The big idea: Association rule learning finds things that occur together — unsupervised, with no labels and nothing being predicted.
Written as {bread, butter} → {jam}: baskets containing the first tend to contain the second.
Where it is used
- Market basket analysis — what is bought together, and so what to place together
- Recommendations — people who took this also took that
- Medical — symptoms and conditions that co-occur
- Web — pages visited in the same session
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| Measure | Question it answers | Formula in words |
|---|---|---|
| Support | How common is this combination? | Baskets with both ÷ all baskets |
| Confidence | When A is bought, how often is B? | Baskets with both ÷ baskets with A |
| Lift | Is this more than chance? | Confidence ÷ how often B occurs anyway |
Lift is the one that matters: Lift > 1 — they occur together more than chance would give. A real association.
Lift = 1 — independent. The rule tells you nothing.
Lift < 1 — they occur together less than chance. Buying one makes the other less likely.
High confidence can still be worthless: "Customers who buy fish also buy bags" might have 80% confidence — but if 90% of all customers buy bags, the lift is 0.89 and fish buyers are actually less likely than average.
Confidence alone rewards whatever is popular. Always check lift.
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It is not causation
- The rule says they co-occur, nothing more
- Nappies and beer is the famous example — neither causes the other
- A third factor usually explains it
Direction matters
- A → B is not the same rule as B → A
- Support is the same; confidence differs
- Everyone who buys caviar buys bread; almost nobody who buys bread buys caviar
Volume is the problem
- A few thousand products give millions of possible rules
- Most are coincidences in the data
- Minimum support and lift thresholds exist to cut that down
Say which measure you used: An answer that computes confidence and stops is half an answer. Compute it, then ask whether lift beats 1 — that is what separates a finding from a restatement of what was already popular.
Interpreting a rule: crime analysis
The data
200 records of city areas per month: 50 had vandalism, 80 had theft, 40 had both.
Support of {vandalism, theft}
40 ÷ 200 = 0.20: both happen in a fifth of records.
Confidence of {vandalism} → {theft}
40 ÷ 50 = 0.80: where there is vandalism, theft follows 80% of the time.
Lift
0.80 ÷ (80 ÷ 200) = 2.0: twice as likely as chance, so police can plan patrols for theft where vandalism rises (predictive policing and resource allocation).
Lift above 1: plan for both together, without claiming one causes the other.
How this is tested — you must compute the measures from a small table and interpret lift honestly. It comes up two ways:
Paper 1 Section A
- Describe association rule learning, 3-4 marks
- Calculate support or confidence
- State what a rule means
Paper 1 Section B — case study
- Judge whether a rule is useful
- Explain why confidence alone misleads
The classic trap: Reading a rule as cause. "Buying nappies causes beer purchases" is not what {nappies} → {beer} says — it says only that they appear in the same baskets more often than chance.
Of 1,000 baskets, 200 contain coffee, 400 contain milk, and 150 contain both. Determine the support, confidence and lift of {coffee} → {milk}, and state whether the rule is useful.
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