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RIPPER Fast Effective Rule Induction. Machine Learning 2003 Merlin Holzapfel & Martin Schmidt [email protected] [email protected]. Rule Sets - advantages. easy to understand usually better than decision Tree learners representable in first order logic > easy to implement in Prolog - PowerPoint PPT Presentation
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RIPPERFast Effective Rule Induction
Machine Learning 2003
Merlin Holzapfel & Martin Schmidt
Rule Sets - advantages
easy to understand usually better than decision Tree learners representable in first order logic
– > easy to implement in Prolog
prior knowledge can be added
Rule Sets - disadvantages
scale poorly with training set size problems with noisy data
– likely in real-world data
goal: – develop rule learner that is efficient on noisy data – competitive with C4.5 / C4.5rules
Problem with Overfitting
overfitting also handles noisy cases underfitting is too general
solution pruning:– reduced error pruning (REP)– post pruning– pre pruning
Post Pruning (C4.5)
overfit & simplify– construct tree that overfits– convert tree to rules– prune every rule separately– sort rules according accuracy– consider order when classifying
bottom - up
Pre pruning
some examples are ignored during concept generation
final concept does not classify all training data correctly
can be implemented in form of stopping criteria
Reduced Error Pruning
seperate and conquer– split data in training and validation set– construct overfitting tree– until pruning reduces accuracy
• evaluate impact on validation set
of pruning a rule• remove rule so it improves accuracy most
Time Complexity
REP has a time complexity of O(n4)– initial phase of overfitting alone has a
complexity of O(n²) alternative concept Grow:
– faster in benchmarks– time complexity still O(n4) with noisy data
Incremental Reduced Error Pruning - IREP
by Fürnkranz & Widmer (1994) competitive error rates faster than REP and Grow
How IREP Works
iterative application of REP random split of sets
bad split has negative influence
(but not as bad as with REP) immediately pruning after a rule is
grown (top-down approach)
no overfitting
Cohens IREP Implementation
build rules until new rule results in too large error rate– divide data (randomly) into growing set(2/3) and pruning
set(1/3)– grow rule from growing set– immediately prune rule
• Delete final sequence of conditions– delete condition that maximizes function v
until no deletion improves value of v
– add pruned rule to ruleset– delete every example covered by rule (p/n)
NP
nNppruneNegprunePosRulev
)(
),,(
Cohens IREP - Algorithm
IREP and Multiple Classes
order classes according to increasing prevalence
(C1,....,Ck)
– find rule set to separate C1 from other classes
IREP(PosData=C1,NegData=C2,...,Ck)
– remove all instances learned by rule set
– find rule set to separate C2 from C3,...,Ck
...
– Ck remains as default class
IREP and Missing Attributes
handle missing attributes:
– for all tests involving A• if attribute A of an instance
is missing test fails
Differences Cohen <> Original
pruning:final sequence <> single final condition
stopping condition:error rate 50% <> accuracy(rule) < accuracy(empty rule)
application:missing attributes, numerical variables, multiple classes
<>
two-class problems
Time Complexity
IREP: O(m log² m), m = number of examples(fixed number of classification noise)
37 Benchmark Problems
Generalization Performance
IREP performs worse on benchmark problems than C4.5rules
won-lost-tie ratio: 11-23-3
error ratio– 1.13 excluding mushroom– 1.52 including mushroom
C4.5rules of rateerror
IREP of rateerror
Improving IREP
three modifications:
– alternative metric in pruning phase
– new stopping heuristics for rule adding
– post pruning of whole rule set(non-incremental pruning)
the Rule-Value Metric
old metric not intuitiveR1: p1 = 2000, n1 = 1000
R2: p1 = 1000, n1 = 1
metric preferes R1 (fixed P,N)
leads to occasional failure to converge new metric (IREP*)
np
nppruneNegprunePosRulev
),,(*
Stopping Condition
50%-heuristics often stops too soon with moderate sized examples
sensitive to the ‘small disjunct problem‘ solution:
– after a rule is added, the total description length of rule set and missclassifications (DL=C+E)
– If DL is d bits larger then the smallest length so far stop (min(DL)+d<DLcurrent)
– d = 64 in Cohen‘s implementation MDL (Minimal Description Length) heuristics
IREP*
IREP* is IREP, improved by the new rule-value metric and the new stopping condition
28-8-1 against IREP 16-21-0 against C4.5rules
error ratio 1.06 (IREP 1.13)respectively 1.04 (1.52) including mushrooms
Rule Optimization
post prunes rules produced by IREP*– The rules are considered in turn– for each rule R, two alternatives are
constructed•Ri‘ new rule
•Ri‘‘ based on Ri
– final rule is chosen according to MDL
RIPPER
1. IREP* is used to obtain a rule set
2. rule optimization takes place
3. IREP* is used to cover remaining positive examples
Repeated Incremental Pruning to Produce Error Reduction
RIPPERk
apply steps 2 and 3 k times
RIPPER Performance
28-7-2 against IREP*
Error Rates
RIPPER obviously is competitive
Efficency of RIPPERk
modifications do not change complexity
Reasons for Efficiency
find model with IREP* and then improve– effiecient first model with right size– optimization takes linear time
C4.5 has expensive optimization improvement process – to large initial model
RIPPER is especially more efficient on
large noisy datasets
Conclusions
IREP is efficient rule learner for large noisy datasets but performs worse than C4.5
IREP improved to IREP* IREP* improved to RIPPER k iterated RIPPER is RIPPERk RIPPERk more efficient and performs
better than C4.5
References
Fast Effective Rule Induction
William W. Cohen [1995]
Incremental Reduced Error Pruning
J. Fürnkranz & G. Widmer [1994] Efficient Pruning Methods
William W. Cohen [1993]