Partial Dependence Plot from an XGBoost Model in R

Partial Dependence Plots (PDPs) are a powerful tool for interpreting complex machine-learning models. They help visualize the relationship between a subset of features and the predicted outcome, holding other features constant. In the context of XGBoost models, PDPs can provide insights into how specific features influence the model's predictions. This article will guide you through the process of generating and interpreting Partial Dependence Plots from an XGBoost model in R.

What are Partial Dependence Plots?

PDPs show the marginal effect of one or two features on the predicted outcome of a machine-learning model. By plotting these effects, you can understand how changes in a particular feature influence the predictions while averaging out the effects of all other features.

Why Use PDPs?

• They help in model interpretation, especially for complex models like XGBoost that are often considered "black boxes."
• PDPs allow you to identify important features and understand their relationship with the target variable.
• They can reveal nonlinearities and interactions between features.

Now we will discuss step by step implementation of Partial Dependence Plot from an XGBoost Model in R Programming Language.

Step 1: Train an XGBoost Model

Before creating a PDP, you need to train an XGBoost model. Here’s a brief example using the xgboost package in R:

# Load necessary libraries
library(xgboost)
library(MASS)  # For the Boston dataset

# Load the dataset
data(Boston)
X <- as.matrix(Boston[, -14])  # Explanatory variables
y <- Boston$medv  # Response variable (median house value)

# Train an XGBoost model
xgb_model <- xgboost(
  data = X,
  label = y,
  nrounds = 100,
  objective = "reg:squarederror"
)

Output:

[1]	train-rmse:17.059007 
[2]	train-rmse:12.263687 
[3]	train-rmse:8.931146 
[4]	train-rmse:6.572166 
[5]	train-rmse:4.907308 
[6]	train-rmse:3.733522 
[7]	train-rmse:2.912337 
[8]	train-rmse:2.362943 
[9]	train-rmse:1.953651 
[10]	train-rmse:1.684866 
[11]	train-rmse:1.528102 
[12]	train-rmse:1.410980 ................................................................................................

This example uses the Boston housing dataset, where the goal is to predict the median house value (medv) based on various features.

Step 2: Install and Load the pdp Package

To generate PDPs, you can use the pdp package, which is specifically designed for creating partial dependence plots and individual conditional expectation (ICE) plots.

# Install and load the pdp package
install.packages("pdp")
library(pdp)

Step 3: Create a Partial Dependence Plot

Once the pdp package is installed and loaded, you can create a PDP for a specific feature. Here’s how to do it for the lstat feature (percentage of lower status of the population) from the Boston dataset:

# Generate a partial dependence plot for the 'lstat' feature
pdp_lstat <- partial(
  object = xgb_model,
  pred.var = "lstat",
  train = X,
  plot = TRUE
)
pdp_lstat

Output:

• object: The trained XGBoost model.
• pred.var: The feature for which you want to create the PDP.
• train: The training data used for the model.
• plot: Setting this to TRUE generates the plot.

This code will produce a plot showing how the predicted median house value changes as the lstat feature varies.

Step 4: Interpreting the PDP

• Monotonic Relationships: If the PDP is a straight line, it indicates a linear relationship between the feature and the target variable. For instance, if the plot for lstat shows a downward slope, it suggests that as the percentage of lower status individuals increases, the median house value decreases.
• Nonlinear Relationships: A curved PDP indicates a nonlinear relationship, where the effect of the feature on the target variable changes at different levels of the feature.
• Flat Lines: A flat line indicates that the feature has little to no effect on the model's predictions.

Step 5: Creating 2D Partial Dependence Plots

You can also create a 2D PDP to visualize the interaction between two features:

# Generate a 2D partial dependence plot for 'lstat' and 'rm' 
pdp_2d <- partial(
  object = xgb_model,
  pred.var = c("lstat", "rm"),
  train = X,
  plot = TRUE,
  chull = TRUE
)
pdp_2d

Output:

This code will generate a 3D surface plot or a contour plot showing how the interaction between lstat and rm affects the predicted median house value.

Conclusion

Partial Dependence Plots are a valuable tool for understanding the relationships between features and the target variable in complex models like XGBoost. By using the pdp package in R, you can easily create and interpret PDPs, gaining insights into the model’s behavior and improving transparency. Whether you're dealing with regression or classification problems, PDPs can help you understand the underlying patterns your model has learned from the data.