MACHINE LEARNING TECHNIQUES - LASA

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14 100% p(TP) Performance improves Performance drops 0% p(FP) 100% 1.3.4 In Practice In this course, you will be asked to validate the performance of different algorithms following the above best practice recommendations. For this, you will first have to create your three sets (training, validation and testing sets) and explore the effect of choosing training and validation sets that are not representative of the testing set. It is expected that performance will be optimal on the training set and will decrease on the validation set. A large number of algorithms we will see in class require knowing the mean and covariance of the probability distribution function of the data. In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value. Further, several of these algorithms assume that the underlying distribution follow a normal distribution. This again is usually not true. Thus, one should keep in mind that, although the estimates of the covariance may be considered optimal, this does not mean that the resulting computation obtained by substituting these values is optimal, even if the assumption of normally distributed classes is correct. Another complication that you will often encounter when dealing with algorithms that require computing the inverse of the covariance matrix of the data is that, with real data, the number of observations of each sample exceeds the number of samples. In this case, the covariance estimates do not have full rank, and so cannot be inverted. There are a number of ways to deal with this. One is to use the pseudoinverse of the covariance matrix. Another way is to proceed to singular value decomposition. 1.4 Focus of this course In this class, we will see a number of architectures that can perform one of these: • Classification • Associative learning • Supervised and unsupervised Learning • Reinforcement Learning; Learning with incomplete cues • Dimensionality Reduction, Denoising • Clustering • Pattern recognition © A.G.Billard 2004 – Last Update March 2011
15 In particular, we will consider a number of Artificial Neural Networks models and will see how they may exhibit different properties (capacity, convergence and stability) depending on their topology, learning and retrieval rules. The tutorial and exercises that will accompany the class with revolve around a number of realworld applications of Machine Learning, namely, for visual processing (face recognition, object recognition), for motor control (Inverse Kinematics), for learning sensory-motor patterns, and for simulating biologically plausible computational processes. © A.G.Billard 2004 – Last Update March 2011
Page 1 and 2: SCHOOL OF ENGINEERING MACHINE LEARN
Page 3 and 4: 3 4. 4 Regression Techniques ......
Page 5 and 6: 5 9.2.2 Probability Distributions,
Page 7 and 8: 7 Journals: • Machine Learning
Page 9 and 10: 9 Performance What would be an opti
Page 11 and 12: 11 1.2.3 Key features for a good le
Page 13: 13 1.3.2 Crossvalidation To ensure
Page 17 and 18: 17 2.1 Principal Component Analysis
Page 19 and 20: 19 ( ) Xʹ′ = W X − µ (2.6) i
Page 21 and 22: 21 2.1.2.2 Reconstruction error min
Page 23 and 24: 23 PCA is an example of PP approach
Page 25 and 26: 25 Algorithm: If one further assume
Page 27 and 28: 27 The CCA algorithm consists thus
Page 29 and 30: 29 Figure 2-6: Mixture of variables
Page 31 and 32: 31 2.3.2 Why Gaussian variables are
Page 33 and 34: 33 • In our general definition of
Page 35 and 36: 35 2.3.5 ICA Ambiguities We cannot
Page 37 and 38: 37 Denote by g the derivative of th
Page 39 and 40: 39 3 Clustering and Classification
Page 41 and 42: 41 An agglomerative clustering star
Page 43 and 44: 43 3.1.1.1 The CURE Clustering Algo
Page 45 and 46: 45 Disadvantages of hierarchical cl
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Page 51 and 52: 51 k ( σ j ) 2 = k ∑ i α = r k
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65 ⎛⎛ min ⎜⎜ w ⎝⎝ N i=
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67 T ( yi − xi w) 2 M ⎛⎛ ⎞
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69 Figure 4-2: Illustration of the
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71 4.4.2 Multi-Gaussian Case It is
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73 5 Kernel Methods These lecture n
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75 The kernel k provides a metric o
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77 M 1 T v = ∑ x ( x ) v M λ i j
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79 1 M The solutions to the dual ei
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81 5.4 Kernel CCA The linear versio
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83 additional ridge parameter induc
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85 Figure 5-3: TOP: Marginal (left)
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87 statistical independence. We def
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89 J j ( µ 1,...., µ K) = ∑∑
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91 A simple pattern recognition alg
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93 ( ) ( , ) f x = sign w x + b (5.
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95 Figure 5-6: A binary classificat
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97 where N is the number of support
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99 5.8 Support Vector Regression In
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101 The optimization problem given
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103 Note that since we never have t
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105 Figure 5-13: Effect of the kern
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107 To better understand the effect
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109 5.9 Gaussian Process Regression
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111 One can then use the above expr
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113 5.9.2 Equivalence of Gaussian P
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115 5.9.3 Curse of dimensionality,
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117 The weight w determines the slo
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119 Figure 5-21: Example of success
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121 • its performance tends to de
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123 neurons. Furthermore, they lear
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125 The sigmoid f x ( x) ( ) = tanh
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127 6.3.2 Information Theory and th
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129 ( R) ⎛⎛det ⎞⎞ I( x, y)
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131 y= ∑ w x ) of Because of the
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133 6.5 Willshaw net David Willshaw
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135 6.6.1 Weights bounds One of the
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137 Figure 6-11: The weight vector
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139 6.6.4 Oja’s one Neuron Model
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141 If y i and y are highly correla
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143 Foldiak’s second model allows
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145 ∂ ∂ J 1 = fy − 1 2 λ 1yf
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147 6.8 The Self-Organizing Map (SO
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149 6. Decrease the size of the nei
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151 the resulting distribution is a
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153 To simplify the description of
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155 C µν −1 where ( ) is the µ
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157 The continuous time Hopfield ne
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159 ∂f If the slope is negative,
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161 7.2 Hidden Markov Models Hidden
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163 Figure 7-2: Schematic illustrat
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165 these two quantities to compute
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167 7.2.4 Decoding an HMM There are
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169 7.2.5 Further Readings Rabiner,
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171 7.3.1 Principle In reinforcemen
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173 general, acting to maximize imm
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175 of reinforcement learning makes
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177 8 Genetic Algorithms We conclud
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179 However, you must define geneti
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181 Often the crossover operator an
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183 ( A λI) x 0 − = (8.5) where
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185 Joint probability: The joint pr
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187 The two most classical distribu
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189 9.2.7 Statistical Independence
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191 1 1 1 1 h x ∫ a b a b 0 a a
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193 9.4 Estimators 9.4.1 Gradient d
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195 9.4.2.1 Maximum Likelihood Mach
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197 10 References • Machine Learn
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