Prerequisite: Rule-Based Classifier

**Learn-One-Rule: **

This method is used in the sequential learning algorithm for learning the rules. It returns a single rule that covers at least some examples (as shown in Fig 1). However, what makes it really powerful is its ability to create relations among the attributes given, hence covering a larger hypothesis space.

For example:IFMother(y, x)andFemale(y), THENDaughter(x, y).Here, any person can be associated with the variablesxandy

**Learn-One-Rule Algorithm**

The Learn-One-Rule algorithm follows a greedy searching paradigm where it searches for the rules with high accuracy but its coverage is very low. It classifies all the positive examples for a particular instance. It returns a single rule that covers some examples.

Learn-One-Rule(target_attribute, attributes, examples, k):Pos = positive examples Neg = negative examples best-hypothesis = the most general hypothesis candidate-hypothesis = {best-hypothesis} while candidate-hypothesis:constraints_list = all contraints in the form "//Generate the next more specific candidate-hypothesisattribute=value" new-candidate-hypothesis = all specializations of candidate- hypothesis by adding all-constraints remove all duplicates/inconsistent hypothesis from new-candidate-hypothesis.//Update best-hypothesisbest_hypothesis = argmax_{(h∈CHs) }Performance(h,examples,target_attribute)//Update candidate-hypothesiscandidate-hypothesis = the k best from new-candidate-hypothesis according to Performance. prediction = most frequent value of target_attribute from examples that match best-hypothesis IF best_hypothesis: return prediction

It involves a PERFORMANCE method that calculates the performance of each candidate hypothesis. (i.e. how well the hypothesis matches the given set of examples in the training data.

Performance(NewRule,h):h-examples = the set of rules that match h return (h-examples)

It starts with the most general rule precondition, then greedily adds the variable that most improves performance measured over the training examples.

**Learn-One-Rule Example**

Let us understand the working of the algorithm using an example:

Day | Weather | Temp | Wind | Rain | PlayBadminton |
---|---|---|---|---|---|

D1 | Sunny | Hot | Weak | Heavy | No |

D2 | Sunny | Hot | Strong | Heavy | No |

D3 | Overcast | Hot | Weak | Heavy | No |

D4 | Snowy | Cold | Weak | Light | Yes |

D5 | Snowy | Cold | Weak | Light | Yes |

D6 | Snowy | Cold | Strong | Light | Yes |

D7 | Overcast | Mild | Strong | Heavy | No |

D8 | Sunny | Hot | Weak | Light | Yes |

Step 1 -best_hypothesis = IF h THEN PlayBadminton(x) = YesStep 2 -candidate-hypothesis = {best-hypothesis}Step 3 -constraints_list = {Weather(x)=Sunny, Temp(x)=Hot, Wind(x)=Weak, ......}Step 4 -new-candidate-hypothesis = {IF Weather=Sunny THEN PlayBadminton=YES, IF Weather=Overcast THEN PlayBadminton=YES, ...}Step 5 -best-hypothesis = IF Weather=Sunny THEN PlayBadminton=YESStep 6 -candidate-hypothesis = {IF Weather=Sunny THEN PlayBadminton=YES, IF Weather=Sunny THEN PlayBadminton=YES...}Step 7 -Go to Step 2 and keep doing it till the best-hypothesis is obtained.

You can refer to Fig 1. for a better understanding of how the best-hypothesis is obtained.

[Step 5 & 6]

Sequential Learning Algorithm uses this algorithm, improving on it and increasing the coverage of the hypothesis space. It can be modified to accept an argument that specifies the target value of interest.