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Please note that the Ceteris Paribus method is moved to the dalex Python package which is actively maintained. If you will experience any problem with pyCeterisParibus please consider the dalex implementation at

pyCeterisParibus is a Python library based on an R package CeterisParibus. It implements Ceteris Paribus Plots. They allow understanding how the model response would change if a selected variable is changed. It’s a perfect tool for What-If scenarios. Ceteris Paribus is a Latin phrase meaning all else unchanged. These plots present the change in model response as the values of one feature change with all others being fixed. Ceteris Paribus method is model-agnostic - it works for any Machine Learning model. The idea is an extension of PDP (Partial Dependency Plots) and ICE (Individual Conditional Expectations) plots. It allows explaining single observations for multiple variables at the same time. The plot engine is developed here.

Why is it so useful?

There might be several motivations behind utilizing this idea. Imagine a person gets a low credit score. The client wants to understand how to increase the score and the scoring institution (e.g. a bank) should be able to answer such questions. Moreover, this method is useful for researchers and developers to analyze, debug, explain and improve Machine Learning models, assisting the entire process of the model design.


Tested on Python 3.5+

PyCeterisParibus is on PyPI. Simply run:

pip install pyCeterisParibus

or install the newest version from GitHub by executing:

pip install git+

or download the sources, enter the main directory and perform:
cd pyCeterisParibus
python install   # (alternatively use pip install .)


A detailed description of all methods and their parameters might be found in documentation.

To build the documentation locally:

pip install -r requirements-dev.txt
cd docs
make html

and open _build/html/index.html


Below we present use cases on two well-known datasets - Titanic and Iris. More examples e.g. for regression problems might be found here and in jupyter notebooks here.

Note, that in order to run the examples you need to install extra requirements from requirements-dev.txt.

Use case - Titanic survival

We demonstrate Ceteris Paribus Plots using the well-known Titanic dataset. In this problem, we examine the chance of survival for Titanic passengers. We start with preprocessing the data and creating an XGBoost model.

import pandas as pd
df = pd.read_csv('titanic_train.csv')

y = df['Survived']
x = df.drop(['Survived', 'PassengerId', 'Name', 'Cabin', 'Ticket'],
    inplace=False, axis=1)
valid = x['Age'].isnull() | x['Embarked'].isnull()
x = x[-valid]
y = y[-valid]

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(x, y,
    test_size=0.2, random_state=42)
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer

# We create the preprocessing pipelines for both numeric and categorical data.
numeric_features = ['Pclass', 'Age', 'SibSp', 'Parch', 'Fare']
numeric_transformer = Pipeline(steps=[
    ('scaler', StandardScaler())])

categorical_features = ['Embarked', 'Sex']
categorical_transformer = Pipeline(steps=[
    ('onehot', OneHotEncoder(handle_unknown='ignore'))])

preprocessor = ColumnTransformer(
        ('num', numeric_transformer, numeric_features),
        ('cat', categorical_transformer, categorical_features)])
from xgboost import XGBClassifier
xgb_clf = Pipeline(steps=[('preprocessor', preprocessor),
('classifier', XGBClassifier())]), y_train)

Here the pyCeterisParibus starts. Since this library works in a model agnostic fashion, first we need to create a wrapper around the model with uniform predict interface.

from ceteris_paribus.explainer import explain
explainer_xgb = explain(xgb_clf, data=x, y=y, label='XGBoost',
    predict_function=lambda X: xgb_clf.predict_proba(X)[::, 1])

Single variable profile

Let's look at Mr Ernest James Crease, the 19-year-old man, travelling on the 3. class from Southampton with an 8 pounds ticket in his pocket. He died on Titanic. Most likely, this would not have been the case had Ernest been a few years younger. Figure 1 presents the chance of survival for a person like Ernest at different ages. We can see things were tough for people like him unless they were a child.

ernest = X_test.iloc[10]
label_ernest = y_test.iloc[10]
from ceteris_paribus.profiles import individual_variable_profile
cp_xgb = individual_variable_profile(explainer_xgb, ernest, label_ernest)

Having calculated the profile we can plot it. Note, that plot_notebook might be used instead of plot when used in Jupyter notebooks.

from ceteris_paribus.plots.plots import plot
plot(cp_xgb, selected_variables=["Age"])

Chance of survival depending on age

Many models

The above picture explains the prediction of XGBoost model. What if we compare various models?

from sklearn.ensemble import RandomForestClassifier
from sklearn.linear_model import LogisticRegression
rf_clf = Pipeline(steps=[('preprocessor', preprocessor),
    ('classifier', RandomForestClassifier())])
linear_clf = Pipeline(steps=[('preprocessor', preprocessor),
    ('classifier', LogisticRegression())]), y_train), y_train)

explainer_rf = explain(rf_clf, data=x, y=y, label='RandomForest',
    predict_function=lambda X: rf_clf.predict_proba(X)[::, 1])
explainer_linear = explain(linear_clf, data=x, y=y, label='LogisticRegression', 
    predict_function=lambda X: linear_clf.predict_proba(X)[::, 1])
plot(cp_xgb, cp_rf, cp_linear, selected_variables=["Age"])

The probability of survival estimated with various models.

