf))
asymmetric_explanations = regressor.explain_factual(X_test, low_high_percentiles=(5,75))
```

#### Explore Alternative Explanations
The `explore_alternatives` will work exactly the same as for classification. 


```python
alternative_explanations = regressor.explore_alternatives(X_test) # default low_high_percentiles=(5, 95)
display(regressor)
```

Alternative plots work as for classification.


```python
alternative_explanations.plot()
alternative_explanations.add_conjunctions().plot()
```

### Probabilistic Regression
The difference between probabilistic regression and regular regression is that the former returns a probability of the prediction being below a certain threshold. This could for example be useful when the prediction is a time to an event, such as time to death or time to failure. 


```python
probabilistic_factual_explanations = regressor.explain_factual(X_test, threshold=200)
probabilistic_factual_explanations.plot()
probabilistic_factual_explanations.plot(uncertainty=True)
```


```python
probabilistic_alternative_explanations = regressor.explore_alternatives(X_test, threshold=200)
probabilistic_alternative_explanations.plot()
```

Regression offers many more options but to learn more about them, see the [demo_regression](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_regression.ipynb) or the [demo_probabilistic_regression](https://github.com/Moffran/calibrated_explanations/blob/main/notebooks/demo_probabilistic_regression.ipynb) notebooks.

### Alternative ways to initialize WrapCalibratedExplainer

A `WrapCalibratedExplainer` can also be initialized with a trained model or with a `CalibratedExplainer` object, as is examplified below. 

```python
fitted_classifier = WrapCalibratedExplainer(classifier.learner)
display(fitted_classifier)
calibrated_classifier = WrapCalibratedExplainer(classifier.explainer)
display(calibrated_classifier)

fitted_regressor = WrapCalibratedExplainer(regressor.learner)
display(fitted_regressor)
calibrated_regressor = WrapCalibratedExplainer(regressor.explainer)
display(calibrated_regressor)
```

When a calibrated explainer is re-fitted, the explainer is reinitialized.

[Top](#calibrated-explanations-documentation)

## Known Limitations
The implementation currently only support numerical input. Use the `utils.helper.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.

See e.g. the [Conditional Fairness Experiment](evaluation/Conditional_Fairness_Experiment.ipynb) for examples on how it can be used.

[Top](#calibrated-explanations-documentation)

## Install

### From PyPI:
Install `calibrated-explanations` from PyPI:

```bash
pip install calibrated-explanations
```

### From conda-forge:
Alternatively, you can install it from conda-forge:

```bash	
conda install -c conda-forge calibrated-explanations
```

<!-- ### From GitHub:
To install the latest version directly from the GitHub repository, use the following command:

