Selective Prediction and Abstention

An assistant that answers 100% of questions at 85% accuracy and one that answers 70% of them at 97% accuracy can have identical training. The difference is a threshold and a fallback path, and for most deployed systems the second is the more valuable product. Selective prediction is the framing that makes this a design decision rather than an accident: pair a predictor \(f\) with a gate \(g\), answer when \(g(x) = 1\), abstain otherwise. The idea is old, going back to Chow's optimal reject rule in 1970, and was formalised for modern learning as selective classification with a target risk (El-Yaniv and Wiener, JMLR 2010; Geifman and El-Yaniv, 2017, arXiv:1705.08500).

Measure with a curve, not a point

Two quantities move together. Coverage is the fraction of inputs answered. Selective risk is the error rate among answered inputs only. Sweeping the gate's threshold traces a risk-coverage curve, and its area (AURC, lower is better) summarises a confidence signal's quality independently of any particular operating point.

This decomposition is what makes the curve useful for diagnosis. A gate can fail in two different ways: the confidence signal may rank examples poorly, in which case the whole curve is flat and no threshold helps, or the ranking may be fine while the threshold sits in the wrong place, in which case the curve is good and you are simply operating at the wrong point on it. Only the first requires a better model.

Where the gate signal comes from

Sequence log-probability is the cheapest option and the weakest, because it is length-biased and confounded by lexical freedom. Self-evaluation, asking the model to judge whether its own answer is correct, is stronger and can be improved substantially by tuning the model for that specific self-evaluation task rather than relying on it zero-shot (Chen et al., 2023, Adaptation with Self-Evaluation to Improve Selective Prediction in LLMs, arXiv:2310.11689). Semantic consistency across samples, a separate trained verifier, and retrieval-based groundedness scores all serve the same role, and in RAG systems the retrieval score is an independent signal worth combining with the generator's.

Choosing the threshold like an engineer

The threshold follows from costs, not from a round number. Let \(c_{\text{wrong}}\) be the cost of a wrong answer, \(c_{\text{abstain}}\) the cost of a deflection (a human handling the ticket, a user leaving), and \(b\) the benefit of a correct answer. Answering is worth it when the expected value clears abstention:

Solve for \(p\) and you have the confidence threshold that maximises expected value. In a medical triage system where \(c_{\text{wrong}}\) dwarfs \(c_{\text{abstain}}\) that threshold is very high, and coverage of 30% is a good outcome. In a search-suggestion feature the ordering reverses and near-total coverage is correct. The number falls out of the business, and the mistake is picking 0.9 because it looks confident.

When it breaks

• Abstention is not free and often not measured. "I don't know" degrades the product, and a system tuned only on selective risk drifts toward abstaining on anything hard. Track coverage as a first-class metric alongside accuracy.
• Users route around the gate. Deflected users rephrase and try again, so an abstention on the first attempt often becomes a confident answer on the third. Measure per-session outcomes, not per-request.
• Thresholds are distribution-specific. A gate calibrated on evaluation traffic behaves differently on a Monday-morning support spike. Monitor coverage as a drift alarm; a sudden coverage change usually means the input distribution moved.
• Calibration and selection are different problems. A model can be badly calibrated in absolute terms and still rank its own errors well, which is all a gate needs. Optimise the ranking (AURC), not the Brier score, unless you need the probabilities themselves.
• Abstention can be gamed by the metric. If an evaluation scores abstentions as non-errors, the highest-scoring system is one that answers nothing. Score abstention explicitly, with the cost it actually carries.