Selective Prediction

Selective prediction evaluates a model that can abstain instead of always returning an answer. It connects Uncertainty estimation, Calibration, Threshold selection, and human review workflows.

A selective predictor has two parts:

$$f(x)=\text{prediction}$$ $$g(x)\in \{0,1\}$$

where $g(x)=1$ means accept the model prediction and $g(x)=0$ means abstain, defer, or request another process.

For a confidence or uncertainty score $s(x)$ and threshold $\tau$:

$$g_{\tau }(x)=1[s(x)\ge \tau ]$$

if higher $s(x)$ means more confidence. If higher score means more uncertainty, the inequality is reversed.

Coverage and Selective Risk

Coverage is the fraction of examples the model accepts:

$$\mathrm{coverage}(\tau )=\frac{1}{n}\sum _{i=1}^n{g}_{\tau }(x_i)$$

Selective risk is the average loss only on accepted examples:

$$\mathrm{risk}(\tau )=\frac{{\sum }_{i=1}^n{g}_{\tau }(x_i)\mathcal{L}(f(x_i),y_i)}{{\sum }_{i=1}^n{g}_{\tau }(x_i)}$$

The core trade-off is:

$$\text{lower risk}\leftrightarrow \text{lower coverage}$$

A useful uncertainty score should reduce risk as coverage decreases.

Decision View

Abstention is not free. If abstained examples go to human review, slower inference, wet-lab validation, or another model, evaluation should include that cost:

$$U(\tau )=\mathrm{Benefit}(\mathrm{accepted}\mathrm{correct})-\mathrm{Cost}(\mathrm{accepted}\mathrm{wrong})-\mathrm{Cost}(\mathrm{abstained})$$

This is why selective prediction should be evaluated with the deployment decision, not only with accuracy.

Common Uses

• Classification systems that route low-confidence cases to a human.
• Retrieval or QA systems that answer only when evidence is strong.
• Molecular or protein screens that escalate uncertain predictions to expensive validation.
• Agent systems that ask for confirmation before high-impact actions.
• OOD-sensitive systems that reject examples outside the applicability domain.
• Prediction-set systems where Conformal prediction returns multiple candidates instead of one.

Checks

• Is the abstention score calibrated or at least monotonic with error risk?
• Is the threshold chosen on validation data, not the test set?
• Are coverage, selective risk, and full-set metric reported together?
• What happens to abstained examples in the actual workflow?
• Is abstention evaluated under distribution shift and hard slices?
• Does the system abstain on the examples where mistakes are expensive?

Related

• Uncertainty estimation
• Conformal prediction
• Calibration
• Threshold selection
• Probability metrics
• Error analysis
• Applicability domain
• OOD generalization
• Human in the loop