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Machine Learning and Association rules Petr Berka, Jan Rauch University of Economics, Prague {berka|rauch}@vse.cz Tutorial Outline Statistics, machine learning and data mining basic concepts, similarities and differences (P. Berka)

  1. Decision trees (search)  top-down (TDIDT)  single, heuristic  ID3, C4.5 (Quinlan), CART (Breiman a kol.)  parallel heuristic  Option trees (Buntine), Random forrest (Breiman)  random  parallel  using genetic programming  bottom-up additional technique during tree pruning Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 31 31

  2. Decision rules – set covering algorithms set covering algorithm 1. create a rule that covers some examples of one class and does not cover any examples of other classes 2. remove covered examples from training data 3. if there are some examples not covered by any rule, go to step 1 each training example covered by single rule = straightforward use during classification Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 32 32

  3. Decision rules in the attribute space IF DIASThigh) THEN risk(yes) IF CHLST(high) THEN risk(yes) IF DIAST(low) CHLST(low) THEN risk(no) Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 33 33

  4. Decision rules (search)  top-down  parallel heuristic  CN2 (Clark, Niblett), CN4 (Bruha) IF DIAST(low) THEN  bottom-up  single heuristic  Find-S (Mitchell)  parallel heuristic IF DIAST(low)  AQ (Michalski) AND CHLST(low) THEN  random  parallel  GA- CN4 (Králík, Bruha) Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 34 34

  5. Decision rules – compositional algorithms (search) KEX algorithm 1 add empty rule to the rule set KB 2 repeat 2 .1 find by rule specialization a rule Ant C that fulfils the user given criteria on length and validity, 2 .2 if this rule significantly improves the set of rules KB build so far then add the rule to KB each training example can be covered by more rules = these rules contribute to the final decision during classification Tutorial @ COMPSTAT 2010 35

  6. KEX algorithm – more details Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 36 36

  7. Association rules IF smoking(no) diast(low) THEN chlst(low) SUC SUC ANT 257 43 300 ANT 66 1036 1102 323 1079 1402  support a/(a+b+c+d) = 0.18  confidence a/(a+b) = 0.86 Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 37 37

  8. Association rule (generating as top-down search) breadth-first depth-first heuristic Apriori (Agrawal), KAD (Ivánek, LISp-Miner (Rauch) Stejskal) combination combination combination . . . 1n 5a 4a 1n 2n 1n 4n 1n 2n 3m 3m 5a 1n 2n 3m 4a 3z 5n 1n 2n 3m 4a 5a 4a 1n 2n 1n 2n 3m 4a 5n 4n 1n 2s 1n 2n 3m 4n 1v 1n 2v 1n 2n 3m 4n 5a 1n 4a 1n 3m 1n 2n 3m 4n 5n 4n 5a 1n 3z 1n 2n 3m 5a 1v 5a . . . 1n 2n 3m 5n 2v Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 38 38

  9. Association rules algorithm apriori algorithm 1. set k=1 and add all items that reach minsup into L 2. repeat 1. increase k 2. consider an itemset C of length k 3. if all subsets of length k-1 of the itemset C are in L then if C reaches minsup then add C into L Tutorial @ COMPSTAT 2010 39

  10. apriori – more details Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 40 40

  11. Neural networks – single neuron m ' 1 for y w x w i i 0 i 1 m ' 0 for y w x w 0 i i i 1 Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 41 41

  12. Neural networks -multilayer perceptron Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 42 42

  13. Backpropagation algorithm = approximation Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 43 43

  14. Genetic algorithms = parallel random search Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 44 44

  15. Genetic algorithms  Genetic operations  Selection  Cross-over  Mutation Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 45 45

  16. Bayesian methods  Naive bayesian classifier (approximation) K P ( E | H ) P ( H ) k P ( H | E ,..., E ) k 1  1 K P ( E )  Bayesian network (search, approximace) n P ( u ,..., u ) P ( u | rodiče ( u )) 1 n i i ii 1 Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 46 46

