ELM Classification: Postprocessing NBC

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1 ELM Classification: Postprocessing by GMM or NBC Amaury Lendasse, Andrey Gritsenko, Emil Eirola, Yoan Miche and Kaj-Mikael Björk MIE Department and Informatics Initiative UIOWA - amaury-lendasse@uiowa.edu

2 Who am I? Belgian: sorry for my french accent :) 2

3 Who am I? Belgian: sorry for my french accent :) Born on April 16 th

4 Who am I? Postdoc at the University of Memphis Postdoc and adjunct Prof. at Aalto Univ. in Finland Prof. at the University of the Basque Country in Spain Lecturer in Arcada Lecturer in Aalto 4

5 Who am I? Associate Prof. at The University of Iowa: 50% MIE and 50% Informatics Initiative Research: Machine Learning, Big Data, Environmental Modeling 5

6 What is Classification? Supervised Learning: we have to predict some output y based on some input x y can have: two values (binary classification) several ranked values (very small, small, medium, big, very big): multi-class problem several unranked values (English, American, French, Belgian): multi-class problem 6

7 What is Classification? Old problem: Fisher, R.A. "The use of multiple measurements in taxonomic problems" Annual Eugenics, 7, Part II, (1936) Many models (classifiers) are available: DL, KNN, LVQ, RBFN, MLP, SVM, ELM, GMM, LDA, NBC What is the object on the right of this handsome guy? 7

8 Two types of Classifiers Classifiers that predict the class: DL, LVQ, RBFN, MLP, SVM, ELM, LDA, Easy to build Classifiers that provide a probability for each class: GMM, NBC, (KNN?) Not so Easy to build or not working 8

9 Two types of Classifiers Classifiers that predict the class: y = Belgian y = French y = American Classifiers that provide a probability for each class: y = [99% Belgian, 1% French, 0% American] y = [49% Belgian, 51% French, 0% American] y = [33% Belgian, 33% French, 34% American] 9

10 Two types of Classifiers Classifiers that predict the class: y = Belgian y = French y = American Classifiers that provide a probability for each class: y = [99% Belgian, 1% French, 0% American] y = [49% Belgian, 51% French, 0% American] y = [33% Belgian, 33% French, 34% American] 10

11 What do we want? A classifier that: is accurate/efficient (to be defined) fast to build (to train) fast to predict the class of a new element provide a probability for each class can be handled by a cute brunette (easy to use, automatic) 11

12 Bayes Formula p(c 1 x) = p(x C 1 )p(c 1 ) p(x C 1 )p(c 1 )+p(x C 2 )p(c 2 )+p(x C 3 )p(c 3 ) 12

13 Bayes Formula p(c 1 x) = p(x C 1 )p(c 1 ) p(x C 1 )p(c 1 )+p(x C 2 )p(c 2 )+p(x C 3 )p(c 3 ) p(c 2 x) = p(x C 2 )p(c 2 ) p(x C 1 )p(c 1 )+p(x C 2 )p(c 2 )+p(x C 3 )p(c 3 ) p(c 3 x) = p(x C 3 )p(c 3 ) p(x C 1 )p(c 1 )+p(x C 2 )p(c 2 )+p(x C 3 )p(c 3 ) 13

14 Naive Bayes Classifier p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 14

15 Naive Bayes Classifier p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 "Naive" conditional independence assumptions p(c 1 x) = dq j=1 3P dq i=1 j=1 p(x j C 1 )p(c 1 ) p(x j C i )p(c i ) 15

16 Naive Bayes Classifier "Naive" conditional independence assumptions p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 p(c 1 x) = dq j=1 3P i=1 p(x j C 1 )p(c 1 ) dq j=1 Easy to estimate p(x j C i )p(c i ) 16

17 Naive Bayes Classifier "Naive" conditional independence assumptions p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 p(c 1 x) = dq j=1 3P i=1 p(x j C 1 )p(c 1 ) dq j=1 Wrong! p(x j C i )p(c i ) 17

18 Gaussian Mixture Model 18

19 Gaussian Distribution Gaussian (Normal) Distribution is a common continuous probability function Has multi-variate extension Parameters: mean and covariance matrix 19 19

20 Gaussian Mixture Model Probability distribution of given data is approximated by a mixture of multiple Gaussians Works for any data distribution, given enough Gaussian components Approximates data density: unsupervised learning method 20

21 Mixture Model 21

22 Mixture of Gaussians 22

23 Mixture of Gaussians density estimation p(x) = P K k=1 kn (x µ k, k ) N (x µ k, k )= 1 1 exp{ 1 (2 ) 2 k 1/2 2 (x µ k) T 1 k (x µ k)} - multivariate Gaussian distribution. I Number of components is a hyper-parameter determined via cross-validation. I Why Gaussian distribution? The least restrictive among all continuous distributions / 19

