# Data Mining - (Decision) Rule

### Table of Contents

## 1 - About

Some forms of predictive data mining generate rules that are conditions that imply a given outcome.

Rules are if-then-else expressions; they explain the decisions that lead to the prediction.

They are produced from a decision tree or association (such as association rule)

For example, a rule might specify that a person:

- who has a bachelor's degree (an attribute)
- and lives in a certain neighbourhood (an other attribute)

is likely to have an income greater than the regional average.

**ODM Basket Analysis rules where antecedent and consequent contain the product ID.**

## 2 - Articles Related

## 3 - Type

### 3.1 - Classification

A classification rule predicts value of a given attribute:

```
If outlook = sunny and humidity = high then play = no
```

### 3.2 - Association

A Association rule predicts value of arbitrary attribute (or combination)

```
If temperature = cool then humidity = normal
If humidity = normal and windy = false then play = yes
If outlook = sunny and play = no then humidity = high
If windy = false and play = no then outlook = sunny and humidity = high
```

## 4 - Set of Rules

rule is easy to interpret, but a complex set of rules probably isn’t.

A sequential cover algorithm for sets of rules with complex conditions. Sets of rules are hard to interpret.

## 5 - Algorithm

Strategies for Learning Each Rule:

- General-to-Specific:
- Start with an empty rule
- Add constraints to eliminate negative examples
- Stop when only positives are covered

- Specific-to-General
- Start with a rule that identifies a single random instance
- Remove constraints in order to cover more positives
- Stop when further generalization results in covering negatives

If more than one rule is triggered (Conflicts),

- choose the “most specific” rule
- Use domain knowledge to order rules by priority

### 5.1 - General-to-Specific

Learning Rules by Sequential Covering (src: Alvarez)

```
Initialize the ruleset R to the empty set
for each class C {
while D is nonempty {
Construct one rule r that correctly classifies
some instances in D that belong to class C
and does not incorrectly classify any non-C instances
# See below "Finding next rule for class C"
Add rule r to ruleset R
Remove from D all instances correctly classified by r
}
}
return the ruleset R
```

Sequential Covering: Finding next rule for class C

```
Initialize A as the set of all attributes over D
while r incorrectly classifies some non-C instances of D
{
write r as antecedent(r) => C
for each attribute-value pair (a=v),
where a belongs to A and v is a value of a,
compute the accuracy of the rule
antecedent(r) and (a=v) => C
let (a*=v*) be the attribute-value pair of
maximum accuracy over D; in case of a tie,
choose the pair that covers the greatest
number of instances of D
update r by adding (a*=v*) to its antecedent:
r = ( antecedent(r) and (a*=v*) ) => C
remove the attribute a* from the set A:
A = A - {a*}
}
```

## 6 - Properties

### 6.1 - Support

Rules have an associated support (What percentage of the population satisfies the rule?).

### 6.2 - Confidence

Confidence is the proportion of the occurrences of the antecedent that result in the consequent e.g. how many times do we get C when we have A and B {A, B} ⇒ C

### 6.3 - Lift

Lift indicates the strength of a rule over the random co-occurrence of the antecedent and the consequent