  17. Naive bayesian classifier  Computing the probabilities P(risk=yes) = 0.71 P(risk=no) = 0.19 P(smoking=yes)|risk=yes) = 0.81 P(smoking=no)|risk=no) = 0.19 . . .  Classification k P(E k |H i ) P(H i ) Class H i with highest value of Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 47 47

  18. Nearest-neighbor methods Algorithm k-NN Learning Add examples [ x i , y i ] into case base Classification 1. For a new example x 1.1. Find x 1 , x 2 , … x K K nearest neighbors 1.2. assign y = ŷ‘ y‗ is the majority class of x 1 , … x K , Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 48 48

  19. Nearest-neighbors in the attribute space  Using examples  Using centroids Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 49 49

  20. Nearest-neighbor methods  Selecting instances to be added  no search  IB1 (Aha)  simple heuristic top-down search  IB2, IB3 (Aha)  clustering (identifying centroids)  simple heuristic top-down search  top-down (divisive)  bottom-up (aglomerative)  approximation  K-NN (given number of clusters) Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 50 50

  21. Further readings  T. Mitchell: Machine Learning. McGraw-Hill, 1997  J. Han, M. Kerber: Data Mining, Concepts and Techniques. Morgan Kaufmann, 2001  I. Witten, E. Frank: Data Mining, Practical Machine Learning tools and Techniques with Java. 2 edition. Morgan Kaufmann, 2005  http://www.aaai.org/AITopics  http://www.kdnuggets.com Tutorial @ COMPSTAT 2010 Tutorial @ COMPSTAT 2010 51 51

  22. Break

  23. Part 3 GUHA Method and LISp-Miner System

  24. GUHA Method and LISp-Miner System Why here?  Association rules coined by Agrawal in 1990 ‘ s  More general rules s tudied since 1960‘s  GUHA method of mechanizing hypothesis formation  Theory based on combination of  Mathematical logic  Mathematical statistics  Several implementations  LISp-Miner system  Relevant tools and theory Tutorial @ COMPSTAT 2010 54

  25. Outline  GUHA – main features  Association rule – couple of Boolean attributes  GUHA procedure ASSOC  LISp-Miner system  Related research Tutorial @ COMPSTAT 2010 55

  26. GUHA – main features Starting questions: Can computers formulate and verify scientific hypotheses? Can computers in a rational way analyse empirical data and produce reasonable reflection of the observed empirical world? Can it be done using mathematical logic and statistics? 1978 Tutorial @ COMPSTAT 2010 56

  27. Examples of hypothesis formation Observational statement Evidence Theoretical statement (1): Theoretical statement observational statement (2), (3) : Theoretical statement ??? observational statement Tutorial @ COMPSTAT 2010 57

  28. From an observational statement to a theoretical statement Evidence Observational statement (1): Theoretical statement observational statement Theoretical statement (2), (3) : Theoretical statement ??? observational statement Justified by some rules of rational inductive inference  Some philosophers reject any possibility of formulating such rules  Nobody believes that there can be universal rules  There are non-trivial rules of inductive inference applicable under some well described  circumstances Some of them are useful in mechanized inductive inference  theoretical assumptions, observational statement Scheme of inductive inference: theoretical statement Tutorial @ COMPSTAT 2010 58

  29. Logic of discovery Scheme of inductive inference: theoretical assumptions, observational statement Five questions: theoretical statement L0: In what languages does one formulate observational and theoretical statements? (What is the syntax and semantics of these languages? What is their relation to the classical first order predicate calculus?) L1: What are rational inductive inference rules bridging the gap between observational and theoretical sentences? (What does it mean that a theoretical statement is justified?) L2: Are there rational methods for deciding whether a theoretical statement is justified (on the basis of given theoretical assumptions and observational statements)? L3: What are the conditions for a theoretical statement or a set of theoretical statements to be of interest (importance) with respect to the task of scientific cognition? L4: Are there methods for suggesting such a set of statements, which is as interesting, as possible? L0 – L2: Logic of induction L3 – L4: Logic of suggestion L0 – L4: Logic of discovery Tutorial @ COMPSTAT 2010 59