```bash	
conda install git+https://github.com/Moffran/calibrated_explanations.git
``` -->

### Dependencies:
The following dependencies are required and will be installed automatically if not already present:

* [crepes](https://github.com/henrikbostrom/crepes)
* [venn-abers](https://github.com/ip200/venn-abers)
* [scikit-learn](https://github.com/scikit-learn/scikit-learn)
* [matplotlib](https://matplotlib.org/)
* [NumPy](https://numpy.org/)
  
[Top](#calibrated-explanations-documentation)


## Contributing
Contributions are welcome.
Please send bug reports, feature requests or pull requests through
the project page on [GitHub](https://github.com/Moffran/calibrated_explanations).
You can find a detailed guide for contributions in
[CONTRIBUTING.md](https://github.com/Moffran/calibrated_explanations/blob/main/CONTRIBUTING.md).

[Top](#calibrated-explanations-documentation)


## Documentation
For documentation, see [calibrated-explanations.readthedocs.io](https://calibrated-explanations.readthedocs.io/en/latest/?badge=latest).
  
[Top](#calibrated-explanations-documentation)


## Further reading and citing

If you use `calibrated-explanations` for a scientific publication, you are kindly requested to cite one of the following papers:
### Published papers
- [Löfström, H](https://github.com/Moffran). (2023). [Trustworthy explanations: Improved decision support through well-calibrated uncertainty quantification](https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1810440&dswid=6197) (Doctoral dissertation, Jönköping University, Jönköping International Business School).
- [Löfström, H](https://github.com/Moffran)., [Löfström, T](https://github.com/tuvelofstrom)., Johansson, U., and Sönströd, C. (2024). [Calibrated Explanations: with Uncertainty Information and Counterfactuals](https://doi.org/10.1016/j.eswa.2024.123154). Expert Systems with Applications, 1-27.
- [Löfström, H](https://github.com/Moffran)., [Löfström, T](https://github.com/tuvelofstrom). (2024). [Conditional Calibrated Explanations: Finding a Path Between Bias and Uncertainty](https://doi.org/10.1007/978-3-031-63787-2_17). In: Longo, L., Lapuschkin, S., Seifert, C. (eds) Explainable Artificial Intelligence. xAI 2024. Communications in Computer and Information Science, vol 2153. Springer, Cham.
- [Löfström, T](https://github.com/tuvelofstrom)., [Löfström, H](https://github.com/Moffran)., Johansson, U. (2024). [Calibrated Explanations for Multi-class](https://raw.githubusercontent.com/mlresearch/v230/main/assets/lofstrom24a/lofstrom24a.pdf). <i>Proceedings of the Thirteenth Workshop on Conformal and Probabilistic Prediction and Applications</i>, in <i>Proceedings of Machine Learning Research</i>, PMLR 230:175-194. [Presentation](https://copa-conference.com/presentations/Lofstrom.pdf)

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

- [Löfström, H.](https://github.com/Moffran), [Löfström, T.](https://github.com/tuvelofstrom), Johansson, U., & Sönströd, C. (2023). [Investigating the impact of calibration on the quality of explanations](https://link.springer.com/article/10.1007/s10472-023-09837-2). Annals of Mathematics and Artificial Intelligence, 1-18. [Code and results](https://github.com/tuvelofstrom/calibrating-explanations).

### Preprints: 
- [Löfström, T](https://github.com/tuvelofstrom)., [Löfström, H](https://github.com/Moffran)., Johansson, U., Sönströd, C., and [Matela, R](https://github.com/rudymatela). (2024). [Calibrated Explanations for Regression](https://arxiv.org/abs/2308.16245). arXiv preprint arXiv:2308.16245. 
- [Löfström, H](https://github.com/Moffran)., [Löfström, T](https://github.com/tuvelofstrom)., and [Hallberg Szabadvary, J](https://github.com/egonmedhatten). (2024). [Ensured: Explanations for Decreasing the Epistemic Uncertainty in Predictions](https://arxiv.org/abs/2410.05479). arXiv preprint arXiv:2410.05479. 

### Citing and bibtex
If you use `calibrated-explanations` for a scientific publication, you are kindly requested to cite one of the papers above. Bibtex entries can be found in [citing](https://github.com/Moffran/calibrated_explanations/blob/main/docs/citing.md#bibtex-entries).
  
[Top](#calibrated-explanations-documentation)

## Acknowledgements
This research is funded by the [Swedish Knowledge Foundation](https://www.kks.se/) 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, ETIAI grant no. 20230040, and PREMACOP grant no. 20220187. Helena Löfström was initially 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](https://github.com/rudymatela) has been our git guru and has helped us with the release process.

We have used both the `ConformalPredictiveSystem` and `DifficultyEstimator` classes from [Henrik Boström](https://github.com/henrikbostrom)s [crepes](https://github.com/henrikbostrom/crepes) package to provide support for regression. The `MondrianCategorizer` class is also supported in the `WrapCalibratedExplainer` as an alternative to using the `bins` parameter to create conditional explanations.

We have used the `VennAbers` class from [Ivan Petej](https://github.com/ip200)s [venn-abers](https://github.com/ip200/venn-abers) package to provide support for probabilistic explanations (both classification and probabilistic regression). 

The `FastExplanation`, created using the `explain_fast` method, is incorporating ideas and code from [ConformaSight](https://github.com/rabia174/ConformaSight) developed by [Fatima Rabia Yapicioglu](https://github.com/rabia174), Allesandra Stramiglio, and Fabio Vitali. 

We are using Decision Trees from `scikit-learn` in the discretizers.

We have copied code from [Marco Tulio Correia Ribeiro](https://github.com/marcotcr)s [lime](https://github.com/marcotcr/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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