MACHINE LEARNING TECHNIQUES - LASA

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176 reinforcement learning we are very much concerned with cases in which optimal solutions cannot be found but must be approximated in some way. Policy Rewar d Value Figure 7-7: Reinforcement learning is characterized by: ❐ Policy: what to do ❐ Reward: what is good ❐ Value function: what is good because it predicts reward ❐ Model: what follows what Model environmen of t © A.G.Billard 2004 – Last Update March 2011
177 8 Genetic Algorithms We conclude these Lecture Notes by covering Genetic Algorithms, a form of stochastic optimization that can be used to learn parameters of several of the methods seen previously in these notes. This introduction to Genetic Algorithms is very brief and serves only as a brief overview of the main concepts. The term genetic algorithm refers to a model introduced by John Holland in 1975 [Holland, 1975]. Genetic Algorithms are a family of computational models inspired by Darwin’s principle of selective evolution. The algorithms encode a potential solution to a specific problem on a simple chromosome-like data structure and apply recombination operators to these structures so as to preserve critical information. An implementation of a genetic algorithm begins with a population of typically random chromosomes. One, then, evaluates these structures and allocates reproductive opportunities in such a way that those chromosomes, which represent a better solution to the target problem, are given more chances to reproduce than those chromosomes, which are poorer solutions. The “goodness” of a solution is typically defined with respect to the current population. Genetic algorithms are often viewed as optimization tool, although the range of problems to which genetic algorithms have been applied is quite broad and goes beyond simple function optimization. They are used to find solutions to complex systems in domains such as: • Finances: Market predictors, risk evaluators • Business: Scheduling, time and storage optimization • Engineering: Dynamics of particles, fluids, etc. © A.G.Billard 2004 – Last Update March 2011
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SCHOOL OF ENGINEERING MACHINE LEARN
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3 4. 4 Regression Techniques ......
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5 9.2.2 Probability Distributions,
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7 Journals: • Machine Learning
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9 Performance What would be an opti
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11 1.2.3 Key features for a good le
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13 1.3.2 Crossvalidation To ensure
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15 In particular, we will consider
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17 2.1 Principal Component Analysis
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19 ( ) Xʹ′ = W X − µ (2.6) i
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21 2.1.2.2 Reconstruction error min
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23 PCA is an example of PP approach
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25 Algorithm: If one further assume
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27 The CCA algorithm consists thus
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29 Figure 2-6: Mixture of variables
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31 2.3.2 Why Gaussian variables are
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33 • In our general definition of
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35 2.3.5 ICA Ambiguities We cannot
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37 Denote by g the derivative of th
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39 3 Clustering and Classification
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41 An agglomerative clustering star
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43 3.1.1.1 The CURE Clustering Algo
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45 Disadvantages of hierarchical cl
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47 Cases where K-means might be vie
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49 3.1.4 Clustering with Mixtures o
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51 k ( σ j ) 2 = k ∑ i α = r k
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53 Theα are the so-called mixing c
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55 Figure 3-16: Clustering with 3 G
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57 When the transformation A is lin
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59 C: X → Y ( ) C x K = arg max
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61 Figure 3-18: Linear combination
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63 Figure 3-19: Bayes classificatio
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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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