Prettifying Partial Density Plots in Python

Give your non-technical stakeholders a glimpse into black-box models with more engaging partial density plots.

People don’t trust what they don’t understand. Artificial intelligence and machine learning algorithms are some of the most powerful technologies we have at our disposal, but they are also the most misunderstood. Hence, one of the most critical responsibilities of a data scientist is to communicate complex information in easy-to-understand ways.

Black Box Models

Perhaps one of the biggest misconceptions about neural networks is the notion that we can’t see directly into the models that produce results. We can see our inputs and outputs, and we can measure the results, but we don’t truly understand the relationship between them. From a practicality standpoint, this is problematic because, like humans, the nature of relationships can change with time. What a vision AI perceives as a truck today may reflect what trucks will look like tomorrow.

Tesla Cybertruck. Source: Mike Mareen / Shutterstock.com

Most changes, however, are not as jarring as Tesla’s Cybertruck. How do we know algorithms are keeping up with gradual changes to common assumptions if we can’t see inside them? We open the box. And one of the best tools we have at our disposal is the partial dependence plot (PDP).

Partial Dependence Plots

The creators of Scikit-Learn describe partial dependence plots this way:

Partial dependence plots (PDP) show the dependence between the target response and a set of ‘target’ features, marginalizing over the values of all other features (the ‘complement’ features).

In other words, PDP allows us to see how a change in a predictor variable affects the change in the target variable. Below is a sample of PDP’s that show the effect that different traits of a home have on the predicted price.

Source: Scikit-Learn

From these plots, we can see that as median income and age of the home increases, predicted price tends to increase. However, as average occupancy in an area increases, predicted price decreases. The lines at the bottom represent the distribution of observations.

These plots are incredibly easy to understand and easy to create. With a fitted model, dataset (X features only), and a list of input features, you can generate the above plots with a single line of code after importing the relevant libraries:

import matplotlib.pyplot as plt
from sklearn.inspection import partial_dependence, plot_partial_dependenceplot_partial_dependence(model, X, features)

These plots are great for almost any type of regression model. However, I have found that non-technical stakeholders sometimes have difficulty interpreting the results when applying PDPs to classification tasks. What’s more, they are not particularly engaging to look at for a presentation. Let’s dress it up and add some functionality to this.

Prettified PDPs

For illustrative purposes, we’ll use the Titanic dataset . We’ll build a simple model using the XGBoost classification model that attempts to identify survivors based on several input features. We are most interested in figuring out how our model uses age as a predictor of survivorship (no pun intended).

from xgboost import XGBClassifierdf = pd.read_csv('titanic.csv')
X = df[['Age', 'SibSp', 'Parch', 'Fare']]
y = df['Survived']model = XGBClassifier()
model.fit(X, y)fig = plt.figure(figsize(10, 9))
plot_partial_dependence(model, X, ['Age'], fig=fig)
plt.show()

As we can see, our model has identified that older persons are less likely to survive, all other factors being equal. We can also see that most passengers were between 20 and 40 years old.

Wouldn’t it be great if we could get a clearer picture of the age distribution by plotting a histogram on the same chart? What about displaying partial dependence values as percentages? Wouldn’t it be nice if we could also visualize the decision boundary? We can do all of this by grabbing the partial dependence values by using the partial_dependence method and plotting the results ourselves. Fortunately, I have already created a function that will do this for you.

from sklearn.inspection import partial_dependence

The above function will produce a PDP for a single input variable and allows for the input of a target name for axis labels and chart title. Furthermore, it provides options to display y-ticks as percentages, change the decision boundary, and return partial dependence values for further analysis. By sticking with the standard settings and passing a name for the target, we get the following:

plot_pdp(model, X, 'Age', target='Survival')

With this, we get a much richer view of the age distribution. We can clearly see where age crosses the decision boundary. We labeled axes in a way that will make it easier for non-technical stakeholders to read and understand. From here, you can play around with the options to see how they change the display of the chart or modify the code to your liking.

If nothing else, I would encourage you to come up with new ways to share your work to create more engagement with non-technical audiences.