Decision Tree Surrogate

The primary metric for a surrogate is fidelity—how well it mimics the black-box teacher's predictions—not accuracy against ground truth. A high-fidelity surrogate faithfully reproduces the teacher's decision boundaries, including its errors. This is measured on a held-out test set by comparing the surrogate's predictions directly to the teacher's outputs. A surrogate with 95% fidelity correctly replicates the teacher's classification for 95% of inputs, providing a trustworthy explanation of the model's logic even if the teacher itself is not perfectly accurate.

The surrogate is trained on a synthetic dataset created by querying the black-box model:

• Step 1: Sample inputs from the original data distribution or generate new instances uniformly across the feature space.
• Step 2: Pass each input through the black-box teacher to obtain predictions (hard labels or probability distributions).
• Step 3: Train a decision tree algorithm like CART or C4.5 on these input-output pairs. The resulting tree learns to approximate the teacher's decision function, not the original data labels, making it a model of the model.

Decision trees are transparent-by-design models. Their logic is expressed as a series of binary splits on feature thresholds, forming a directed acyclic graph from root to leaves. Each path from root to leaf represents a conjunctive rule (e.g., IF income > $80k AND age < 30 THEN approve). This structure allows non-technical stakeholders to trace the exact reasoning behind any prediction. Unlike linear surrogates, trees naturally capture feature interactions and non-linear decision boundaries without requiring the user to mentally combine coefficients.

A critical design tension exists between the surrogate's complexity and its faithfulness:

• Shallow trees (depth 3-5): Highly interpretable but may oversimplify the teacher's logic, resulting in low fidelity.
• Deep trees (depth 10+): Higher fidelity but risk becoming as opaque as the original model. The optimal depth is found by plotting fidelity vs. number of leaf nodes and selecting the knee point where additional complexity yields diminishing returns. A common heuristic is to limit the tree to 15-25 leaves for a balance of accuracy and human comprehensibility.

Decision trees are notoriously unstable—small changes in training data can produce radically different tree structures. For surrogates, this undermines trust. To mitigate:

• Train on a large, densely sampled synthetic dataset covering the input space uniformly.
• Use ensemble surrogates (e.g., extracting the most frequent rules across multiple trees).
• Apply rule regularization during training to penalize overly complex splits.
• Prefer algorithms like the SIRUS algorithm, which extracts a stable rule list from a random forest of shallow trees, providing a more robust surrogate than a single deep tree.

Decision tree surrogates degrade significantly when the black-box model operates on high-dimensional input spaces (e.g., images, text embeddings, or hundreds of tabular features). Trees rely on axis-aligned splits, which become inefficient at partitioning spaces with complex, oblique decision boundaries. In these cases:

• The tree may require thousands of nodes to achieve acceptable fidelity, destroying interpretability.
• Feature engineering is necessary to reduce dimensionality before surrogate training.
• Alternative global surrogates like Explainable Boosting Machines (EBMs) or Generalized Additive Models (GAMs) may provide better fidelity-interpretability tradeoffs for high-dimensional problems.

An interpretable model trained to approximate the entire decision boundary of a black-box model across the whole input space. A decision tree surrogate is the canonical example of a global surrogate, providing a complete but approximate explanation of the original model's behavior. Unlike local methods that explain single predictions, global surrogates aim to capture the overall logic of the teacher model in a single, inspectable structure.

A model compression technique where a smaller student model is trained to replicate the behavior of a larger teacher model. In the context of interpretability, the student is deliberately chosen to be a transparent architecture like a decision tree. The distillation process transfers the teacher's dark knowledge—the rich similarity structure encoded in its softmax outputs—into a form that humans can directly audit and understand.

A student model whose quality is measured by its fidelity—the degree to which its predictions match those of the teacher on unseen data. For decision tree surrogates, fidelity is the primary evaluation metric, not accuracy against ground-truth labels. A high-fidelity surrogate faithfully reproduces the black-box model's decisions, while a low-fidelity one introduces its own biases, making explanations misleading rather than illuminating.

The fundamental design tension between a model's predictive performance and its transparency. Complex models like deep neural networks achieve high accuracy but resist direct interpretation. Decision tree surrogates navigate this tradeoff by sacrificing some fidelity to the teacher in exchange for complete structural transparency. The goal is to find the Pareto-optimal point where the tree is simple enough to understand yet faithful enough to trust.

The process of deriving a set of symbolic, human-readable if-then rules from a trained neural network. A decision tree surrogate is a natural vehicle for rule extraction, as each path from root to leaf directly translates into a conjunctive rule. These extracted rules can be audited by domain experts, checked for safety violations, and even deployed in regulated environments where black-box models are prohibited.

The standard paradigm where an interpretable student model is trained to explain a pre-existing, fully trained black-box teacher. Decision tree surrogates are post-hoc by nature—they are built after the teacher's training is complete, using only the teacher's input-output pairs. This decoupling allows organizations to explain legacy models without retraining them, making surrogates a non-invasive interpretability solution.