MACHINE LEARNING TECHNIQUES - LASA

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6.6.1 Weights bounds ..................................................................................................... 135
6.6.2 Weight decay ......................................................................................................... 136
6.6.3 Principal Components ............................................................................................ 137
6.6.4 Oja’s one Neuron Model ........................................................................................ 139
6.6.5 Convergence of the Weights Decay rule ............................................................... 139
6.7 Anti-Hebbian learning ................................................................................................. 140
6.7.1 Foldiak’s models .................................................................................................... 141
6.7.2 CCA Revisited ....................................................................................................... 143
6.7.3 ICA Revisited ......................................................................................................... 145
6.8 The Self-Organizing Map (SOM) ................................................................................ 147
6.8.1 Kohonen Network .................................................................................................. 147
6.8.2 Bayesian self-organizing map ................................................................................ 150
6.9 Static Hopfield Network .............................................................................................. 151
6.9.1 Hopfield Network Structure .................................................................................... 152
6.9.2 Learning Phase ...................................................................................................... 152
6.9.3 Retrieval Phase ..................................................................................................... 153
6.9.4 Capacity of the static Hopfield Network ................................................................. 154
6.9.5 Convergence of the Static Hopfield Network ......................................................... 155
6.10 Continuous Time Hopfield Network and Leaky-Integrator Neurons ...................... 155
7. 7 Markov-Based Models ......................................................................................... 160
7.1 Markov Process .......................................................................................................... 160
7.2 Hidden Markov Models ............................................................................................... 161
7.2.1 Formalism .............................................................................................................. 161
7.2.2 Estimating a HMM ................................................................................................. 163
7.2.3 Determining the number of states .......................................................................... 166
7.2.4 Decoding an HMM ................................................................................................. 167
7.2.5 Further Readings ................................................................................................... 169
7.3 Reinforcement Learning ............................................................................................. 170
7.3.1 Principle ................................................................................................................. 171
7.3.2 Defining the Reward .............................................................................................. 172
7.3.3 Markov World ......................................................................................................... 173
7.3.4 Estimating the policy .............................................................................................. 174
7.3.5 Summary ............................................................................................................... 175
8. 8 Genetic Algorithms .............................................................................................. 177
8.1 Principle ....................................................................................................................... 178
8.2 Encoding ...................................................................................................................... 178
8.3 Breeding and Selection .............................................................................................. 179
8.4 The Algorithm .............................................................................................................. 181
8.5 Convergence ............................................................................................................... 181
9. 9 Annexes ................................................................................................................ 182
9.1 Brief recall of basic transformations from linear algebra ....................................... 182
9.1.1 Eigenvalue Decomposition .................................................................................... 182
9.1.2 Singular Value Decomposition (SVD) .................................................................... 184
9.1.3 Frobenius Norm ..................................................................................................... 184
9.2 Recall of basic notions of statistics and probabilities ............................................ 184
9.2.1 Probabilities ........................................................................................................... 184
© A.G.Billard 2004 – Last Update March 2011