MACHINE LEARNING TECHNIQUES - LASA

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178 • Biological Sciences: Dynamics of groups In Robotics, GA have been used successfully to optimize parameters of controllers in order to evolve the Artificial Neural Networks Controllers. The GA is used to determine the weights or the topology of the network. 8.1 Principle Genetic Algorithms provide a form of simulated evolution. The basic idea goes along the following steps: • Start from a basic random population of parents • Apply a process of selection • Breed pairs of parents • Produce pairs of children with only the good properties of the parents • Reject bad children The process leads to the evolution of a population of children that are better than the parents. 8.2 Encoding To use a genetic algorithm, you must encode solutions to your problem in a structure that can be stored in the computer. This object is a genome (or chromosome). Thus, the first step before using a GA consists in a) defining a representation of the problem (this is often the most difficult step, as it requires some a priori knowledge on where the important features of the problem lie); b) defining the parameters to optimize (e.g. the weights in a neural networks); c) encoding the parameters into a chromosome; and d) creating a whole population, i.e. generate several random chromosomes. You can use any representation for the individual genomes in the genetic algorithm. Holland worked primarily with strings of bits, but you can use arrays, trees, lists, or any other object. © A.G.Billard 2004 – Last Update March 2011
179 However, you must define genetic operators (initialization, mutation, crossover, comparison) for any representation that you decide to use Each chromosome must represent a complete solution to the problem you are trying to optimize. 8.3 Breeding and Selection In order to evaluate the goodness of each solution, you must define a selection criterion. This criterion is often referred to as the fitness function. The rest of the algorithm will breed the chromosomes, so as to maximize the fitness function. Applying iteratively crossover and mutation to the chromosomes in the population to generate new solutions does this. Figure 8-1: Crossover: Given 2 selected chromosomes; genetic material is swapped between them around a selected point. Typically crossover is defined so that two individuals (the parents) combine to produce two more individuals (the children). But you can define asexual crossover or single-child crossover as well. The primary purpose of the crossover operator is to get genetic material from the previous generation to the subsequent generation. © 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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125 The sigmoid f x ( x) ( ) = tanh
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MACHINE LEARNING TECHNIQUES - LASA

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