Clearly, XGBoost offers a better fit than Logistic Regression. Also, it predicts a higher chance of survival at child's age than the Random Forest model does.

Profiles for many variables

This time we have a look at Miss. Elizabeth Mussey Eustis. She is 54 years old, travels at 1. class with her sister Marta, as they return to the US from their tour of southern Europe. They both survived the disaster.

elizabeth = X_test.iloc[1]
label_elizabeth = y_test.iloc[1]
cp_xgb_2 = individual_variable_profile(explainer_xgb, elizabeth, label_elizabeth)
plot(cp_xgb_2, selected_variables=["Pclass", "Sex", "Age", "Embarked"])

Profiles for many variables.

Would she have returned home if she had travelled at 3. class or if she had been a man? As we can observe this is less likely. On the other hand, for a first class, female passenger chances of survival were high regardless of age. Note, this was different in the case of Ernest. Place of embarkment (Cherbourg) has no influence, which is expected behaviour.

Feature interactions and average response

Now, what if we look at passengers most similar to Miss. Eustis (middle-aged, upper class)?

from ceteris_paribus.select_data import select_neighbours
neighbours = select_neighbours(X_train, elizabeth, 
    selected_variables=['Pclass', 'Age', 'SibSp', 'Parch', 'Fare', 'Embarked'], 
cp_xgb_ns = individual_variable_profile(explainer_xgb, neighbours)
plot(cp_xgb_ns, color="Sex", selected_variables=["Pclass", "Age"], 
    aggregate_profiles='mean', size_pdps=6, alpha_pdps=1, size=2)

Interaction with gender. Apart from charts with Ceteris Paribus Profiles (top of the visualisation), we can plot a table with observations used to calculate these profiles (bottom of the visualisation).

There are two distinct clusters of passengers determined with their gender, therefore a PDP average plot (on grey) does not show the whole picture. Children of both genders were likely to survive, but then we see a large gap. Also, being female increased the chance of survival mostly for second and first class passengers.

Plot function comes with extensive customization options. List of all parameters might be found in the documentation. Additionally, one can interact with the plot by hovering over a point of interest to see more details. Similarly, there is an interactive table with options for highlighting relevant elements as well as filtering and sorting rows.

Multiclass models - Iris dataset

Prepare dataset and model

iris = load_iris()

def random_forest_classifier():
    rf_model = RandomForestClassifier(n_estimators=100, random_state=42)['data'], iris['target'])
    return rf_model, iris['data'], iris['target'], iris['feature_names']

Wrap model into explainers

rf_model, iris_x, iris_y, iris_var_names = random_forest_classifier()

explainer_rf1 = explain(rf_model, iris_var_names, iris_x, iris_y,
                       predict_function= lambda X: rf_model.predict_proba(X)[::, 0], label=iris.target_names[0])
explainer_rf2 = explain(rf_model, iris_var_names, iris_x, iris_y,
                       predict_function= lambda X: rf_model.predict_proba(X)[::, 1], label=iris.target_names[1])
explainer_rf3 = explain(rf_model, iris_var_names, iris_x, iris_y,
                       predict_function= lambda X: rf_model.predict_proba(X)[::, 2], label=iris.target_names[2])

Calculate profiles and plot

cp_rf1 = individual_variable_profile(explainer_rf1, iris_x[0], iris_y[0])
cp_rf2 = individual_variable_profile(explainer_rf2, iris_x[0], iris_y[0])
cp_rf3 = individual_variable_profile(explainer_rf3, iris_x[0], iris_y[0])

plot(cp_rf1, cp_rf2, cp_rf3, selected_variables=['petal length (cm)', 'petal width (cm)', 'sepal length (cm)'])

Multiclass models


You're more than welcomed to contribute to this package. See the guideline.


Work on this package was financially supported by the ‘NCN Opus grant 2016/21/B/ST6/0217’.