Unsupervised Deep Learning (D2L1 Insight@DCU Machine Learning Workshop 2017)
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The document discusses various techniques for unsupervised and semi-supervised learning in deep learning, highlighting the importance of learning from unlabelled data. It covers methods like autoencoders, the manifold hypothesis, and the use of energy-based models, alongside assumptions necessary for modeling data. The work emphasizes current advancements and ongoing research in this field.
Unsupervised Deep Learning (D2L1 Insight@DCU Machine Learning Workshop 2017)
- 1. Kevin McGuinness [email protected] Research Fellow Insight Centre for Data Analytics Dublin City University DEEP LEARNING WORKSHOP Dublin City University 27-28 April 2017 Unsupervised Deep Learning Day 2 Lecture 1 1
- 2. Motivation Vast amounts of unlabelled data Most data has structure; we would like to discover hidden structure Modelling the probability density of the data P(X) Fighting the curse of dimensionality Visualizing high-dimensional data Supervised learning tasks: learning from fewer training examples 2
- 3. Semi-supervised and transfer learning Myth: you can’t do deep learning unless you have a million labelled examples for your problem. Reality ● You can learn useful representations from unlabelled data ● You can transfer learned representations from a related task ● You can train on a nearby surrogate objective for which it is easy to generate labels 3
- 4. Using unlabelled examples: 1D example Max margin decision boundary 4
- 5. Using unlabelled examples: 1D example Semi supervised decision boundary 5
- 6. Using unlabelled examples: 2D example 6
- 7. Using unlabelled examples: 2D example 7
- 8. A probabilistic perspective ● P(Y|X) depends on P(X|Y) and P(X) ● Knowledge of P(X) can help to predict P(Y|X) ● Good model of P(X) must have Y as an implicit latent variable Bayes rule 8
- 10. Example x1 x2 Cluster 1 Cluster 2 Cluster 3 Cluster 4 1 2 3 4 1 2 3 4 4D BoW representation Separable! https://github.com/kevinmcguinness/ml-examples/blob/master/notebooks/Semi_Supervised_Simple.ipynb 10
- 11. Assumptions To model P(X) given data, it is necessary to make some assumptions “You can’t do inference without making assumptions” -- David MacKay, Information Theory, Inference, and Learning Algorithms Typical assumptions: ● Smoothness assumption ○ Points which are close to each other are more likely to share a label. ● Cluster assumption ○ The data form discrete clusters; points in the same cluster are likely to share a label ● Manifold assumption ○ The data lie approximately on a manifold of much lower dimension than the input space. 11
- 12. Examples Smoothness assumption ● Label propagation ○ Recursively propagate labels to nearby points ○ Problem: in high-D, your nearest neighbour may be very far away! Cluster assumption ● Bag of words models ○ K-means, etc. ○ Represent points by cluster centers ○ Soft assignment ○ VLAD ● Gaussian mixture models ○ Fisher vectors Manifold assumption ● Linear manifolds ○ PCA ○ Linear autoencoders ○ Random projections ○ ICA ● Non-linear manifolds: ○ Non-linear autoencoders ○ Deep autoencoders ○ Restricted Boltzmann machines ○ Deep belief nets 12
- 13. The manifold hypothesis The data distribution lie close to a low-dimensional manifold Example: consider image data ● Very high dimensional (1,000,000D) ● A randomly generated image will almost certainly not look like any real world scene ○ The space of images that occur in nature is almost completely empty ● Hypothesis: real world images lie on a smooth, low-dimensional manifold ○ Manifold distance is a good measure of similarity Similar for audio and text 13
- 14. The manifold hypothesis x1 x2 Linear manifold wT x + b x1 x2 Non-linear manifold 14
- 15. The Johnson–Lindenstrauss lemma Informally: “A small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. The map used for the embedding is at least Lipschitz continuous.” Intuition: Imagine threading a string through a few points in 2D The manifold hypothesis guesses that such a manifold generalizes well to unseen data 15
- 16. Energy-based models Often intractable to explicitly model probability density Energy-based model: high energy for data far from manifold, low energy for data near manifold of observed data Fitting energy-based models ● Push down on area near observations. ● Push up everywhere else. Examples Encoder-decoder models: measure energy with reconstruction error ● K-Means: push down near prototypes. Push up based on distance from prototypes. ● PCA: push down near line of maximum variation. Push up based on distance to line. ● Autoencoders: non-linear manifolds... LeCun et al, A Tutorial on Energy-Based Learning, Predicting Structured Data, 2006 http://yann.lecun.com/exdb/publis/pdf/lecun-06.pdf 16
- 17. Autoencoders Encoder W1 Decoder W2 hdata reconstruction Loss (reconstruction error) Latent variables (representation/features) 17
- 18. Autoencoders Encoder W1 hdata Classifier WC Latent variables (representation/features) prediction y Loss (cross entropy) 18
- 19. Autoencoders Need to somehow push up on energy far from manifold ● Undercomplete autoencoders: limit the dimension of the hidden representation. ● Sparse autoencoders: add penalty to make hidden representation sparse. ● Denoising autoencoders: add noise to the data, reconstruct without noise. ● Contractive autoencoders: regularizer to encourage gradient of hidden layer activations wrt inputs to be small. Can stack autoencoders to attempt to learn higher level features Can train stacked autoencoders by greedy layerwise training Finetune for classification using backprop 19
- 21. Greedy layerwise training Input Reconstruction of input Layer 1 Reconstruction of layer 1 Layer 2 Reconstruction of layer 2 Layer 3 Supervised objective Y Backprop 21
- 22. Unsupervised learning from video Slow feature analysis ● Temporal coherence assumption: features should change slowly over time in video Steady feature analysis ● Second order changes also small: changes in the past should resemble changes in the future Train on triples of frames from video Loss encourages nearby frames to have slow and steady features, and far frames to have different features Jayaraman and Grauman. Slow and steady feature analysis: higher order temporal coherence in video CVPR 2016. https://arxiv.org/abs/1506.04714 22
- 23. Learning to see by moving: ego-motion prediction L1 L1 L2 Lk L2 Lk F1 F2 ... ... transform parameters BaseCNN Siamese net Idea: predict relationship between pairs of images. E.g. predict the transform. Translation, rotation. Can use real-world training data if you know something about the ego-motion Can easily simulate training data by transforming images: 8.7% error MNIST w/ 100 examples Agrawal et al. Learning to see by moving. ICCV. 2015. 23
- 24. Split-brain autoencoders Simultaneously train two networks to predict one part of the data from the other. E.g. predict chrominance from luminance and vice versa. Predict depth from RGB. Concat two networks and use features for other tasks. Zhang et al., Split-Brain Autoencoders: Unsupervised Learning by Cross-Channel Prediction, arXiv 2016 24
- 25. Split-brain autoencoders Zhang et al., Split-Brain Autoencoders: Unsupervised Learning by Cross-Channel Prediction, arXiv 2016 25
- 26. Ladder networks Combine supervised and unsupervised objectives and train together ● Clean path and noisy path ● Decoder which can invert the mappings on each layer ● Loss is weighted sum of supervised and unsupervised cost 1.13% error on permutation invariant MNIST with only 100 examples Rasmus et al. Semi-Supervised Learning with Ladder Networks. NIPS 2015. http://arxiv.org/abs/1507.02672 26
- 27. Summary Many methods available for learning from unlabelled data ● Autoencoders (many variations) ● Restricted boltzmann machines ● Video and ego-motion ● Semi-supervised methods (e.g. ladder networks) Very active research area! 27
- 28. Questions? 28