Anchors

Anchors are designed to maximize precision—the proportion of instances covered by the rule where the prediction holds. Unlike LIME, which optimizes for fidelity, Anchors explicitly guarantee that a rule achieves a user-specified precision threshold (e.g., 95%) with high probability. This is achieved through a PAC (Probably Approximately Correct) learning framework that provides statistical guarantees.

• Precision target: User-defined, typically 90-99%
• Confidence level: Statistical bound on the precision estimate
• Coverage trade-off: Higher precision often reduces the number of instances the rule applies to

Anchors generate human-readable logical rules composed of feature predicates. Each rule takes the form: "IF condition A AND condition B THEN prediction Y." These conditions are expressed in natural, domain-relevant terms rather than abstract feature weights.

• Predicate types: Categorical thresholds (e.g., age > 30), categorical values (e.g., education = Masters)
• Rule sparsity: Rules typically contain 1-5 conditions for interpretability
• Example: "IF income > $50K AND credit_score > 700 THEN loan_approved = Yes"

Anchors are built using a bottom-up construction algorithm that iteratively adds feature predicates to maximize coverage while maintaining the precision constraint. The algorithm generates synthetic perturbations of the instance being explained and evaluates candidate rules against the model's behavior on these perturbations.

• Multi-armed bandit: Efficiently explores the space of candidate rules using KL-LUCB algorithm
• Perturbation strategy: Samples from a perturbation distribution around the instance
• Beam search: Maintains a beam of candidate rules, expanding the most promising ones

The core principle behind Anchors is local sufficiency: a rule is sufficient if, when the rule conditions are met, changes to other features do not change the prediction. This formalizes the intuition that the identified features are the "anchors" that fix the prediction in place.

• Invariance property: Prediction remains stable under perturbations of non-anchor features
• Neighborhood definition: Defined by the perturbation distribution around the instance
• Contrast with LIME: LIME approximates the decision boundary locally; Anchors identify a region where the prediction is invariant

While precision is the primary constraint, Anchors optimize for coverage—the proportion of instances in the perturbation space that satisfy the rule conditions. Higher coverage means the explanation applies more broadly, making it more useful for understanding model behavior across similar cases.

• Coverage-precision trade-off: Relaxing precision requirements increases achievable coverage
• Global insight: High-coverage anchors reveal systematic model behaviors
• Submodular optimization: Coverage exhibits diminishing returns, guiding efficient rule construction

Anchors are fully model-agnostic, requiring only query access to the model's prediction function. This makes them applicable to any black-box classifier, including deep neural networks, gradient-boosted trees, and ensemble methods. No gradient information or internal model access is needed.

• Input types: Tabular data, text (via word presence predicates), and images (via superpixel predicates)
• Output types: Works with any classification model producing probability scores
• Limitation: Computational cost scales with the number of model queries required for perturbation evaluation

A foundational local explainability technique that approximates a complex model's decision boundary around a specific prediction using an interpretable surrogate model. Unlike Anchors, which generates high-precision if-then rules, LIME focuses on feature importance weights. The key distinction is that LIME's explanations are local linear approximations, while Anchors provide decision rules that guarantee the prediction remains stable when the rule conditions hold, offering stronger formal guarantees for coverage and precision.

A method that identifies the minimal changes to an input feature vector required to flip a model's prediction to a desired alternative outcome. While Anchors define the sufficient conditions for a prediction to remain fixed, counterfactuals define the necessary changes to alter it. Together, they form a complete explanatory picture: Anchors tell the user 'why this decision stands,' and counterfactuals tell them 'what to change to get a different result,' which is critical for recourse in automated decision systems.

Quantitative measures designed to automatically score how accurately a generated explanation reflects the model's true internal decision process. For Anchors, faithfulness is measured by the precision metric—the fraction of instances covered by the anchor rule where the model's prediction remains consistent. High precision is the defining characteristic of an anchor; a rule with low precision fails to 'anchor' the prediction and is not a valid explanation. This contrasts with plausibility metrics, which measure human acceptance rather than mechanistic fidelity.

The principle of providing the shortest possible justification that is still complete enough to justify a model's decision. Anchors directly operationalize this concept by searching for minimal sufficient rules—the smallest set of feature conditions that guarantee a prediction with high probability. The algorithm uses a beam search to balance rule length (complexity) against coverage (generality), ensuring the resulting explanation is both concise and statistically robust. This makes Anchors ideal for high-stakes domains where operators need quick, unambiguous decision rules.

A critical metric in the Anchors framework that measures the proportion of instances in a dataset to which an anchor rule applies. While precision ensures the rule is correct when it fires, coverage ensures it is useful across a meaningful subset of the data. The Anchor algorithm explicitly optimizes for coverage subject to a precision constraint, formalized as: maximize coverage(A) subject to precision(A) ≥ τ, where τ is a user-defined precision threshold. This trade-off is central to generating practical, high-impact explanations.

A class of model-agnostic interpretability methods that probe a black-box model by systematically perturbing input features and observing the resulting prediction changes. Anchors belong to this family, extending the neighborhood sampling approach used by LIME. However, Anchors introduce a multi-armed bandit formulation to efficiently explore the perturbation space and construct rules with formal precision guarantees. This statistical rigor distinguishes Anchors from simpler perturbation methods that lack confidence bounds on their explanations.