  30. GUHA Procedure Simple definition of a large set of relevant DATA observational statements Generation and verification of particular observational statements All the prime observational statements Observational : Theoretical statement = 1:1 Tutorial @ COMPSTAT 2010 60

  31. Outline  GUHA – main features  Association rule – couple of Boolean attributes  Data matrix and Boolean attributes  Association rule  4ft-quantifiers  GUHA procedure ASSOC  LISp-Miner  Related research Tutorial @ COMPSTAT 2010 61

  32. Data matrix and Boolean attributes … … A 1 A 2 A m A 1 (3) A 2 (7,9) A 1 (3) A 2 (7,9) … … 3 9 6 1 1 1 … … 7 5 7 0 0 0 … … … … … … … … … … 4 7 5 0 1 0 Data matrix M Boolean attributes , , Tutorial @ COMPSTAT 2010 62

  33. Association rule succedent antecedent M a b 4ft quantifier c d 1 … is true in M F (a,b,c,d) = 0 … is false in M Tutorial @ COMPSTAT 2010 63

  34. Important simple 4ft-quantifiers (1) M a b c d a p a Base Founded implication: p , Base a b a p a Base Double founded implication: p , Base a b c a d p a Base Founded equivalence: p , a b c d Base Tutorial @ COMPSTAT 2010 64

  35. Important simple 4ft-quantifiers (2) M a b c d a a c ( 1 ) p a Base Above Average: p , Base a b a b c d a a C S „Classical―: a b a b c d C , S Tutorial @ COMPSTAT 2010 65

  36. 4ft-quantifiers – statistical hypothesis tests (1) M Lower critical implication for 0 < p 1, 0 < < 0.5 a b c d ! , , p Base The rule corresponds to the statistical test (on the level ) of the null hypothesis ! p; H 0 : P( | ) p against the alternative one H 1 : P( | ) > p. Here P( | ) is the conditional probability of the validity of under the condition . Tutorial @ COMPSTAT 2010 66

  37. 4ft-quantifiers – statistical hypothesis tests (2) M Fisher‘s quantifie r for 0 < < 0.5 a b c d , Base The rule corresponds to the statistical test (on the level of the null hypothesis , Base of independence of and against the alternative one of the positive dependence. Tutorial @ COMPSTAT 2010 67

  38. Outline  GUHA – main features  Association rule – couple of Boolean attributes  GUHA procedure ASSOC  LISp-Miner  Related research Tutorial @ COMPSTAT 2010 68

  39. GUHA procedure ASSOC Set of relevant Data matrix M Set of relevant 4ft-quantifier Generation and verification of all relevant All prime Tutorial @ COMPSTAT 2010 69

  40. GUHA – selected implementations (1) 1966 - MINSK 22 (I. Havel)  Boolean data matrix simplified version association rules punch tape end of 1960s - IBM 7040 (I. Havel)  1976 IBM 370 (I. Havel, J. Rauch)  Boolean data matrix association rules statistical quantifiers bit strings punch cards Tutorial @ COMPSTAT 2010 70

  41. GUHA – selected implementations (2) Early 1990s – PC-GUHA  MS DOS A. Sochorová, P. Hájek, J. Rauch Since 1995 GUHA+-  Windows D. Coufal + all. Since 1996 LISp-Miner  Windows M. Šimůnek + J. Rauch + all. 7 GUHA procedures KEX related research Since 2006 Ferda, M. Ralbovský + all.  Tutorial @ COMPSTAT 2010 71

  42. Outline  GUHA – main features  Association rule – couple of Boolean attributes  GUHA procedure ASSOC  LISp-Miner  Overview  Application examples  Related research Tutorial @ COMPSTAT 2010 72

  43. LISp-Miner overview http://lispminer.vse.cz  4ft-Miner  SD4ft-Miner  KL-Miner  SDKL-Miner  CF-Miner  SDCF-Miner 4ftAction-Miner i.e. 7 GUHA procedures  KEX LMDataSource Tutorial @ COMPSTAT 2010 73

