MACHINE LEARNING TECHNIQUES - LASA

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180 Figure 8-2: Mutation: Each location is mutated with a very small probability. When using a binary encoding, mutation let the bit go from 0 to 1 or vice-versa. In real number encoding, mutation adds or substracts a small random number. The mutation operator introduces a certain amount of randomness to the search. It can help the search find solutions that crossover alone might not encounter. Subsequently, GA uses various selection criteria so as to pick the best individuals for mating (and subsequent crossover), based on the value returned by the fitness function. For instance, parents can be chosen with some probability depending on: • their fitness (Roulette-wheel selection) • their rank according to the fitness (Rank-based selection) The selection method determines how individuals are chosen for mating. If you use a selection method that picks only the best individual, then the population will quickly converge to that individual. So the selector should be biased toward better individuals, but should also pick some that are not quite as good (but hopefully have some good genetic material in them). Some of the more common methods include roulette wheel selection (the likelihood of picking an individual is proportional to the individual's score), tournament selection (a number of individuals are picked using roulette wheel selection, then the best of these is (are) chosen for mating), and rank selection (pick the best individual every time). Threshold selection can also be effective. © A.G.Billard 2004 – Last Update March 2011
181 Often the crossover operator and selection method are too effective and they end up driving the genetic algorithm to create a population of individuals that are almost exactly the same. When the population consists of similar individuals, the likelihood of finding new solutions typically decreases. On one hand, you want the genetic algorithm to find good individuals, but on the other you want it to maintain diversity. A common problem in optimization (not just genetic algorithms) is how to define an objective function that accurately (and consistently) captures the effects of multiple objectives. In general, genetic algorithms are better than gradient search methods if your search space has many local optima. Since the genetic algorithm traverses the search space using the genotype rather than the phenotype, it is less likely to get stuck on a local high or low. 8.4 The Algorithm In summary, the Genetic Algorithm goes as follows: 1. Define a basic population of chromosomes. 2. Evaluate the fitness of each chromosome. 3. Select parents with a probability (rank-based, roulette-wheel) 4. Breed pairs of parents (cross-over). 5. Apply mutation on children. 6. Evaluate fitness of children. 7. Population size is kept constant through a rejection process. Throw away the worst solutions of the old population or of the old population + the new children. 8. Start again at point 3. 9. The GA stops when either satisfactory level of fitness is attained, or when the population is uniform (local minima). 8.5 Convergence There is, to this day, no theoretical proof that a GA will eventually converge, nor that it will converge to the global optimum of the fitness function. There are, however, a number of “rules of thumb” that one might follow to ensure good performance of the algorithm. Convergence of a GA depends on choosing correctly the parameters. One should keep in mind the following: • If the mutation is too small (not frequent enough and making small steps), there will not be enough exploration. Hence, the algorithm might get stuck in some local optimum. • If, conversely, the mutation is too strong (too frequent and too important steps), the algorithm will be very slow to converge. • Cross-over can slow down convergence, by destroying good solutions. • Convergence depends importantly on the encoding and on the location of the genes on the chromosomes. • The number of “children” produced at each generation determines the speed at which one explores the environment. © 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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127 6.3.2 Information Theory and th
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