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a/AI & Data Mining/Week 5/Lecture 9 - PRISM.md b/AI & Data Mining/Week 5/Lecture 9 - PRISM.md new file mode 100644 index 0000000..2ac41ba --- /dev/null +++ b/AI & Data Mining/Week 5/Lecture 9 - PRISM.md @@ -0,0 +1,95 @@ +# Covering Algorithms + +- Each class in turn; find set of rules covering all examples +- At each stage, rule is identified that covers some examples +- Example is covered if satisfying conditions in the antecedent (LHS) of the rule +- Consider dataset with 2 predicting numeric attributes, and two class values. +- ![](Pasted%20image%2020241017130933.png) + +# PRISM: Simple Covering Algorithm + +- Generates rule by adding tests that maximise probability of desired class +- Similar to situation in decision trees; problem of selecting attribute to split on +- Each new test reduces rules coverage +- Rule becomes more specific as tests are added +- Search strategy is general-to-specific +- ![](Pasted%20image%2020241017131053.png) + +## Selecting a Test + +Goal: Maximise probability of desired class +- $t$ = total number of examples covered by rule +- $p$ = number of positive examples of the class covered by rule +- $t - p$ = number of errors made by rule +- => Select test that maximises ratio $p/t$ +Stop Condition: $t-p=0$ +- $p = t$, $p/t=1$ +- Or, set of examples cannot be split further. + +## Example: Contact Lenses Dataset | Class = Hard + +### Selecting 1st Test of 1st Rule + +- Rule to Seek: If ? { then recommendation = Hard } +![](Pasted%20image%2020241017131525.png) + +#### Modified Rule and Coverage + +- Rule with best test added: If astigmatism = Yes { then recommendation = Hard } +![](Pasted%20image%2020241017131740.png) + +### Selecting 2nd Test of 1st Rule + +- If astigmatism = Yes and ? { then recommendation = Hard } + +![](Pasted%20image%2020241017131912.png) + +#### Modified Rule and its Coverage + +- Rule with best test added: If astigmatism = Yes and tear rate = Normal { then recommendation = Hard } +![](Pasted%20image%2020241017132019.png) + +### Selecting 3rd Test of 1st Rule + +- If astigmatism = Yes and tear rate = Normal and ? { then recommendation = Hard } +![](Pasted%20image%2020241017132059.png) +- PRISM will use test with highest sample size, therefore using Myope. + +### 1st Rule for Class = Hard + +- Final Rule: +If astigmatism = Yes + and tear rate = Normal + and spectacle prescription = Myope + then recommendation = Hard + +$p/t = 3/3 = 1$ + +# Pseudo-code for PRISM + +For each class C + Init E to set of training examples + While E contains examples in class C + Create rule R with empty LHS predicting class C + Until p/t=1, do + For each attribute A not mentioned in R, and each value v + Consider adding condition A=v to LHS of R + Select A and v to maximise p/t + Break Ties by choosing largest sample + Add A=v to R + Remove examples covered by R from E + +# Separate and Conquer + +- PRISM with outer loop removed generates list of rules for one class +- PRISM with outer loop removed is separate and conquer algorithm + - Identify useful rule + - Separate examples covered + - Conquer remaining examples + +# Rule Execution + +- Default Rule + - If no rules cover example, prediction is the majority class (most frequent in training data) +- Conflict Resolution Strategy + - If more than one rule covers an example, select predicted class with highest recurrance in training data diff --git a/Client Server Systems/PHPStorm Repo b/Client Server Systems/PHPStorm Repo index 9b6cf0b..2238305 160000 --- a/Client Server Systems/PHPStorm Repo +++ b/Client Server Systems/PHPStorm Repo @@ -1 +1 @@ -Subproject commit 9b6cf0badd74c750b1a3afecd3703e6297cb23f9 +Subproject commit 2238305d6545c6fb92f00f8f24f72e8c1c1d7cbb diff --git a/Pasted image 20241017130933.png b/Pasted image 20241017130933.png new file mode 100644 index 0000000000000000000000000000000000000000..7d961deb7d56c89a2edb80805404789b434b095f GIT binary patch literal 72618 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