1. State the rule without interpretive shorthand
A threshold classifier assigns a category according to whether an observed feature crosses a declared boundary. With two binary features, the pair of comparison results defines four possible combinations. The arithmetic can be simple while the measurement choices remain consequential. Write the rule in symbols and ordinary language: for example, upper when x > c and lower otherwise, provided x is valid. Do not substitute words such as strong or weak for a missing definition. This guide concerns transparent research classification, not investment advice or evidence of predictive performance.
2. Declare units and transformations first
A boundary is meaningless without its feature's units. A zero threshold on a growth rate separates positive from nonpositive growth; zero on a change in that rate separates acceleration from nonacceleration. A threshold on a standardized value instead refers to a chosen reference distribution. Record the transformation, frequency, seasonal treatment, and eligible data vintage before naming categories. If a moving normalization changes the effective raw-data boundary, describe that movement explicitly. A fixed threshold in transformed space does not necessarily represent a fixed economic boundary in the original units.
3. Make equality and rounding explicit
Scikit-learn's Binarizer uses a strict greater-than comparison: equality belongs to the lower output. NumPy's digitize documents alternative interval-edge conventions. These are programming choices, not competing economic theories. Select the convention deliberately and test the exact boundary plus nearby values. Perform comparisons on the declared precision of the input, not on a shortened display string. A small positive value shown as 0.00 can still be above zero internally. If rounding is part of the model, freeze that operation and its order rather than letting presentation settings determine categories.
4. Distinguish declared thresholds from estimated thresholds
A rule can use a boundary chosen in advance or one estimated from a training sample, such as a historical quantile. The latter adds a fitting step even when the final comparison is elementary. Preserve the calibration period, estimation method, and update schedule. A threshold chosen after viewing later outcomes carries information from those outcomes into the classifier. Scikit-learn's leakage guidance applies to these preparatory choices as well as more complex estimators. Simplicity makes a rule easier to inspect, but does not make a retrospective selection process causal.
5. Keep invalid and uncertain inputs distinct
An invalid or unavailable input cannot establish a lower state merely because a comparison fails. Validate finiteness, availability, and freshness before applying the rule. A valid observation near a boundary is a different situation: its category may be defined but sensitive. A separate boundary flag can retain that information without pretending to quantify a probability. If the design allows abstention, declare the uncertainty band and how a joint label behaves when only one axis is unresolved. Keep this treatment separate from any later decision or action policy.
6. Audit a fictional two-feature rule
In the fictional table, both features use a threshold of zero and a strict greater-than rule. Positive values are upper; zero and negative values are lower; missing values are unavailable. Case C tests equality, and case D tests the difference between numeric precision and display rounding. The table is a set of hand-constructed specification cases, not observations from an economy or market. Passing these cases would establish consistency with this small rule, not statistical validity, useful regime boundaries, calibrated confidence, or a successful historical strategy.
7. Version changes instead of rewriting decisions
Changing an input definition, equality convention, threshold, or freshness policy changes the classifier. Assign a new version and distinguish recomputed history from previously recorded decisions. Useful checks include identical outputs for identical valid inputs, correct behavior on both sides of each boundary, and explicit handling of missing values. Compare versions on the same eligible information set to isolate rule changes from data revisions. Report disagreement counts with their denominator and inspect the affected cases. A version that produces fewer switches is different, but not automatically better for every research purpose.
Inspect the comparison
| Fictional case | Feature X | Feature Y | Result under strict > 0 |
|---|---|---|---|
| A | 0.2 | -0.1 | X upper; Y lower |
| B | -0.2 | 0.1 | X lower; Y upper |
| C | 0 | 0 | X lower; Y lower |
| D | 0.004 (displayed as 0.00) | -0.1 | X upper; Y lower |
| E | Missing | 0.1 | Joint category unavailable |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.