Anchor Explanations

The two fundamental metrics for evaluating anchor quality. Precision measures the fraction of instances where the anchor rule correctly predicts the model's output, while coverage quantifies how many instances in the dataset satisfy the anchor's conditions. A perfect anchor achieves precision ≥ a user-specified threshold (e.g., 0.95) with maximum possible coverage.

• Precision: Proportion of correct predictions among instances where the anchor applies
• Coverage: Probability that the anchor applies to a randomly drawn instance
• Trade-off: Higher precision typically reduces coverage, requiring careful threshold selection

The algorithmic backbone of anchor discovery, framing the search for high-precision rules as a multi-armed bandit problem. Each candidate feature condition is treated as an arm, and the algorithm sequentially selects arms to add to the anchor while estimating precision through perturbation sampling. This approach efficiently explores the combinatorial space of possible rules without exhaustive enumeration.

• Uses KL-LUCB (Lower-Upper Confidence Bound) strategy for arm selection
• Balances exploration of new conditions with exploitation of known high-precision rules
• Provides statistical guarantees on precision estimates

The mechanism for generating synthetic neighbors around the instance being explained. Unlike LIME's Gaussian perturbations, anchor explanations use a discrete perturbation space that respects feature semantics—masking words in text, occluding superpixels in images, or sampling from empirical marginal distributions for tabular data. The perturbation strategy directly impacts which anchors are discoverable.

• Text: Replaces tokens with UNK or samples from vocabulary
• Tabular: Samples values from training data marginal distributions
• Images: Masks superpixels while preserving spatial structure

An anchor is formally defined as a sufficient condition for a prediction: if the anchor rule holds, the model's prediction remains fixed with high probability regardless of changes to other features. This contrasts with LIME's linear approximations, which only capture local decision boundary slopes. Anchors provide if-then guarantees that are inherently easier for non-technical stakeholders to audit and trust.

• Formal property: P(prediction = y | anchor holds) ≥ τ
• τ (tau): User-defined precision threshold, typically 0.95
• Non-anchor features: Free to vary arbitrarily without breaking the guarantee

The iterative process of building anchors by starting with an empty rule and greedily adding feature predicates. At each step, candidate conditions are evaluated using the multi-armed bandit to select the addition that maximizes coverage while maintaining precision above the threshold. The algorithm terminates when no further conditions can be added without dropping below the precision requirement.

• Empty anchor: Initially applies to all instances (maximum coverage, low precision)
• Greedy addition: Each step adds the condition that yields highest coverage gain
• Stopping criterion: Precision falls below τ or no candidates remain

While both are model-agnostic, local explanation methods, anchors provide fundamentally different guarantees. LIME produces a linear approximation of the decision boundary, which may be inaccurate in highly non-linear regions. Anchors produce logical rules with precision guarantees, making them more suitable for high-stakes applications where explanation reliability is critical.

• LIME: Weighted linear model, no formal precision guarantees
• Anchors: If-then rules with statistical precision bounds
• Interpretability: Anchors are self-contained rules requiring no understanding of feature weights
• Computational cost: Anchors are more expensive to compute due to bandit search