Semi-Supervised Learning with Ladder Networks

Annual Conference on Neural Information Processing Systems, pp. 3546-3554, 2015.

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Keywords:
convolutional neural networksmulti-layer perceptronsMulti-prediction deep Boltzmann machinestacked what-where autoencoderladder networkMore(15+)
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We showed how a simultaneous unsupervised learning task improves convolutional neural networks and multi-layer perceptrons networks reaching the state-of-the-art in various semi-supervised learning tasks

Abstract:

We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on top of the Ladder network proposed by Valpola [1] which we e...More

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Introduction
  • The authors introduce an unsupervised learning method that fits well with supervised learning.
  • Some methods have been able to simultaneously apply both supervised and unsupervised learning [3, 5], often these unsupervised auxiliary tasks are only applied as pre-training, followed by normal supervised learning [e.g., 6].
  • For instance, the autoencoder approach applied to natural images: an auxiliary decoder network tries to reconstruct the original input from the internal representation.
  • The autoencoder will try to preserve all the details needed for reconstructing the image at pixel level, even though classification is typically invariant to all kinds of transformations which do not preserve pixel values
Highlights
  • In this paper, we introduce an unsupervised learning method that fits well with supervised learning
  • We showed how a simultaneous unsupervised learning task improves convolutional neural networks and multi-layer perceptrons networks reaching the state-of-the-art in various semi-supervised learning tasks
  • The performance obtained with very small numbers of labels is much better than previous published results which shows that the method is capable of making good use of unsupervised learning
  • The same model achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning
  • The proposed model is simple and easy to implement with many existing feedforward architectures, as the training is based on backpropagation from a simple cost function
  • The largest improvements in performance were observed in models which have a large number of parameters relative to the number of available labeled samples
Methods
  • The authors ran experiments both with the MNIST and CIFAR-10 datasets, where the authors attached the decoder both to fully-connected MLP networks and to convolutional neural networks.
  • The authors compared the performance of the simpler -model (Sec. 3) to the full Ladder network.
  • The authors' focus was exclusively on semi-supervised learning.
  • The authors make claims neither about the optimality nor the statistical significance of the supervised baseline results.
  • The source code for all the experiments is available at https://github.com/arasmus/ladder
Results
  • The same model achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning.
Conclusion
  • The authors showed how a simultaneous unsupervised learning task improves CNN and MLP networks reaching the state-of-the-art in various semi-supervised learning tasks.
  • The same model achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning.
  • With CIFAR-10, the authors started with a model which was originally developed for a fully supervised task
  • This has the benefit of building on existing experience but it may well be that the best results will be obtained with models which have far more parameters than fully supervised approaches could handle
Summary
  • Introduction:

    The authors introduce an unsupervised learning method that fits well with supervised learning.
  • Some methods have been able to simultaneously apply both supervised and unsupervised learning [3, 5], often these unsupervised auxiliary tasks are only applied as pre-training, followed by normal supervised learning [e.g., 6].
  • For instance, the autoencoder approach applied to natural images: an auxiliary decoder network tries to reconstruct the original input from the internal representation.
  • The autoencoder will try to preserve all the details needed for reconstructing the image at pixel level, even though classification is typically invariant to all kinds of transformations which do not preserve pixel values
  • Methods:

    The authors ran experiments both with the MNIST and CIFAR-10 datasets, where the authors attached the decoder both to fully-connected MLP networks and to convolutional neural networks.
  • The authors compared the performance of the simpler -model (Sec. 3) to the full Ladder network.
  • The authors' focus was exclusively on semi-supervised learning.
  • The authors make claims neither about the optimality nor the statistical significance of the supervised baseline results.
  • The source code for all the experiments is available at https://github.com/arasmus/ladder
  • Results:

    The same model achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning.
  • Conclusion:

    The authors showed how a simultaneous unsupervised learning task improves CNN and MLP networks reaching the state-of-the-art in various semi-supervised learning tasks.
  • The same model achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning.
  • With CIFAR-10, the authors started with a model which was originally developed for a fully supervised task
  • This has the benefit of building on existing experience but it may well be that the best results will be obtained with models which have far more parameters than fully supervised approaches could handle
Tables
  • Table1: A collection of previously reported MNIST test errors in the permutation invariant setting followed by the results with the Ladder network. * = SVM. Standard deviation in parenthesis
  • Table2: CNN results for MNIST
  • Table3: Test results for CNN on CIFAR-10 dataset without data augmentation
Download tables as Excel
Related work
  • Early works in semi-supervised learning [28, 29] proposed an approach where inputs are first x assigned to clusters, and each cluster has its class label. Unlabeled data would affect the shapes and sizes of the clusters, and thus alter the classification result. Label propagation methods [30] estimate

    P y | , but adjust probabilistic labels q y n based on the assumption that nearest neighbors are ( x) ( ( ))

    likely to have the same label. Weston et al [15] explored deep versions of label propagation.

    There is an interesting connection between our -model and the contractive cost used by Rifai et al [16]: a linear denoising function zi(L) = aizi(L) + bi, where ai and bi are parameters, turns the denoising cost into a stochastic estimate of the contractive cost. In other words, our -model seems to combine clustering and label propagation with regularization by contractive cost.
Funding
  • The Academy of Finland has supported Tapani Raiko
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