Learning. CS461 Artificial Intelligence Pinar Duygulu. Bilkent University, Spring Slides are mostly adapted from AIMA and MIT Open Courseware

Transcription

1 1 Learning CS 461 Artificial Intelligence Pinar Duygulu Bilkent University, Slides are mostly adapted from AIMA and MIT Open Courseware

2 2 Learning What is learning?

3 3 Induction David Hume Bertrand Russell If asked why we believe the sun will rise tomorrow, we shall naturally answer, 'Because it has always risen every day.' We have a firm belief that it will rise in the future, because it has risen in the past. The real question is: Do any number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future? It has been argued that we have reason to know the future will resemble the past, because what was the future has constantly become the past, and has always been found to resemble the past, so that we really have experience of the future, namely of times which were formerly future, which we may call past futures. But such an argument really begs the very question at issue. We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures?

4 4 Kinds of Learning

5 5 Learning a function

6 6 Aspects of function learning

7 7 Example Problem

8 8 Memory

9 9 Averaging

10 10 Sensor noise

11 11 Generalization

12 12 The red and the black

13 13 What is the right hypothesis?

14 14 What is the right hypothesis?

15 15 What is the right hypothesis?

16 16 How about this?

17 17 Variety of learning methods

18 18 Nearest Neighbor

19 19 Decision trees

20 20 Neural Networks

21 21 Machine learning successes

22 22 Supervised learning

23 23 Best hypothesis

24 24 Learning Conjunctions

25 25 Algorithm

26 26 Algorithm Start with N equal to all the negative examples and h = true Then loop, adding conjuncts that rue out negative examples until N is empty Inside the loop consider every feature that would not rule out any positive examples

27 27 Simulation

28 28 Now, we consider all the the features that would not exclude any positive examples. Those are features f3 and f4. f3 would exclude 1 negative example; f4 would exclude 2. So we pick f4.

29 29 Simulation Now we remove the examples from N that are ruled out by f4 and add f4 to h. Now, based on the new N, n3 = 1 and n4 = 0. So we pick f3.

30 30 Simulation Because f3 rules out the last remaining negative example, we're done!

31 31 A harder Problem

32 32 Disjunctive Normal form

33 33 Learning DNF

34 34 Algorithm The idea is that each disjunct will cover or account for some subset of the positive examples. So in the outer loop, we make a conjunction that includes some positive examples and no negative examples, and add it to our hypothesis. We keep doing that until no more positive examples remain to be covered.

35 35 Choosing a feature

36 36 Simulation

37 37 How well does it work?

38 38 Cross validation

39 39 Learning curves

40 40 Learning curves

41 41 Simple Gifts

42 42 Noisy data

43 43 Pseudo code: Noisy DNF Learning

44 44 Epsilon is our data

45 45 Overfitting curve

46 46 Hypothesis complexity

47 47 Bias vs variance

48 48

49 49

50 50

51 51

52 52

53 53

54 54 Picking epsilon

55 55 Domains

56 56 Congressional Voting

57 57 Decision Trees

58 58 Hypothesis class

59 59

60 60

61 61 Tree Bias

62 62 Trees vs DNF

63 63 Trees vs DNF

64 64 Algorithm

65 65 Let's split

66 66 Entropy

67 67 Let's split

68 68 Let's split

69 69 Stopping

70 70 Simulation

71 71 Exclusive OR

72 72 Congressional voting

73 73 Naïve Bayes

74 74 Example

75 75

76 76

77 77 Prediction P

78 78 Learning Algorithm

79 79 Prediction Algorithm

80 80 Laplace Correction

81 81 Example with correction

82 82 Prediction with correction

83 83 Hypothesis space

84 84 Exclusive OR

85 85 Probabilistic Inference

86 86 Bayes' rule

87 87 Why is Bayes Naive

88 88 Learning Algorithm

89 89 Prediction Algorithm

90 90 Feature Spaces

91 91 Predicting Bankruptcy

92 92 Nearest neighbor

93 93 What do we mean by nearest?

94 94 Scaling

95 95 Predicting Bankruptcy

96 96 Predicting Bankruptcy

97 97 Hypothesis

98 98 Time and space

99 99 Noise

100 Noise 100

101 K-nearest neighbor 101

102 Curse of dimensionality 102

103 Test domains 103

104 Decision trees 104

105 Numerical attributes 105

106 106

107 Considering splits 107

108 Considering splits 108

109 Bankruptcy example 109

110 Heart disease 110

111 More than 22 MPG? 111

112 Bankruptcy example 112

113 1-Nearest Neighbor hypothesis 113

114 Decision tree hypothesis 114

115 Linear hypothesis 115

116 Linearly separable 116

117 Not linearly separable 117

118 Linear hypothesis class 118

119 Hyperplane geometry 119

120 120

121 Perceptron algorithm 121

122 Bankruptcy example- 49 iterations 122

123 Gradient Ascent 123

124 Gradient ascent/descent 124

125 Perceptron training via gradient descent 125

126 Artificial Neural Networks (Feedforward Nets) 126

127 Single Perceptron Unit 127

128 Beyond linear separability 128

129 Multi-layer perceptron 129

130 Multilayer perceptron 130

131 Multilayer perceptron learning 131

132 Sigmoid unit 132

133 133

134 Gradient descent 134

135 Gradient descent single unit 135

136 Derivative of the sigmoid 136

137 Gradient of unit output 137

138 Gradient of error 138

139 Gradient of Unit Output 139

140 Generalized delta rule 140

141 Backpropagation 141

142 Backpropagation example 142

143 Training neural nets 143

144 Applications 144

145 Applications 145

146 146 The vertical face-finding part of Rowley, Baluja and Kanade s system Figure from Rotation invariant neural-network based face detection, H.A. Rowley, S. Baluja and T. Kanade, Proc. Computer Vision and Pattern Recognition, 1998, copyright IEEE Adapted from David 1998, Forsyth, UC Berkeley

147 147 Architecture of the complete system: they use another neural net to estimate orientation of the face, then rectify it. They search over scales to find bigger/smaller faces. Figure from Rotation invariant neural-network based face detection, H.A. Rowley, S. Baluja and T. Kanade, Proc. Computer Vision and Pattern Recognition, 1998, copyright 1998, IEEE Adapted from David Forsyth, UC Berkeley

148 148 Figure from Rotation invariant neural-network based face detection, H.A. Rowley, S. Baluja and T. Kanade, Proc. Computer Vision and Pattern Recognition, 1998, copyright 1998, IEEE Adapted from David Forsyth, UC Berkeley

149 Limitations 149

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