  44. LISp-Miner, application examples  Stulong data set  4ft-Miner (enhanced ASSOC procedure): ? B (Biochemical)  B (Physical, Social)  SD4ft-Miner: ? B (Biochemical)  normal risk: B (Physical, Social) Tutorial @ COMPSTAT 2010 74

  45. Stulong data set (1) http://euromise.vse.cz/challenge2004/ 75

  46. Stulong data set (2) http://euromise.vse.cz/challenge2004/data/entry/ Tutorial @ COMPSTAT 2010 76

  47. Social characteristcs Education Marital status Responsibility in a job Tutorial @ COMPSTAT 2010 77

  48. Physical examinations Weight [kg] Height [cm] Skinfold above musculus triceps [mm] Skinfold above musculus subscapularis [mm] …… additional attributes Tutorial @ COMPSTAT 2010 78

  49. Biochemical examinations Cholesterol [mg%] Triglycerides in mg% Tutorial @ COMPSTAT 2010 79

  50. LISp-Miner, application examples  Stulong data set  4ft-Miner (enhanced ASSOC procedure): ? B (Biochemical)  B (Physical, Social)  SD4ft-Miner: ? B (Biochemical)  normal risk: B (Physical, Social) Tutorial @ COMPSTAT 2010 80

  51. ? B (Biochemical) B (Physical, Social) In the ENTRY data matrix, are there some interesting relations between Boolean attributes describing combination of results of Physical examination and Social characteristics and results of Biochemical examination? ? ENTRY B (Physical, Social) a b B (Biochemical) c d ? evaluated using 4-fould table Tutorial @ COMPSTAT 2010 81

  52. Applying GUHA procedure 4ft-Miner ? B (Biochemical) B (Physical, Social) B (Physical, Social) ? B (Biochemical) B (Physical, Social) Entry data matrix B (Biochemical) ? Generation and verification of ? ? All prime Tutorial @ COMPSTAT 2010 82

  53. Defining B (Social, Physical) (1) B (Social, Physical) = B (Social) B (Physical) 2 B (Social) = [ B (Education), B (Marital Status), B (Responsibility_Job)] 0 4 B (Physical) = [ B (Weight), B (Height), B (Subscapular), B (Triceps)] 1 Tutorial @ COMPSTAT 2010 83

  54. Defining B (Social, Physical) (2) Education: basic school, apprentice school, secondary school, university B (Education): Subsets of length 1 - 1 Education (basic school), Education (apprentice school) Education (secondary school), Education (university) Tutorial @ COMPSTAT 2010 84

  55. Note: Attribute A with categories 1, 2, 3, 4, 5 Literals with coefficients Subset (1 – 3): A(1), A(2), A(3), A(4), A(5) A(1, 2), A(1, 3), A(1, 4), A(1, 5) `` A(2, 3), A(2, 4), A(2, 5) A(3, 4), A(3, 5) A(4, 5) A(1, 2, 3), A(1, 2, 4), A(1, 2, 5) A(2, 3, 4), A(2, 3, 5) A(3, 4, 5) Tutorial @ COMPSTAT 2010 85

  56. Defining B (Social, Physical) (3) Set of categories of Weight: 52, 53, 54, 55, …….., 130, 131, 132, 133 B (Weight): Intervals of length 10 - 10: Weight(52 – 61), Weight(53 – 62), … 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,...., 128, 129, 130, 131, 132, 133 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,...., 128, 129, 130, 131, 132, 133 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,...., 128, 129, 130, 131, 132, 133 ,...., 52, 53, 54, 55, 56, ...., 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133 86

  57. Defining B (Social, Physical) (4) Set of categories of Triceps: (0;5 , (5;10 , (10;15 , …, (25;30 (30;35 (35;40 B (Triceps): Cuts 1 - 3 Left cuts 1 – 3 i.e. Triceps(low) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(1 – 5) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(1 – 10) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(1 – 15) Tutorial @ COMPSTAT 2010 87

