Terminology: thresholded vs probabilistic regression

This page maps two terms used for the same CE regression mode.

In user-facing docs and APIs, use probabilistic regression. In architecture and implementation discussions, thresholded regression may be used to describe the threshold mechanism.

Both terms refer to regression with a non-None threshold query that returns calibrated event probabilities with interval bounds.

For full guarantees, assumptions, explicit non-guarantees, and feature-level interval limits, use Calibrated interval semantics.

Use in docs

  • User-facing guides, quickstarts, notebooks, and API docs: probabilistic regression

  • ADRs and implementation details that discuss mechanism: thresholded regression

  • If both terms appear on one page, state once that they map to the same mode

Section 1: Definition analysis

1.1 What does “probabilistic regression” mean?

Definition source: docs/foundations/concepts/probabilistic_regression.md.

It refers to regression predictions queried as probability events by threshold, for example P(y <= t) or interval events. The output is a calibrated event probability plus interval bounds.

User-level API pattern:

probabilities, probability_interval = explainer.predict_proba(
    x_test[:1],
    threshold=150,
    uq_interval=True,
)

1.2 What does “thresholded regression” mean?

Definition source: docs/improvement/adrs/ADR-021-calibrated-interval-semantics.md.

It is the same regression mode described from the implementation angle:

  • Regression output is queried through threshold events

  • CPS provides event scoring

  • Venn-Abers calibrates event probabilities

Implementation path example from IntervalRegressor.predict_probability():

# Converts regression predictions to probabilities by thresholding
proba = self.split["cps"].predict(y_hat=..., y=y_threshold, ...)
# Then calibrates with Venn-Abers
va = VennAbers(None, (self.ce.y_cal[cal_va] <= y_threshold).astype(int), ...)

1.3 Evidence of equivalence

  • ADR-021 section “Thresholded regression: CPS probabilities calibrated by Venn-Abers” explicitly describes the same path as the probabilistic regression flow.

  • Runtime API signal is identical: this mode is selected by providing threshold.

1.4 Why two terms exist

Aspect

“Thresholded regression”

“Probabilistic regression”

Emphasis

Mechanism (threshold operation)

Output (calibrated probabilities)

Primary audience

Architecture and implementation contributors

Practitioners and API users

Typical context

ADRs, plugin internals, design notes

Quickstarts, concept guides, notebooks

Section 2: Terminology inventory

2.1 Representative “probabilistic regression” usage

File

Context

README.md

Feature and quickstart routing

docs/get-started/index.md

Navigation and mode routing

docs/get-started/quickstart_regression.md

Task workflow

docs/foundations/concepts/probabilistic_regression.md

Dedicated concept page

notebooks/core_demos/demo_probabilistic_regression.ipynb

End-to-end example

2.2 Representative “thresholded regression” usage

File

Context

docs/improvement/adrs/ADR-021-calibrated-interval-semantics.md

Architecture semantics

docs/improvement/adrs/ADR-013-interval-calibrator-plugin-strategy.md

Plugin strategy terminology

docs/improvement/legacy_user_api_contract.md

Historical contract references

docs/foundations/governance/optional_telemetry.md

Technical telemetry context

2.3 Code usage patterns

  • Public call sites use threshold= as the mode switch.

  • Internal APIs include both threshold and y_threshold names.

  • Explanation containers expose probabilistic-regression state through is_probabilistic_regression.

Section 3: Context-specific usage

3.1 User-facing documentation

Preferred term: probabilistic regression.

Reason: it communicates task intent and expected output without requiring implementation knowledge.

3.2 Technical architecture and implementation

Preferred term: thresholded regression when discussing mechanics.

Reason: it makes the threshold-event conversion explicit for contributors and plugin authors.

3.3 Evaluation and benchmarking

Benchmark materials often use thresholded regression to separate this mode from percentile regression.

Section 4: Historical issues and current state

4.1 Historical issue: missing explicit mapping

Earlier materials mixed terms without a clear mapping statement.

Current state: ADR-021 now includes explicit terminology guidance, and this page serves as the Tier 3 terminology reference route.

4.2 Historical issue: mixed naming in tests and comments

Earlier test docstrings and comments mixed the terms without context labels.

Current state: core user-facing naming is probabilistic regression; technical notes may still use thresholded regression when describing mechanism.

4.3 Ongoing risk

Terminology drift can return when new docs are added quickly.

Control: keep this mapping in Tier 3 reference pages and keep Tier 1 and Tier 2 pages mode-specific with short semantics routing to Calibrated interval semantics.