1. A classification boundary is a rule
A threshold divides a feature space; it does not establish a sharp physical boundary in the economy. Nearly identical inputs on opposite sides can receive different names, while distant observations inside one region receive the same name. Preserve the underlying values and threshold alongside the label. Scikit-learn's threshold guide distinguishes estimated scores from the decision rule that converts them into labels. In a transparent feature-threshold exercise, the boundary is directly specified rather than inferred from a probability model. Its precision is a property of the rule, not proof of certainty.
2. Measure distance in meaningful units
For one feature, distance is the absolute value of the difference between the feature and its threshold. For two features, inspect both distances instead of allowing a large distance on one axis to hide proximity on the other. Raw distances with different units are not automatically comparable. If standardisation is used, preserve its training window and scale definition. A margin is not a probability of correctness. Scikit-learn's calibration documentation treats probability calibration as a separate relationship between predicted probabilities and observed outcomes; a geometric distance does not establish that relationship by itself.
3. Separate measurement, rule and model uncertainty
An input can be uncertain because it may be revised, because its observation period is old or because its measurement is noisy. The boundary can be uncertain because several plausible definitions exist. A fitted model introduces parameter and specification uncertainty as well. These sources call for different checks. Perturbing a threshold examines rule sensitivity; substituting an eligible vintage examines measurement sensitivity. Neither automatically gives a confidence interval. State the perturbation range and its rationale, and do not attach probability coverage unless a defensible statistical procedure actually supports that interpretation.
4. Specify abstention before examining outcomes
Abstention means withholding a categorical output under a declared condition. A boundary rule might abstain when either feature lies within a specified margin of its threshold. Define whether the endpoints are included and what happens when one input is missing. Keep a boundary abstention distinct from a data-quality failure. Choose or validate the policy using information permitted by the study design, then freeze it for evaluation. The scikit-learn threshold guide warns about overfitting when threshold selection reuses model-training data. Time-ordered research also needs to prevent later observations from influencing earlier choices.
5. Apply an explicitly fictional margin rule
The example assumes two already comparable synthetic features, both with threshold zero. It abstains whenever either absolute feature value is less than or equal to 0.10. A row with growth 0.06 and inflation 0.35 is therefore withheld despite positive signs. A row exactly at 0.10 is also withheld because the endpoints are included. Rows with values -0.24 and 0.35, or 0.14 and -0.22, lie outside both margins. Two of four rows receive classifications, giving 50% coverage. These assumptions illustrate a rule, not a validated tolerance or observed reliability.
6. Do not confuse abstention with persistence
Withholding a new label is different from retaining the previous label. If an earlier classification remains visible, mark it as carried forward with its original decision time and current status. Hysteresis uses different conditions for entering and leaving a state; confirmation requires a condition to persist over a declared sequence. Both introduce memory and can delay changes. A margin-based abstention rule need not do either. Keep these policies separate in documentation so a stable-looking sequence cannot conceal repeated uncertainty, repeated use of stale information or unrecorded changes to the decision rule.
7. Report coverage without promising better accuracy
Selective-prediction research, including the SelectiveNet paper, studies rejection and the trade-off between coverage and error on accepted cases. That concept motivates reporting how often a rule abstains, but its empirical results do not validate a regime threshold. Count accepted, withheld and unavailable cases separately. Error rates require a defensible target; an unobserved 'true regime' cannot be assumed. Examine where abstentions cluster and whether they exclude entire difficult episodes. Lower coverage is not automatically better research. This guide offers an uncertainty framework, not investment advice or a recommendation to change exposure.
Inspect the comparison
| Fictional growth feature | Fictional inflation feature | Boundary check | Output |
|---|---|---|---|
| 0.06 | 0.35 | Growth distance <= 0.10 | Abstain |
| -0.24 | 0.35 | Both distances > 0.10 | Lower growth / higher inflation |
| 0.14 | -0.22 | Both distances > 0.10 | Higher growth / lower inflation |
| 0.10 | 0.35 | Growth exactly on included margin | Abstain |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.