  58. Defining B (Social, Physical) (5) Set of categories of Triceps: (0;5 , (5;10 , (10;15 , …, (25;30 (30;35 (35;40 B (Triceps): Cuts 1 - 3 Right cuts 1 – 3 i.e. Triceps(high) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(35 – 40) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(30 – 40) (0;5 , (5;10 , (10;15 , (15;20 , (20;25 , (25;30 , (30;35 , (35;40 i.e. Triceps(25 – 45) Tutorial @ COMPSTAT 2010 88

  59. Defining B (Social, Physical) (6) B (Social, Physical): Examples of Education (basic school) Education (university) Marital_Status(single) Weight (52 – 61) Marital_Status(divorced ) Weight (52 – 61) Triceps (25 – 45) Weight (52 – 61) Height (52 – 61) Subscapular(0 – 10) Triceps (25 – 45) Tutorial @ COMPSTAT 2010 89

  60. Note: Types of coefficients See examples above Tutorial @ COMPSTAT 2010 90

  61. Defining B (Biochemical) Analogously to B (Social, Physical) Examples of B (Biochemical): Cholesterol (110 – 120), Cholesterol (110 – 130), …, Cholesterol (110 – 210) Cholesterol ( 380 ), Cholesterol ( 370 ), …, Cholesterol ( 290) Cholesterol ( 380) Triglicerides ( 50), … Cholesterol ( 380) Triglicerides ( 300 ), … …, Tutorial @ COMPSTAT 2010 91

  62. ? in Defining ? ? corresponds to a condition concerning 4ft( , , M ) M a b c d 17 types of 4ft-quantifiers Tutorial @ COMPSTAT 2010 92

  63. Two examples of ? M a b a p a B Founded implication p,B c d a b : at least 100p per cent of objects of M p,B satisfying satisfy also and there are at least Base objects satisfying both and a a c ( 1 ) p a B + Above average p,B a b a b c d : the relative frequency of objects of M satisfying + among the objects p,B satisfying is at least 100p per cent higher than the relative frequency of in the whole data matrix M and there are at least Base objects satisfying both and Tutorial @ COMPSTAT 2010 93

  64. Solving B (Social, Physical) 0.9,50 B (Biochemical) (1) 0.9,50 B (Biochemical) B (Social, Physical) Tutorial @ COMPSTAT 2010 94

  65. Solving B (Social, Physical) 0.9,50 B (Biochemical) (2) PC with 1.66 GHz, 2 GB RAM 2 min. 40 sec. 5 . 10 6 rules verified 0 true rules Problem: Confidence 0.9 in 0.9,50 too high Solution: Use confidence 0.5 Tutorial @ COMPSTAT 2010 95

  66. Solving B (Social, Physical) 0.5,50 B (Biochemical) (1) 0.5,50 B (Biochemical) B (Social, Physical) Tutorial @ COMPSTAT 2010 96

  67. Solving B (Social, Physical) 0.5,50 B (Biochemical) (2) 30 rules with confidence 0.5 Problem: The strongest rule has confidence only 0.526, see detail Solution: Search for rules expressing 70% higher relative frequency than average It means to use 0.7,50 instead of + 0.5,50 Tutorial @ COMPSTAT 2010 97

  68. Solving B (Social, Physical) 0.5,50 B (Biochemical) (3) Detail of results - the strongest rule Entry Triglicerides( 115) Triglicerides( 115) Subscapular(0;10 51 46 Subscapular(0;10 303 729 Subscapular(0;10 0.53, 51 Triglicerides( 115) Tutorial @ COMPSTAT 2010 98

  69. Solving B (Social, Physical) 0.7,50 B (Biochemical) (1) + + B (Biochemical) 0.7,50 B (Social, Physical) Tutorial @ COMPSTAT 2010 99

  70. Solving B (Social, Physical) 0.7,50 B (Biochemical) (2) + 14 rules with relative frequency of succedent 0.7 than average, example – see detail Tutorial @ COMPSTAT 2010 100

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