TreeSHAP: Optimized for Tree-Based Models

While KernelSHAP provides a universal way to approximate SHAP values for any model, its reliance on sampling and local linear regression can be computationally intensive, especially for complex models or large datasets. When working specifically with tree-based ensemble models like decision trees, Random Forests, XGBoost, LightGBM, or CatBoost, there's a much more efficient approach: TreeSHAP.

Developed by Lundberg et al. alongside the main SHAP framework, TreeSHAP is an algorithm specifically designed to calculate exact SHAP values for tree-based models significantly faster than KernelSHAP. It achieves this speedup by leveraging the inherent structure of decision trees.

How TreeSHAP Exploits Tree Structure

Recall that calculating Shapley values requires evaluating the model's output for different subsets of features ($S$). For a general black-box model, this involves retraining or approximating the model on each subset, which is computationally prohibitive. KernelSHAP approximates this process.

Tree-based models, however, have a specific structure that TreeSHAP exploits. The prediction for an instance $x$ is determined by the unique path it takes from the root node to a leaf node. The decisions along this path depend only on the values of the features used in the split conditions.

TreeSHAP uses a specialized algorithm based on the idea of conditional expectations. Instead of perturbing inputs like LIME or KernelSHAP, it calculates the exact conditional expectation $E[f(x) | x_S]$, which represents the expected output of the model if we only knew the values of the features in subset $S$. The algorithm efficiently computes these expectations for all possible subsets $S$ by pushing them down the tree simultaneously.

Imagine we want to calculate the contribution of "Feature A". TreeSHAP considers paths down the tree. When it encounters a split based on "Feature A", it follows the path corresponding to the instance's actual value for Feature A. When it encounters a split on a different feature, say "Feature B", it must consider both the left and right branches. TreeSHAP efficiently calculates the weighted average of the outcomes down both branches, where the weights are determined by the proportion of training samples that went down each path at that split point. This process effectively integrates out the effect of features not in the current subset $S$ being considered.

Illustration of TreeSHAP calculating conditional expectations. Splits on features within the subset $S$ (like Age) are followed directly. Splits on features outside $S$ (like Income, Tenure) require averaging predictions based on the proportion of data reaching each child node, effectively marginalizing their effect.

This specialized algorithm avoids the sampling required by KernelSHAP and computes the SHAP values exactly and efficiently, often orders of magnitude faster.

Advantages of TreeSHAP

1. Speed: It is significantly faster than KernelSHAP for supported tree models. The computational complexity is approximately $O(TLD^2)$, where $T$ is the number of trees, $L$ is the maximum number of leaves, and $D$ is the maximum depth. This is much better than the exponential complexity of the exact Shapley value calculation or the sampling-based cost of KernelSHAP.
2. Exactness: Unlike KernelSHAP which provides approximations, TreeSHAP computes the theoretically exact SHAP values for the given tree model.
3. Feature Interactions: TreeSHAP can also be extended to compute SHAP interaction values efficiently, helping to understand how pairs of features interact to influence the prediction.

Using TreeSHAP in Python

The shap library makes using TreeSHAP straightforward. You typically train your tree-based model first (e.g., using scikit-learn, XGBoost, LightGBM) and then pass the trained model to the shap.TreeExplainer.

import shap
import xgboost
import pandas as pd

# Assume 'model' is a trained XGBoost model (or RandomForest, LightGBM, etc.)
# Assume 'X' is your input data (Pandas DataFrame or NumPy array) used for training or explanation

# 1. Create the explainer object
explainer = shap.TreeExplainer(model)

# 2. Calculate SHAP values for a set of instances (e.g., X_explain)
# X_explain could be your test set, or a subset of interest
shap_values = explainer.shap_values(X_explain)

# 'shap_values' will be a NumPy array (or list of arrays for multi-class classification)
# Shape typically: (num_instances, num_features)
# For multi-class: list[num_classes] of arrays, each (num_instances, num_features)

# Example: Get SHAP values for the first instance
print(shap_values[0])

# Example: Get the base value (expected prediction over the background dataset)
print(explainer.expected_value)

The explainer.expected_value corresponds to the base value $E[f(x)]$ used in the SHAP explanation formula: $f(x) = E[f(x)] + \sum_{i=1}^{M} \phi_i$. This is essentially the average prediction of the model over the training dataset (or a background dataset if provided explicitly).

Overview

The primary limitation of TreeSHAP is its specificity. It only works for tree-based models. If you are working with linear models, SVMs, neural networks, or other model types, you will need to use a different approach like KernelSHAP, DeepSHAP (for deep learning), or LinearSHAP (for linear models).

However, given the prevalence and high performance of models like XGBoost and LightGBM in tabular data competitions and applications, TreeSHAP is an extremely valuable and widely used tool for interpreting their predictions efficiently and accurately. It forms the basis for many of the powerful SHAP visualizations you will encounter next.