1. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Thursday, 12 April 2007 William H. Hsu Department of Computing and Information Sciences, KSU http://www.cis.ksu.edu/Spring-2007/Courses/CIS732 Readings: Chapter 10, Mitchell Association Rule references Classification Rule Learning (concluded) and Association Rule Learning Lecture 34 of 42

2. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Lecture Outline Readings: Sections 10.1-10.5, Mitchell Suggested Exercises: 10.1, 10.2 Mitchell Sequential Covering Algorithms –Learning single rules by search Beam search Alternative covering methods –Learning rule sets First-Order Rules –Learning single first-order rules –FOIL: learning first-order rule sets

3. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Lecture Outline Readings: Sections 10.6-10.8, Mitchell; Section 21.4, Russell and Norvig Suggested Exercises: 10.5, Mitchell Induction as Inverse of Deduction –Problem of inductive learning revisited –Operators for automated deductive inference Resolution rule for deduction First-order predicate calculus (FOPC) and resolution theorem proving –Inverting resolution Propositional case First-order case Inductive Logic Programming (ILP) –Cigol –Progol

4. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Sequential Covering Algorithm (CN2): Review Algorithm Sequential-Covering (Target-Attribute, Attributes, D, Threshold) –Learned-Rules  {} –New-Rule  Learn-One-Rule (Target-Attribute, Attributes, D) –WHILE Performance (Rule, Examples) > Threshold DO Learned-Rules += New-Rule// add new rule to set D.Remove-Covered-By (New-Rule)// remove examples covered by New-Rule New-Rule  Learn-One-Rule (Target-Attribute, Attributes, D) –Sort-By-Performance (Learned-Rules, Target-Attribute, D) –RETURN Learned-Rules What Does Sequential-Covering Do? –Learns one rule, New-Rule –Takes out every example in D to which New-Rule applies (every covered example)

5. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition IF {Humidity = Normal} THEN Play-Tennis = Yes IF {Wind = Strong} THEN Play-Tennis = No IF {Wind = Light} THEN Play-Tennis = Yes IF {Humidity = High} THEN Play-Tennis = No … Learn-One-Rule via (Beam) Search: Review IF {} THEN Play-Tennis = Yes … IF {Humidity = Normal, Outlook = Sunny} THEN Play-Tennis = Yes IF {Humidity = Normal, Wind = Strong} THEN Play-Tennis = Yes IF {Humidity = Normal, Wind = Light} THEN Play-Tennis = Yes IF {Humidity = Normal, Outlook = Rain} THEN Play-Tennis = Yes

6. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Learn-One-Rule Algorithm: Review Algorithm Learn-One-Rule (Target-Attribute, Attributes, D) –New-Rule  most general rule possible –New-Rule-Neg  Neg –WHILE NOT New-Rule-Neg.Empty() DO// specialize New-Rule 1. Candidate-Literals  Generate-Candidates()// NB: rank by Performance() 2. Best-Literal  argmax L  Candidate-Literals Performance (Specialize-Rule (New- Rule, L), Target-Attribute, D)// all possible new constraints 3. New-Rule.Add-Precondition (Best-Literal)// add the best one 4. New-Rule-Neg  New-Rule-Neg.Filter-By (New-Rule) –RETURN (New-Rule)

7. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Learn-One-Rule: Subtle Issues How Does Learn-One-Rule Implement Search? –Effective approach: Learn-One-Rule organizes H in same general fashion as ID3 –Difference Follows only most promising branch in tree at each step Only one attribute-value pair (versus splitting on all possible values) –General to specific search (depicted in figure) Problem: greedy depth-first search susceptible to local optima Solution approach: beam search (rank by performance, always expand k best) Easily generalizes to multi-valued target functions (how?) Designing Evaluation Function to Guide Search –Performance (Rule, Target-Attribute, D) –Possible choices Entropy (i.e., information gain) as for ID3 Sample accuracy (n c / n  correct rule predictions / total predictions) m estimate: (n c + mp) / (n + m) where m  weight, p  prior of rule RHS

8. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Variants of Rule Learning Programs Sequential or Simultaneous Covering of Data? –Sequential: isolate components of hypothesis (e.g., search for one rule at a time) –Simultaneous: whole hypothesis at once (e.g., search for whole tree at a time) General-to-Specific or Specific-to-General? –General-to-specific: add preconditions, Find-G –Specific-to-general: drop preconditions, Find-S Generate-and-Test or Example-Driven? –Generate-and-test: search through syntactically legal hypotheses –Example-driven: Find-S, Candidate-Elimination, Cigol (next time) Post-Pruning of Rules? –Recall (Lecture 8-9 of 42): very popular overfitting recovery method What Statistical Evaluation Method? –Entropy –Sample accuracy (aka relative frequency) –m-estimate of accuracy

9. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition First-Order Rules What Are First-Order Rules? –Well-formed formulas (WFFs) of first-order predicate calculus (FOPC) –Sentences of first-order logic (FOL) –Example (recursive) Ancestor (x, y)  Parent (x, y). Ancestor (x, y)  Parent (x, z)  Ancestor (z, y). Components of FOPC Formulas: Quick Intro to Terminology –Constants: e.g., John, Kansas, 42 –Variables: e.g., Name, State, x –Predicates: e.g., Father-Of, Greater-Than –Functions: e.g., age, cosine –Term: constant, variable, or function(term) –Literals (atoms): Predicate(term) or negation (e.g.,  Greater-Than (age(John), 42)) –Clause: disjunction of literals with implicit universal quantification –Horn clause: at most one positive literal (H   L 1   L 2  …   L n )

10. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Learning First-Order Rules Why Do That? –Can learn sets of rules such as Ancestor (x, y)  Parent (x, y). Ancestor (x, y)  Parent (x, z)  Ancestor (z, y). –General-purpose (Turing-complete) programming language PROLOG Programs are such sets of rules (Horn clauses) Inductive logic programming (next time): kind of program synthesis Caveat –Arbitrary inference using first-order rules is semi-decidable Recursive enumerable but not recursive (reduction to halting problem L H ) Compare: resolution theorem-proving; arbitrary queries in Prolog –Generally, may have to restrict power Inferential completeness Expressive power of Horn clauses Learning part

11. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition First-Order Rule: Example Prolog (FOPC) Rule for Classifying Web Pages –[Slattery, 1997] –Course (A)  Has-Word (A, “instructor”), not Has-Word (A, “good”), Link-From (A, B), Has-Word (B, “assign”), not Link-From (B, C). –Train: 31/31, test: 31/34 How Are Such Rules Used? –Implement search-based (inferential) programs –References Chapters 1-10, Russell and Norvig Online resources at http://archive.comlab.ox.ac.uk/logic-prog.html

12. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition First-Order Inductive Learning (FOIL): Algorithm Algorithm FOIL (Target-Predicate, Predicates, D) –Pos  D.Filter-By(Target-Predicate)// examples for which it is true –Neg  D.Filter-By(Not (Target-Predicate))// examples for which it is false –WHILE NOT Pos.Empty() DO// learn new rule Learn-One-First-Order-Rule (Target-Predicate, Predicates, D) Learned-Rules.Add-Rule (New-Rule) Pos.Remove-Covered-By (New-Rule) –RETURN (Learned-Rules) Algorithm Learn-One-First-Order-Rule (Target-Predicate, Predicate, D) –New-Rule  the rule that predicts Target-Predicate with no preconditions –New-Rule-Neg  Neg –WHILE NOT New-Rule-Neg.Empty() DO// specialize New-Rule 1. Candidate-Literals  Generate-Candidates()// based on Predicates 2. Best-Literal  argmax L  Candidate-Literals FOIL-Gain (L, New-Rule, Target- Predicate, D)// all possible new literals 3. New-Rule.Add-Precondition (Best-Literal)// add the best one 4. New-Rule-Neg  New-Rule-Neg,Filter-By (New-Rule) –RETURN (New-Rule)

13. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Specializing Rules in FOIL Learning Rule: P(x 1, x 2, …, x k )  L 1  L 2  …  L n. Candidate Specializations –Add new literal to get more specific Horn clause –Form of literal Q(v 1, v 2, …, v r ), where at least one of the v i in the created literal must already exist as a variable in the rule Equal(x j, x k ), where x j and x k are variables already present in the rule The negation of either of the above forms of literals

14. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Information Gain in FOIL Function FOIL-Gain (L, R, Target-Predicate, D) Where –L  candidate predicate to add to rule R –p 0  number of positive bindings of R –n 0  number of negative bindings of R –p 1  number of positive bindings of R + L –n 1  number of negative bindings of R + L –t  number of positive bindings of R also covered by R + L Note –- lg (p 0 / p 0 + n 0 ) is optimal number of bits to indicate the class of a positive binding covered by R –Compare: entropy (information gain) measure in ID3

15. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition FOIL: Learning Recursive Rule Sets Recursive Rules –So far: ignored possibility of recursive WFFs New literals added to rule body could refer to target predicate itself i.e., predicate occurs in rule head –Example Ancestor (x, y)  Parent (x, z)  Ancestor (z, y). Rule: IF Parent (x, z)  Ancestor (z, y) THEN Ancestor (x, y) Learning Recursive Rules from Relations –Given: appropriate set of training examples –Can learn using FOIL-based search Requirement: Ancestor  Predicates (symbol is member of candidate set) Recursive rules still have to outscore competing candidates at FOIL-Gain –NB: how to ensure termination? (well-founded ordering, i.e., no infinite recursion) –[Quinlan, 1990; Cameron-Jones and Quinlan, 1993]

16. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition FOIL: Summary Extends Sequential-Covering Algorithm –Handles case of learning first-order rules similar to Horn clauses –Result: more powerful rules for performance element (automated reasoning) General-to-Specific Search –Adds literals (predicates and negations over functions, variables, constants) –Can learn sets of recursive rules Caveat: might learn infinitely recursive rule sets Has been shown to successfully induce recursive rules in some cases Overfitting –If no noise, might keep adding new literals until rule covers no negative examples –Solution approach: tradeoff (heuristic evaluation function on rules) Accuracy, coverage, complexity FOIL-Gain: an MDL function Overfitting recovery in FOIL: post-pruning

17. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Apriori: A Generate-and-Test Approach Any subset of a frequent itemset must be frequent –if {toner, paper, DVD-Rs} is frequent, so is {toner, paper} –Every transaction having {toner, paper, DVD-Rs} also contains {toner, paper} Apriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! Method: –generate length (k+1) candidate itemsets from length k frequent itemsets, and –test the candidates against DB The performance studies show its efficiency and scalability Agrawal & Srikant 1994, Mannila, et al. 1994

18. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition The Apriori Algorithm—An Example Database TDB 1 st scan C1C1 L1L1 L2L2 C2C2 C2C2 2 nd scan C3C3 L3L3 3 rd scan TidItems 10A, C, D 20B, C, E 30A, B, C, E 40B, E Itemsetsup {A}2 {B}3 {C}3 {D}1 {E}3 Itemsetsup {A}2 {B}3 {C}3 {E}3 Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} Itemsetsup {A, B}1 {A, C}2 {A, E}1 {B, C}2 {B, E}3 {C, E}2 Itemsetsup {A, C}2 {B, C}2 {B, E}3 {C, E}2 Itemset {B, C, E} Itemsetsup {B, C, E} 2

19. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition The Apriori Algorithm Pseudo-code: C k : Candidate itemset of size k L k : frequent itemset of size k L 1 = {frequent items}; for (k = 1; L k !=  ; k++) do begin C k+1 = candidates generated from L k ; for each transaction t in database do increment the count of all candidates in C k+1 that are contained in t L k+1 = candidates in C k+1 with min_support end return  k L k ;

20. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Important Details of Apriori How to generate candidates? –Step 1: self-joining L k –Step 2: pruning How to count supports of candidates? Example of Candidate-generation –L 3 ={abc, abd, acd, ace, bcd} –Self-joining: L 3 *L 3 abcd from abc and abd acde from acd and ace –Pruning: acde is removed because ade is not in L 3 –C 4 ={abcd}

21. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition How to Generate Candidates? Suppose the items in L k-1 are listed in an order Step 1: self-joining L k-1 insert into C k select p.item 1, p.item 2, …, p.item k-1, q.item k-1 from L k-1 p, L k-1 q where p.item 1 =q.item 1, …, p.item k-2 =q.item k-2, p.item k-1 < q.item k-1 Step 2: pruning forall itemsets c in C k do forall (k-1)-subsets s of c do if (s is not in L k-1 ) then delete c from C k

22. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Challenges of Frequent Pattern Mining Challenges –Multiple scans of transaction database –Huge number of candidates –Tedious workload of support counting for candidates Improving Apriori: general ideas –Reduce passes of transaction database scans –Shrink number of candidates –Facilitate support counting of candidates

23. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Partition: Scan Database Only Twice Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB –Scan 1: partition database and find local frequent patterns –Scan 2: consolidate global frequent patterns A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association in large databases. In VLDB’95

24. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Partition Patterns and Databases Frequent patterns can be partitioned into subsets according to f- list –F-list=f-c-a-b-m-p –Patterns containing p –Patterns having m but no p –… –Patterns having c but no a nor b, m, p –Pattern f Completeness and non-redundency

25. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Grow long patterns from short ones using local frequent items –“abc” is a frequent pattern –Get all transactions having “abc”: DB|abc –“d” is a local frequent item in DB|abc  abcd is a frequent pattern FP-Growth Algorithm

26. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Benefits of the FP-tree Structure Completeness –Preserve complete information for frequent pattern mining –Never break a long pattern of any transaction Compactness –Reduce irrelevant info—infrequent items are gone –Items in frequency descending order: the more frequently occurring, the more likely to be shared –Never be larger than the original database (not count node-links and the count field)

27. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Terminology Induction and Deduction –Induction: finding h such that   D. (B  D  x i ) |  f(x i ) –Inductive learning: B  background knowledge (inductive bias, etc.) –Developing inverse deduction operators Deduction: finding entailed logical statements F(A, B) = C where A  B |  C Inverse deduction: finding hypotheses O(B, D) = h where   D. (B  D  x i ) |  f(x i ) –Resolution rule: deductive inference rule (P  L,  L  R |  P  R) Propositional logic: boolean terms, connectives ( , , ,  ) First-order predicate calculus (FOPC): well-formed formulas (WFFs), aka clauses (defined over literals, connectives, implicit quantifiers) –Inverse entailment: inverse of resolution operator Inductive Logic Programming (ILP) –Cigol: ILP algorithm that uses inverse entailment –Progol: sequential covering (general-to-specific search) algorithm for ILP

28. Kansas State University Department of Computing and Information Sciences CIS 732: Machine Learning and Pattern Recognition Summary Points Induction as Inverse of Deduction –Problem of induction revisited Definition of induction Inductive learning as specific case Role of induction, deduction in automated reasoning –Operators for automated deductive inference Resolution rule (and operator) for deduction First-order predicate calculus (FOPC) and resolution theorem proving –Inverting resolution Propositional case First-order case (inverse entailment operator) Inductive Logic Programming (ILP) –Cigol: inverse entailment (very susceptible to combinatorial explosion) –Progol: sequential covering, general-to-specific search using inverse entailment Next Week: Knowledge Discovery in Databases (KDD), Final Review