Anchors

An Anchor is defined as a rule IF (condition) THEN (prediction) where the condition is a set of predicates on input features. The rule's precision is the probability that the prediction remains the same for instances where the anchor holds, even if other unspecified features are perturbed. This precision must meet a user-defined threshold (e.g., 0.95), ensuring the explanation is a sufficient condition for the model's output, not just a correlative one.

The algorithm treats the model as a black-box, requiring only input-output access. It explains individual predictions (local interpretability) by identifying the decisive features for a single instance, rather than providing a global model summary. It uses a perturbation-based approach, generating neighbors of the instance by randomly altering non-anchor features to test the stability of the prediction.

• Method: For an instance, it searches for a rule with high coverage (applies to many similar instances) and high precision.
• Output: A human-readable rule like IF (Age > 50) AND (Blood_Pressure = 'High') THEN (Predict 'High Risk').

The core algorithm performs a beam search over possible rules (candidate anchors). It starts with an empty rule and iteratively adds feature predicates that maximize precision.

Key steps:

• Candidate Generation: Propose new anchors by adding a feature condition to existing candidates.
• Precision Evaluation: For each candidate, sample perturbed instances where the anchor is true but other features are randomly changed. Query the model to estimate the precision.
• Coverage Calculation: Coverage is the fraction of instances in the perturbation distribution for which the anchor applies. The algorithm balances high precision with reasonable coverage.
• Stopping Criterion: The search stops when it finds an anchor where the estimated precision confidence interval is above the predefined threshold (e.g., 0.95 with 95% confidence).

Anchors naturally provide contrastive explanations. By showing the minimal features that 'lock in' a prediction, they implicitly answer "Why this prediction and not another?" For example, an anchor for a loan denial might be IF (Credit_Score < 600), indicating that this condition alone is sufficient for the denial, regardless of other positive factors like income.

This relates directly to the Sufficiency evaluation metric: an anchor is a validated sufficient explanation. If the anchor conditions are met, the model's prediction is robustly determined, which is a stronger guarantee than feature importance scores which only indicate correlation.

The quality of an anchor is empirically validated through the perturbation process, which is a form of explanation robustness testing. This addresses a key weakness of other methods like LIME, where explanations can be unstable.

• Robustness Check: The anchor is tested against many perturbed versions of the original input.
• Faithfulness Proxy: High precision under perturbation is a practical proxy for local fidelity and faithfulness, as it demonstrates the explanation captures a truly decisive part of the model's local decision boundary.
• Comparison: Unlike SHAP which provides additive attribution, Anchors provide a discrete, logical rule validated for robustness.

Primary Use Cases:

• High-Stakes Decisions: Credit, healthcare, and compliance where auditable, rule-based justifications are required.
• Debugging Models: Identifying spurious, locally sufficient rules that reveal model flaws.
• Human Simulatability: Rules are often easier for humans to understand and verify than numerical attributions.

Key Limitations:

• Computational Cost: The perturbation-based sampling can be expensive for high-dimensional data or slow models.
• Discrete Features: Works best with categorical or discretized numerical features; continuous features require binning.
• Local Scope: Does not provide global model understanding, only instance-specific explanations.

A foundational model-agnostic explanation method that approximates a complex model locally around a single prediction using a simpler, interpretable surrogate model (like linear regression).

• Contrast with Anchors: While LIME provides a local linear approximation of the model's decision boundary, Anchors provide a high-precision rule (if-then conditions) that guarantees the prediction remains unchanged for perturbations within the rule's scope. LIME offers importance weights; Anchors offer a logical condition.

A unified framework for feature attribution based on cooperative game theory, specifically Shapley values. It assigns each feature an importance value for a specific prediction, representing its average marginal contribution across all possible feature combinations.

• Contrast with Anchors: SHAP provides a detailed, additive score for every feature. Anchors provide a sufficient condition (a rule) for the prediction. SHAP answers 'how much did each feature contribute?'. Anchors answer 'what feature values guarantee this prediction?'.

Explanations that describe the minimal changes required to an input to achieve a different, desired model outcome. They answer the question: "What would need to be different for the prediction to change?"

• Relation to Anchors: Counterfactuals are complementary. An Anchor rule defines the 'safe' region for the current prediction. A counterfactual points to the nearest point outside that Anchor's region, showing the minimal perturbation to flip the prediction. Together, they bound the model's local decision.

A core quantitative metric for evaluating explanations. It measures how accurately an explanation reflects the true reasoning process of the underlying model.

• Direct Application to Anchors: The precision of an Anchor (the probability the prediction holds when the rule is satisfied) is a direct measure of its faithfulness. A high-precision Anchor (e.g., 0.95) is highly faithful—when you see its conditions, the model's prediction is robust. This makes Anchors inherently evaluable via their own precision metric.

A general validation technique that systematically modifies input features to observe the impact on model outputs and explanations.

• Foundation of Anchors: The Anchor algorithm relies on perturbation. It generates candidate rules and tests them by perturbing features not in the rule (e.g., by sampling from a background distribution). The rule's precision is estimated by the fraction of perturbed samples where the original prediction remains unchanged. This makes perturbation the core mechanism for Anchor validation.

An explanation quality metric that asks: Is the set of highlighted features sufficient for the model to make its prediction?

• Anchors as Sufficient Conditions: An Anchor is the embodiment of a sufficiency test. By definition, if the Anchor's conditions (e.g., IF Age > 50 AND Blood_Pressure = 'High') are met, the prediction (e.g., THEN High_Risk) holds with high probability. Therefore, a valid Anchor directly provides a sufficient explanation for the model's local behavior.