Selective Prediction

The mathematical process of aligning a model's predicted probability with the empirical likelihood of correctness. A perfectly calibrated model that outputs a 70% confidence score should be correct exactly 70% of the time.

• Platt Scaling: Fits a logistic regression model on top of raw logits to smooth probability estimates.
• Isotonic Regression: A non-parametric method that learns a monotonic mapping from scores to calibrated probabilities.
• Temperature Scaling: A single-parameter variant of Platt scaling that divides logits by a learned temperature constant T > 0.
• Expected Calibration Error (ECE) measures the weighted average gap between confidence and accuracy across bins.

A decision boundary mechanism that routes low-confidence predictions to a fallback path—either a human reviewer, a secondary model, or a safe default action. This is formalized as a cost-sensitive classification problem.

• Chow's Rule: The optimal rejection policy minimizes expected risk by comparing the maximum posterior probability against a cost ratio threshold.
• Abstention Class: Some architectures add an explicit 'abstain' output class trained on synthetic or naturally uncertain examples.
• Selective Risk: The error rate computed only on accepted predictions. The goal is to minimize selective risk while maintaining a target coverage (fraction of inputs answered).
• Common in medical imaging where ambiguous scans are flagged for radiologist review rather than risking a missed diagnosis.

The simplest selective prediction baseline uses the maximum softmax probability (MSP) as a confidence proxy. If max(P(y|x)) < τ, the model abstains.

• Limitation: Modern deep networks are notoriously overconfident on out-of-distribution (OOD) inputs, assigning high softmax scores to nonsensical data.
• Energy-Based Models: The energy score (negative log of the denominator in softmax) provides a more reliable OOD detection signal than MSP.
• Mahalanobis Distance: Computes class-conditional Gaussian distances in feature space, offering superior uncertainty estimates compared to raw softmax.
• Threshold τ is typically tuned on a held-out validation set to balance coverage against selective risk.

A Bayesian approximation technique that enables uncertainty estimation in standard neural networks without architectural changes. By keeping dropout active during inference and running multiple stochastic forward passes, the model produces a distribution of predictions.

• Epistemic Uncertainty: Captured by the variance across MC samples—high variance indicates the model lacks knowledge about the input.
• Aleatoric Uncertainty: Inherent data noise, modeled by predicting both a mean and variance per output.
• Predictive Entropy: The entropy of the averaged predictive distribution serves as a robust abstention signal.
• Typically 10–50 forward passes are sufficient; the computational overhead is acceptable for batch processing but challenging for real-time inference.

Training multiple independent models with different random initializations and evaluating their disagreement provides state-of-the-art uncertainty quantification. Disagreement among ensemble members strongly correlates with prediction error.

• Ensemble Diversity: Each member sees the same data but converges to a different local minimum due to the non-convex loss landscape.
• Variance of Predictions: The standard deviation of softmax outputs across ensemble members is a powerful abstention metric.
• Mutual Information: Measures the information gain about model parameters from observing the label—decomposes total uncertainty into epistemic and aleatoric components.
• The primary drawback is the N× computational cost for both training and inference, making this impractical for large foundation models.

A distribution-free framework that provides finite-sample statistical guarantees on coverage. Conformal prediction produces prediction sets rather than single labels, with a provable marginal coverage rate.

• Split Conformal: Reserves a calibration set to compute nonconformity scores; for a new input, includes all labels with scores below a quantile threshold.
• Adaptive Prediction Sets (APS): Accumulates sorted softmax probabilities until the cumulative sum exceeds the threshold, producing smaller sets for easy examples and larger sets for uncertain ones.
• Risk-Controlling Prediction Sets (RCPS): Extends conformal prediction to control any monotone loss function, enabling guarantees on task-specific metrics beyond miscoverage.
• The model abstains when the prediction set is empty or exceeds a maximum allowed size, providing a principled alternative to heuristic thresholding.

A specialized model or layer that evaluates an input prompt or generated output to assign a risk score, triggering a refusal or sanitization action if a toxicity or policy threshold is breached. Unlike Selective Prediction's focus on epistemic uncertainty, safety classifiers target content-based harm.

• Operates as a pre- or post-processing guard
• Often a fine-tuned BERT or DeBERTa variant for low latency
• Complements confidence-based abstention with content-based filtering

The task of identifying inputs that differ significantly from the training data distribution. This is the primary trigger for Selective Prediction's reject option.

• Detects semantic shift (novel concepts) and covariate shift (input style changes)
• Methods include Mahalanobis distance, energy-based models, and density estimation
• Prevents silent failures on unfamiliar data

A runtime inference technique that applies a logit bias or token mask to force the LLM to generate outputs that strictly adhere to a predefined grammar, schema, or vocabulary restriction.

• Guarantees valid JSON, SQL, or domain-specific syntax
• Reduces the need for abstention by structurally preventing invalid outputs
• Often used alongside Selective Prediction for high-stakes structured generation

A post-processing mechanism that verifies generated statements against a retrieval corpus or knowledge graph to suppress non-factual or ungrounded content. While Selective Prediction abstains before generation, hallucination filters catch errors after.

• Uses entailment models or citation verification
• Can trigger a regeneration request or fallback response
• Critical for RAG systems where grounding is expected

An automated operational safeguard that immediately halts model inference or revokes API access when a critical volume of policy violations or anomalous queries is detected within a time window.

• Operates at the system level, not the individual prediction level
• Prevents cascading failures and abuse campaigns
• Complements per-prediction abstention with systemic protection

A defense-in-depth architecture that combines multiple heterogeneous safety classifiers via a voting or cascading mechanism to reduce false negatives. Selective Prediction can be one component in such an ensemble.

• Stacks regex filters, embedding-based detectors, and neural classifiers
• Majority voting or weighted confidence fusion for final decisions
• Reduces both false positives (over-refusal) and false negatives (missed violations)