24 ELM 24

25 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? A simple BUT very smart idea! Prof. Guang-Bin Huang, NTU, Singapore 25

26 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Good old MLP 26

27 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Good old MLP 27

28 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Good old MLP 28

29 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Notations 29

30 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Notations 30

31 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Training 31

32 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Training 32

33 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? Training 33

34 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? First Example 34

35 ELM: A Robust Modeling Technique? Yes! What is Extreme Learning Machine? First Example 35

36 ELM: A Robust Modeling Technique? Yes! My first Simple Test 36

37 ELM: A Robust Modeling Technique? Yes! My first Simple Test 37

38 (TR)OP-ELM 38 38

39 ELM: A Robust Modeling Technique? Yes! So you know ELM 39

40 ELM: A Robust Modeling Technique? Yes! So you know ELM 40

41 ELM: A Robust Modeling Technique? Yes! So you know ELM 41

42 ELM: A Robust Modeling Technique? Yes! So you know ELM 42

43 ELM: A Robust Modeling Technique? Yes! Regularization Approaches 43

44 ELM: A Robust Modeling Technique? Yes! Regularization Approaches 44

45 ELM: A Robust Modeling Technique? Yes! Regularization Approaches 45

46 ELM: A Robust Modeling Technique? Yes! Regularization Approaches 46

47 ELM: A Robust Modeling Technique? Yes! Regularization Approaches 47

48 ELM: A Robust Modeling Technique? Yes! Regularization Approaches Provides a ranking of the variables 48

49 ELM: A Robust Modeling Technique? Yes! Tikhonov Regularization 49

50 ELM: A Robust Modeling Technique? Yes! Tikhonov Regularization 50

51 ELM: A Robust Modeling Technique? Yes! Elastic Net 51

52 ELM: A Robust Modeling Technique? Yes! Elastic Net 52

53 ELM: A Robust Modeling Technique? Yes! Drawback of these methods 53

54 ELM: A Robust Modeling Technique? Yes! OP-ELM 54

55 ELM: A Robust Modeling Technique? Yes! PRESS is Exact but Fast LOO Calculation 55

56 ELM: A Robust Modeling Technique? Yes! TROP-ELM 56

57 ELM: A Robust Modeling Technique? Yes! TROP-ELM: TR-PRESS 57

58 ELM: A Robust Modeling Technique? Yes! TROP-ELM: Global Methodology 58

59 ELM: A Robust Modeling Technique? Yes! TROP-ELM 59

60 New Idea: ELM + GMM p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 60

61 New Idea: ELM + GMM p(c 1 x) = p(x C 1)p(C 1 ) 3P p(x C i )p(c i ) i=1 Ŷ 61

62 New Idea: ELM + GMM Ŷ p(c 1 ŷ) = p(ŷ C 1)p(C 1 ) 3P p(ŷ C i )p(c i ) i=1 62

63 New Idea: ELM + GMM Approximated using GMM Ŷ p(c 1 ŷ) = p(ŷ C 1)p(C 1 ) 3P p(ŷ C i )p(c i ) i=1 63

64 Experiments 64

65 Results (1) 65

66 Are the Probabilities correctly evaluated? Let s ask an expert to analyze the misclassifications! No, it is boring (not automatic) and usually not possible 66

67 Are the Probabilities correctly evaluated? Let s ask an expert to analyze the misclassifications! No, it is boring (not automatic) and usually not possible 67

68 Are the Probabilities correctly evaluated? If the correct class corresponds to one of the two largest probabilities 68

69 Are the Probabilities correctly evaluated? If the output of the classifier is a probability THEN let s draw the classification randomly using this probability Seriously? 69

70 Are the Probabilities correctly evaluated? If the output of the classifier is a probability THEN let s draw the classification randomly using this probability Classifiers that provide a probability for each class: y = [99% Belgian, 1% French, 0% American] y = [49% Belgian, 51% French, 0% American] y = [33% Belgian, 33% French, 34% American] 70

71 Are the Probabilities correctly evaluated? 71

72 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 72

73 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 73

74 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 74

75 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 75

76 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 76

77 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 77

78 Conclusions? We wanted a classifier that: is accurate: similar to the state of the art fast to built: the fastest? fast to predict the class of a new element: Oh yes baby! Provide a probability for each class: Yes we can! can be handled by a cute brunette: to be determined Big Data? Basic version accepted to IWANN 15, journal version: under review 78

79 Thank You! Questions? 79

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