Local Surrogate

The defining characteristic of a local surrogate is its focus on local fidelity—accurately mimicking the black-box model's behavior only in a small region around the instance of interest. This is achieved by generating a perturbed dataset weighted by proximity to the target instance. A model with high local fidelity may have poor global fidelity, as it is intentionally blind to the overall decision boundary. This trade-off is central to techniques like LIME, where an interpretable model like a sparse linear regressor is trained on these locally weighted samples.

To build a local surrogate, the input space around the target instance must be sampled. This is done by generating perturbed instances—modified versions of the original input. For tabular data, this involves sampling from a normal distribution around feature values. For text, it means removing words. For images, it means turning superpixels on or off. The surrogate is then trained on these perturbations, with each sample weighted by its cosine or Euclidean distance to the original instance, ensuring the model focuses on the immediate locality.

The 'surrogate' itself must be a glass-box model whose logic is transparent to a human. Common choices include:

• Sparse Linear Models: Provide feature weights that directly indicate importance and direction.
• Shallow Decision Trees: Offer a visualizable flowchart of local logic with only a few splits.
• Rule Lists: Generate simple if-then conditions that govern the local prediction. The complexity of the surrogate is intentionally constrained to ensure human comprehensibility.

The primary output of a local surrogate is a set of feature attribution scores for a single prediction. For a linear surrogate, the learned coefficients directly quantify the contribution of each feature to the black-box's output for that specific instance. This answers the question, 'Why did the model make this prediction for this specific customer?' rather than 'How does the model work overall?' This is critical for adverse action reasoning in credit denial or medical diagnosis scenarios.

A global surrogate is a single interpretable model trained to approximate the entire black-box model across the full input space. A local surrogate is a distinct model trained for each individual prediction that requires an explanation. While a global decision tree surrogate might have thousands of nodes to capture overall logic, a local linear surrogate is intentionally simple, capturing only the local gradient of the decision boundary. Local surrogates are preferred when the global model behavior is too complex to summarize with a single simple model.

Local surrogates navigate a critical tension: the simpler the surrogate model (e.g., a linear model with 5 features), the easier it is to interpret, but the lower its capacity to faithfully capture the local non-linearities of the black-box. The R² score (coefficient of determination) between the surrogate's predictions and the black-box's predictions on the perturbed neighborhood is used to measure local faithfulness. A low R² warns the user that the explanation may be an oversimplification of a highly complex local decision boundary.