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Department of Computer Science 6 King’s College Rd, Toronto University of Toronto M5S 3G4, Canada http://learning.cs.toronto.edu fax: +1 416 978 1455 Copyright c Geo ff rey Hinton 2010. August 2, 2010 UTML TR 2010–003 A Practical Guide to Training Restricted Boltzmann Machines Version 1 Geo ff rey Hinton Department of Computer Science, University of Toronto
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A Practical Guide to Training Restricted Boltzmann Machines Version 1 Geo ff rey Hinton Department of Computer Science, University of Toronto Contents 1 Introduction 3 2 An overview of Restricted Boltzmann Machines and Contrastive Divergence 3 3 How to collect statistics when using Contrastive Divergence 5 3.1 Updating the hidden states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Updating the visible states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Collecting the statistics needed for learning . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 A recipe for getting the learning signal for CD 1 . . . . . . . . . . . . . . . . . . . . . . 6 4 The size of a mini-batch 6 4.1 A recipe for dividing the training set into mini-batches . . . . . . . . . . . . . . . . . . 7 5 Monitoring the progress of learning 7 5.1 A recipe for using the reconstruction error . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 Monitoring the overfitting 8 6.1 A recipe for monitoring the overfitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 7 The learning rate 8 7.1 A recipe for setting the learning rates for weights and biases . . . . . . . . . . . . . . . 8 8 The initial values of the weights and biases 9 8.1 A recipe for setting the initial values of the weights and biases . . . . . . . . . . . . . 9 9 Momentum 9 1
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9.1 A recipe for using momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 10 Weight-decay 10 10.1 A recipe for using weight-decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 11 Encouraging sparse hidden activities 11 11.1 A recipe for sparsity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 12 The number of hidden units 12 12.1 A recipe for choosing the number of hidden units . . . . . . . . . . . . . . . . . . . . . 12 13 Di ff erent types of unit 13 13.1 Softmax and multinomial units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 13.2 Gaussian visible units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 13.3 Gaussian visible and hidden units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 13.4 Binomial units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 13.5 Rectified linear units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 14 Varieties of contrastive divergence 15 15 Displaying what is happening during learning 16 16 Using RBM’s for discrimination 16 16.1 Computing the free energy of a visible vector . . . . . . . . . . . . . . . . . . . . . . . 17 17 Dealing with missing values 17 1 1 If you make use of this technical report to train an RBM, please cite it in any resulting publication. 2
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1 Introduction Restricted Boltzmann machines (RBMs) have been used as generative models of many di ff erent types of data including labeled or unlabeled images (Hinton et al., 2006a), windows of mel-cepstral coe cients that represent speech (Mohamed et al., 2009), bags of words that represent documents (Salakhutdinov and Hinton, 2009), and user ratings of movies (Salakhutdinov et al., 2007). In their conditional form they can be used to model high-dimensional temporal sequences such as video or motion capture data (Taylor et al., 2006) or speech (Mohamed and Hinton, 2010). Their most important use is as learning modules that are composed to form deep belief nets (Hinton et al., 2006a). RBMs are usually trained using the contrastive divergence learning procedure (Hinton, 2002).
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