Surrogate Model

Surrogate models operate on two distinct scopes of explanation:

• Global Surrogate: Trained to approximate the entire decision boundary of the black-box model across the full input space. Provides a complete, high-level understanding of overall model behavior.
• Local Surrogate: Trained only on predictions in the immediate neighborhood of a specific instance. Explains a single prediction without needing to capture global complexity. The choice between global and local scope represents a fundamental tradeoff between comprehensiveness and local fidelity.

The quality of a surrogate is measured by its fidelity—the degree to which its predictions match those of the black-box teacher on unseen data. This is distinct from accuracy against ground-truth labels.

• High-fidelity surrogates faithfully reproduce the teacher's behavior, including its errors and biases.
• Low-fidelity surrogates may be misleading, providing explanations that do not reflect the actual model's decision process. Fidelity is typically measured using R-squared for regression or agreement rate for classification tasks.

The student model must be transparent-by-design. Acceptable surrogate architectures include:

• Linear models (logistic regression, LASSO) providing feature-level coefficients.
• Decision trees (CART, C4.5) yielding human-readable flowcharts.
• Generalized Additive Models (GAMs) with visualizable shape functions.
• Rule lists (SIRUS, RuleFit) producing sparse if-then logic. The constraint is absolute: if the surrogate itself requires explanation, it has failed its purpose. Structural interpretability is non-negotiable.

Surrogate models embody the fundamental tension between predictive performance and transparency:

• The black-box teacher occupies the high-accuracy, low-interpretability region.
• The surrogate must operate in the high-interpretability region, accepting some fidelity loss.
• The goal is not perfect replication but sufficient fidelity for the explanation task at hand. This tradeoff is managed through careful model selection and the use of soft targets from the teacher to transfer richer information than hard labels alone.

A defining strength of the surrogate approach is its complete model agnosticism. The technique treats the black-box teacher as an opaque oracle:

• No access to internal weights, gradients, or architecture is required.
• Only the input-output mapping of the teacher is used for training.
• The same surrogate methodology works identically on neural networks, gradient-boosted trees, ensembles, or proprietary APIs. This property makes surrogates uniquely suited for explaining third-party or legacy models where internal access is impossible.

Surrogate models are trained on a generated dataset of input-output pairs sampled from the teacher:

• Inputs are drawn from the original training distribution or a perturbed neighborhood around an instance.
• The teacher generates predictions (soft or hard labels) for each sampled input.
• The surrogate learns to map these inputs to the teacher's outputs, not the ground truth. This process effectively transfers the teacher's learned function into an interpretable form, capturing both its knowledge and its systematic errors.

A student model whose quality is measured by its fidelity—the degree to which its predictions match the teacher model—rather than solely by accuracy on ground-truth labels.

• Fidelity: The percentage of test instances where the student and teacher agree.
• Why it matters: A surrogate with 95% fidelity but 85% accuracy is still a faithful explanation of the teacher's behavior.
• Tradeoff: High fidelity often requires a more complex surrogate, reducing interpretability.
• R-Fidelity: A stricter metric measuring agreement on the teacher's ranking of class probabilities.

A globally interpretable tree-based model trained on the input-output pairs of a black-box model to provide a faithful, high-level approximation of its decision logic.

• Algorithms: CART, C4.5, or C5.0 trained on the teacher's predictions.
• Output: A human-readable flowchart of if-then rules.
• Depth control: Limiting tree depth balances interpretability and fidelity.
• Advantage: No need for original training data—only the ability to query the black-box model.
• Limitation: Axis-aligned splits may oversimplify complex, non-linear boundaries.

A simple linear model, such as LASSO or logistic regression, trained to mimic a complex model's predictions locally or globally to provide feature-level importance scores.

• Global linear proxy: A single linear model approximating the entire black-box.
• Local linear proxy: A weighted linear model fitted around one prediction.
• LASSO advantage: L1 regularization forces sparse coefficients, highlighting only the most important features.
• Output: Coefficients directly interpreted as the average effect of each feature on the prediction.