lift concept

Definition	Confidence divided by the consequent's support, so that lift one is the independence baseline. It fails at low support. Chapter 5.
Example	Confidence 0.8 for bread implies butter against a butter base rate of 0.4 is lift 2.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `lift`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 5.2.
Assumptions and scope	Confidence over the consequent’s support, the joint support over the product of the two supports. It is one under independence, symmetric in the two itemsets, and bounded by the reciprocal of the consequent’s support. It fails at low support. One transaction in N containing both items, and neither elsewhere, gives lift N, which is why the rules with the highest lift are the ones chapter 8’s multiple-comparison rule applies to.
Prior art	none recorded
Evidence	`lean/DataMiningAsObservation/Lift.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

Confidence over the base rate of the consequent.

Equation

Book equation 5.2.

\[\mathrm{lift}(X\to Y)=\frac{c(X\to Y)}{s(Y)}=\frac{s(X\cup Y)}{s(X)\,s(Y)}.\]

Conditions

Confidence over the consequent’s support, the joint support over the product of the two supports. It is one under independence, symmetric in the two itemsets, and bounded by the reciprocal of the consequent’s support.
It fails at low support. One transaction in N containing both items, and neither elsewhere, gives lift N, which is why the rules with the highest lift are the ones chapter 8’s multiple-comparison rule applies to.

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

Ledger

none

First stated

TSK chapter 5 on objective measures, as chapter 5 section 5.1 of Data Mining as Observation states it.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 5 section 5.1 to 5.3, 5.5	support, confidence, lift, the Apriori principle, FP-growth, closed and maximal itemsets, objective measures, Simpson’s paradox, cross-support	TSK 2e chapter 5

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Lift.lean, theorems lift_indep, lift_symm, lift_le_inv, lift_single, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 5.

Apriori principle; multiple comparisons; safe pruning; harness.

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.

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