aggregation concept

Definition	Combining rows or groups into one number. An average lies between its members, and an aggregate over strata can pass a bar that one stratum fails and can reverse the sign every group shows. Chapter 2 section 2.7 and chapter 10 section 10.4. Also aggregat.
Example	Strata scoring 0.95, 0.93, 0.97, and 0.66 average 0.878 and pass a bar of 0.85, while the minimum, 0.66, fails it.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `aggregation`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 10.7.
Assumptions and scope	Combining rows or groups into one number, a mean, a sum, or a rate. An average lies between the smallest and largest member, a weighted aggregate over strata can pass a bar while one stratum fails it, and an aggregate can reverse the sign every group shows. Aggregate recall barely moves while anti-hubs fail, the aggregate staleness rate describes neither reader, and the report takes the worst group and counts the groups too thin to score.
Prior art	none recorded
Evidence	`turboquant-pro/docs/HUBNESS_PRIMER.md:86-131`, `lean/DataMiningAsObservation/Ensemble.lean`, `lean/DataMiningAsObservation/Simpson.lean`, `lean/DataMiningAsObservation/RecallAtK.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

An aggregate over strata passes a bar that one stratum fails.

Equation

Book equation 10.7.

\[\text{verdict}=\min_{i:\ n_i\ge n_{\min},\ |Q_i|\ge q_{\min}}\ \mathrm{score}_i,\qquad \text{ABSTAIN otherwise}.\]

Conditions

Combining rows or groups into one number, a mean, a sum, or a rate. An average lies between the smallest and largest member, a weighted aggregate over strata can pass a bar while one stratum fails it, and an aggregate can reverse the sign every group shows.
Aggregate recall barely moves while anti-hubs fail, the aggregate staleness rate describes neither reader, and the report takes the worst group and counts the groups too thin to score.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 2 section 2.7 and chapter 10 section 10.4 of Data Mining as Observation, with the aggregate staleness rate of chapter 13 section 13.3.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 2 section 2.7	the aggregate staleness rate describing neither reader	chapter 13 of this book, section 13.3
chapter 10 section 10.2	anti-hubs as where compressed indexes fail first, aggregate recall barely moves	`turboquant-pro/docs/HUBNESS_PRIMER.md:86-131`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Ensemble.lean, theorems average_between, sq_average_le, average_const, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/Simpson.lean, theorems pooled_eq_weighted, reversal, no_reversal_of_equal_sizes, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/RecallAtK.lean, theorems recallAtK_mem_unit, recallAtK_eq_one_iff, aggregate_le_of_failing, aggregate_example, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 2, 5, 8, 10, 11, 12, 13.

min-over-strata; Simpson's paradox; stratification; anti-hub recall; sampling.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

← accuracyalignment →